[HN Gopher] An alarming trend in K-12 math education: a guest po...
___________________________________________________________________
An alarming trend in K-12 math education: a guest post and an open
letter
Author : feross
Score : 220 points
Date : 2021-12-03 17:47 UTC (5 hours ago)
(HTM) web link (scottaaronson.blog)
(TXT) w3m dump (scottaaronson.blog)
| 6f4f06c00484d34 wrote:
| people who push for "equitable" education do not send their
| children to public schools.
|
| equity for thee, not for me.
| sh1mmer wrote:
| I find it interesting with many of these criticisms that subject
| matter experts on maths, sciences, etc think that they are also
| subject matter experts on the pedagogy of maths, science, etc
| especially at a high school level.
|
| Many advanced practitioners don't even have a good grasp of
| college level/post-grad pedagogy which they'd use more in their
| day to day work.
|
| Using a skill isn't the same as teaching it, and just like
| anything else there are plenty of fallacies to be had. I'd be
| more persuaded by angry hot takes from High School teachers
| worried that their students aren't going to hit the grades they
| deserve / learn the things they need than anything else.
|
| Even then, single high school teachers experiences are closer to
| anecdotes than actual pedagogical research, with which the
| original proposal is backed.
| dfdz wrote:
| You are missing the key point: these experts on maths,
| sciences, etc are not arguing HOW to teach maths, sciences,
| etc.
|
| They are only arguing WHAT is important to teach.
|
| High school math teachers do not have the perspective to
| understand what kind of math is needed for jobs in engineering,
| data science, etc (The fact is that a background in algebra and
| calculus is necessary for almost all of these jobs).
| itronitron wrote:
| Which jobs require a background in algebra and calculus, and
| what exactly do you consider to satisfy the requirements of a
| background?
| gopher_space wrote:
| Whenever public discourse turns to topics within my domain I
| realize that even one degree of separation from a subject means
| you're basically just making stuff up.
|
| How many people on the planet are worth listening to when it
| comes to teaching math?
| rahimnathwani wrote:
| "I'd be more persuaded by angry hot takes from High School
| teachers worried that their students aren't going to hit the
| grades they deserve / learn the things they need than anything
| else."
|
| How about this teacher, who teaches math at San Francisco's top
| public school: https://cheesemonkeysf.blogspot.com/
| VLM wrote:
| The biggest problem I see with this article is not the obvious
| intended political sizzle but an assumption early in the article
| along the lines of the only purpose of public education is the
| eventual production of STEM college graduates and everyone else
| can and should go directly to hell and absolutely no resources or
| encouragement should be provided for any other educational
| outcome. It makes you wonder how the public school system is not
| in a continuous state of civil rights lawsuits over the equal
| protection clause.
|
| "every child must master algebra, preferably by eighth grade, for
| algebra is the gateway to the college-prep curriculum, which in
| turn is the path to higher education." But that's not the life
| path for perhaps 90%+ of the population. I don't think we can
| justify burning tax dollars to exclusively and solely support a
| tiny minority of kids at the expense of nearly all the other
| kids.
|
| I would not be bothered by mindless STEM boosterism if it were
| not for pages like this:
|
| https://datausa.io/profile/cip/electrical-engineering#tmap_o...
|
| It offends me as a EE type person that the top job title for
| graduating engineers is software dev, where they'd have been
| better off with a CS degree, or no degree. Meanwhile I'm told by
| the other side that we have a terrifying massive shortage of
| engineering grads, despite that clearly not being the case and it
| being VERY difficult for new kids to get a job in the field. I'm
| led to believe by "shortage" they actually mean a "shortage of
| people willing to work 80 hrs/wk for minimum wage and no bennies"
| or "shortage of experts with decades years of masterful
| experience willing to accept apprentice level pay scales"
|
| We simply seem to have too many STEM grads for our economy to
| support. I don't see any realistic reason for future improvement
| in that situation. Meanwhile public education policy, meant to
| serve EVERYONE, is telling most of the kids to go to hell. And
| those are the kids running the rest of the economy and we're
| relying on them to grow the economy enough to support the 5% of
| STEM workers whom are the only important people to educate
| according to "public" education, which is now really only college
| prep STEM education and F every other kid.
|
| This path cannot possibly end well.
|
| The best way to handle algebra education as applied to the entire
| student body, is to acknowledge that for 95% of the population,
| learning how to change the oil in a car or how to identify when
| someone is using statistics as propaganda, would be a more
| valuable life skill. Yes I acknowledge STEM is and will remain
| important for a tiny subset of both kids and future jobs, but...
| naasking wrote:
| > But that's not the life path for perhaps 90%+ of the
| population. I don't think we can justify burning tax dollars to
| exclusively and solely support a tiny minority of kids at the
| expense of nearly all the other kids.
|
| Sure, but that's not what they're objecting to. They're
| objecting specifically to cutting off avenues to those advanced
| paths, and in ways that harm underprivileged students more.
| Quote:
|
| > the bottom line is that rather than trying to elevate under-
| served students, _such "reforms" reduce access and options for
| all students_. In particular, the CMF encourages schools to
| stop offering Algebra I in middle school, while placing
| obstacles (such as doubling-up, compressed courses, or outside-
| of-school private courses) in the way of those who want to take
| advanced math in higher grades. When similar reforms were
| implemented in San Francisco, they resulted in an "inequitable
| patchwork scheme" of workarounds that affluent students could
| access but that their less privileged counterparts could not.
| yakkityyak wrote:
| My armchair take of the situation is that the administrators of
| K-12 education are too focused on the potential value of kids
| actually using these math frameworks instead of how they sort of
| rewire how to logically reason about things.
|
| I'm having trouble finding the right words to describe myself,
| but I vividly remember how many moments of epiphany I had when I
| took Calculus and Linear Algebra. I don't directly use either of
| them at all in my day job, but I feel like they were foundational
| in developing reasoning skills.
| leephillips wrote:
| This is, I believe, the fundamental problem. Administrators,
| and, to some degree, math teachers themselves, don't like or
| understand math. They constantly talk about what it's "for", as
| if math class serves a purpose similar to car repair shop
| class. They seem to understand that you can have an English
| class treating poetry, or a history class, without needing to
| justify them with practical applications. I think most of this
| bunch have no concept of studying math for its own sake, and
| the idea that you might do so for enjoyment would probably seem
| incomprehensibly bizarre. During my brief stints teaching math
| in high schools, my attitude was that I was guiding students
| along the path to becoming people--members of their
| civilization.
| kevin_thibedeau wrote:
| At some point they'll cut out all the foundational mathematics
| needed for hard science and engineering. Then only foreign
| students will be qualified for bachelor's programs. Complex
| numbers will be first at the chopping block.
| humanistbot wrote:
| The manufactured outrage over the California math recommendations
| keep getting posted on HN. Read the actual text of the plans here
| [1]. The FAQ is at [2] and directly responds to these
| characterizations. They are not banning gifted & talented
| programs or advanced students taking accelerated courses. They
| are not taking algebra out of the curriculum, although they are
| cutting geometry a bit, which doesn't make as much sense today as
| it did 100 years ago when far more people grew up to be farmers
| or ranchers. They are adding more statistics and probability,
| which I think are crucial in today's society.
|
| What they are fundamentally doing is breaking up the classic U.S.
| staged path where you learn algebra for a year, then geometry for
| a year, then back to algebra / pre-calc for a year, then maybe
| take statistics or calculus as an elective, etc. Instead, all
| branches of math will be taught in an integrated approach focused
| around applied problems.
|
| This is how a lot of European math courses are taught. In fact, I
| think HN would appreciate the shift from focusing on pure numbers
| and classic formulas to more applied uses of math, including
| algorithms, probability, data collected and analyzed in charts,
| etc. Students also forget a lot of algebra when they do a year of
| geometry by itself, then have to go back to algebra / pre-calc.
|
| It also does mean that in the transition, it will be harder for
| students to "test out" of the classic algebra I/II, geometry,
| pre-calc sequence, because it will just be "year X integrated
| math." But the framework does not forbid gifted and talented
| programs or anything like that. There will just be a few awkward
| years while the curriculum shifts.
|
| Now, there are some on the left who advocated for the elimination
| of gifted and talented programs altogether, for equity reasons.
| They did not get what they wanted in the new California
| framework. That hasn't stopped a lot of people from looking at
| what California is doing and imagining it is actually some kind
| of Harrison Bergeron dystopia, when that is absolutely not the
| case.
|
| [1] https://www.cde.ca.gov/ci/ma/cf/
|
| [2] https://www.cde.ca.gov/ci/ma/cf/mathfwfaqs.asp
| PragmaticPulp wrote:
| I had originally assumed the criticisms were exaggerated, but
| the more I read about the new curriculum the less comfortable I
| am.
|
| It seems every defense is built around hedges like this one:
|
| > although they are cutting geometry a bit, which doesn't make
| as much sense today as it did 100 years ago when far more
| people grew up to be farmers or ranchers
|
| Which suggests to me that they really _are_ trying to walk back
| the complexity of the education, perhaps as part of a goal to
| force the variance of educational progress into a narrower
| range within classes.
|
| The language is so vague that it's hard to understand exactly
| what they're trying to do, which I think is their point. If
| they wanted to emphasize advanced education topics it would
| have been front and center in the plan. Instead, it seems like
| a footnote that we're supposed to assume will get taken care of
| in some future iteration of this integrative math program.
| octernion wrote:
| The entire point is not to emphasize the advanced education
| topics -- which are actually offered pretty universally in
| California schools -- but to increase the number of students
| actually _taking_ those classes through the entire pipeline,
| and to embed those concepts in a more consistent, structured
| way.
|
| I'm not sure why how you get "walk back the complexity of
| education" when it's obvious that the current system is
| broken.
| syki wrote:
| I believe you are mistaken. One of the goals is to deny
| that people have different intellectual abilities. They
| seek to get rid of tracking and advanced courses. These
| reforms are related to what is being advocated by
| www.equitablemath.org. From their website:
|
| _Students are tracked (into courses /pathways and within
| the classroom)._
|
| This is a sign of white supremacy in their view.
|
| See this PDF:
|
| https://equitablemath.org/wp-
| content/uploads/sites/2/2020/11...
| rflrob wrote:
| From your PDF:
|
| > Administrators should examine programs and policies and
| how white supremacy impacts student outcomes (e.g.,
| tracking, course selection, intervention rosters).
|
| > White supremacy culture shows up in math classrooms
| when... Students are tracked
|
| I interpreted this to mean that tracking is (like course
| selection) a student outcome that can be impacted by
| "white supremacy culture", not that tracking is,
| inherently and unavoidably, a sign of white supremacy. If
| there's burglars around, unlocked doors are usually
| correlated with burglary; that doesn't mean you can't
| leave your doors unlocked, but you're going to want to be
| careful about it. Similarly, if you live in a society
| with pervasive racism (read: most societies), it's
| possible to track students in a way that doesn't
| reinforce those racist trends, but probably only if
| you're careful about it.
|
| I think I probably agree with you that "white supremacy
| culture" is, as a term, perhaps more aggressive than it
| needs to be. Not being deeply embedded in this debate,
| I'd assume it's going to turn off more people who hear
| it, think "I'm not a klansman, so this isn't something I
| need to address" than it will engage people who think
| racism is bad but haven't considered how their own
| (probably unexamined) practices are leading to outcomes
| they don't want.
| magicalist wrote:
| What does this have to do with the actual changes being
| made?
| syki wrote:
| Same agenda from two different organizations. Effectively
| implementing the reforms will lead to a system where
| advanced math courses are taken by students in k-12 whose
| parents have money.
| threatofrain wrote:
| A central pillar of Equitable Math is that _all_ children
| must _always_ be at the same level up until their last
| year. This is what is in contention, and not whether the
| Common Core needs more revision in terms of depth or
| rearrangement of subjects.
|
| Under the Common Core, children in middle school who are
| ready for Algebra may opt for Algebra, and children who
| benefit from a delay may opt for a delay -- but this is
| viewed by Equitable Math as sustaining White Supremacy in
| math education.
| magicalist wrote:
| > _all children must always be at the same level up until
| their last year_
|
| But that's not what's happening, so, again, what does
| that have to do with the actual changes being made?
| syki wrote:
| It's the goal.
| magicalist wrote:
| ...of some people but not the recommendations?
| threatofrain wrote:
| Equitable Math is not "some people". It's the original
| branding for the program under contention in this forum.
| magicalist wrote:
| Are the Equitable Math folks the entirety of the
| stakeholders involved? Will "all children be at the same
| level up until their last year"?
|
| If no to both, it does seem an awful lot like invoking
| the motivations of some of the people involved as a
| boogeyman rather than making an argument about the final
| recommendations themselves.
| threatofrain wrote:
| Under current proposals, which have yet to be finalized,
| there are zero specifications for alternative tracks in
| math, including zero specification for Algebra in middle
| school. You seem to think that Equitable Math is an
| entirely separate proposal, and thus the authors of
| Equitable Math are just "some people". They are program
| architects. And the stakeholders? Why, all of California
| of course, including textbook publishers making decisions
| for 8th grade Algebra textbooks.
|
| For schools under the Equitable Math proposals, the
| _goal_ will be that for any given grade level, all
| children will be at the same level up until their last
| year. The explicitly stated reasoning by the program
| authors is that alternative tracks in math are a form of
| disparity which promotes White Supremacy. Will this in
| fact be the _final_ final proposal? That is what is under
| debate right now.
| syki wrote:
| Not all proponents of Jim Crow laws were hate filled but
| enough were that one can ascribe to the legislators of
| the Deep South that supported those laws as being hate
| filled. What you are being told are the intended
| consequences of the people writing the proposals and are
| now asking about the totality of the beliefs of the
| stakeholders. You are welcome to believe whatever you
| want about the motivations of the people writing the
| proposals as I am. But please don't confuse their
| intentions with the intentions of all stakeholders. No
| one is doing this.
| octernion wrote:
| So you are mad at the imaginary goal that you made up.
| Got it.
| PragmaticPulp wrote:
| > I'm not sure why how you get "walk back the complexity of
| education"
|
| The parent comment literally admitted that they were
| removing specific complex topics.
|
| That is what I was responding to.
| burnished wrote:
| But also replacing it with other perhaps more pertinent
| advanced topics? Hard to have a fruitful discussion
| without a curricula to discuss
| magicalist wrote:
| > _The parent comment literally admitted that they were
| removing specific complex topics._
|
| you quoted and responded to
|
| > _although they are cutting geometry a bit, which doesn
| 't make as much sense today as it did 100 years ago when
| far more people grew up to be farmers or ranchers_
|
| so which _specific_ and _complex_ topics are you
| referring to in the OP?
| syki wrote:
| I teach math at a community college. It is all about removing
| complexity. The idea in education is that everyone is
| intellectually equal. Therefore the racial achievement gap in
| mathematics is due to racism. The solution is to change
| things. Too many POC students aren't placing into college
| level math therefore get rid of placement test and get rid of
| remedial courses. Create new college algebra with just in
| time tutoring and voila, no more racial achievement gap. If
| you dumb things down enough everyone passes and we can pat
| ourselves on the back and claim to have solved the racial
| achievement gap.
|
| My complaint about these reforms is that the root cause of
| the issue is not being addressed. This has long term negative
| effects. My own anecdotal experience is that what used to be
| a C is now an A or a B in my classes and I'm passing people
| who don't know anything. I'm judged by the passing rate so
| I'm maximizing that metric. These reforms are just doing what
| I'm doing but in a less forthright way.
| bsanr wrote:
| >The idea in education is that everyone is intellectually
| equal. Therefore the racial achievement gap in mathematics
| is due to racism. The solution is to change things.
|
| If we're going to go there: I went from being a straight-A
| math student in Pre-Calculus to a C (verging on D) student
| in my AP Calculus course in high school. In college, I
| retook Calculus and aced it, receiving one of the highest
| final scores in the class. The first course was taught by a
| black woman. The second was taught by a white man. The last
| was taught by a black man. I am a black man.
|
| People in this conversation are frequently quick to dismiss
| the value of anti-racist (and, for that matter, anti-
| sexist) policy and execution in STEM pedagogy. They lean on
| and extrapolate erroneously from the notion of many great
| mathematical thinkers' probable hereditary advantages to a
| general, in-born hierarchy of fitness for STEM thinking.
| Coincidentally, this shields them from tough conversations
| regarding their own fitness to teach, and especially to
| teach children whose backgrounds they cannot or will not
| find sympathy and empathy for. I will admit that the
| solution is not so simple as my anecdote might suggest, but
| the implied path shares character with the correct one, in
| recognizing the farcical nature of assuming that the status
| quo - especially in this country - is a product of actual
| potential playing out as it must necessarily so, and not of
| history overshadowing even the best of intentions (though
| they are usually less than that).
| talentedcoin wrote:
| What specifically about the courses being taught by black
| people do you think helped you do better?
| jeegsy wrote:
| Is it possible that you aced calculus later on because
| you were in effect taking it a second time?
| syki wrote:
| Definitely agree. There's no reason for me to believe
| that I'm good at teaching. My students' failings could be
| mostly a reflection of my own failing in teaching.
|
| I don't dismiss the value of anti-racist policy and
| attempts to rid myself of negative biases that affect my
| students. My compliant is when I'm told, and I have been
| told this by an educator, that the act of requiring
| knowledge of algebra is itself racist. That's when I feel
| we've gone too far. I don't necessarily think algebra
| should be required but the reasoning for getting rid of
| that requirement shouldn't be because black students are
| not passing it at a high enough rate.
|
| My belief is that far too many people are going to
| college. The degree therefore is being watered down. If
| we lived in a country where everyone had guaranteed
| access to food, shelter, and medical care then the
| emphasis on college wouldn't be so pronounced and
| colleges could then concentrate on what's needed.
|
| I don't believe your comment should have been downvoted.
| Thank you for sharing your experience and thoughts.
| int_19h wrote:
| The problem is that our societies have made college a
| status symbol - everybody is supposed to strive for a
| degree even if what they're planning to do doesn't
| require it. This is particularly pronounced for white
| collar jobs, even though many of them are really more
| akin to tradecraft, and should be properly taught in
| trade school.
|
| (I would argue that the majority of what we call
| "software engineering" is actually of this nature.)
| Spooky23 wrote:
| The whole thing is a classic case of using averages to
| drive policy and action.
|
| Your C student with an A doesn't need your math class, they
| need an A.
|
| The employer filters all non college graduates and then
| filters by GPA. With most employers, knowing what you are
| doing is not ranked 1st or 2nd. Price and qualification is
| up front.
| jimbokun wrote:
| > I'm judged by the passing rate so I'm maximizing that
| metric.
|
| We really need to divorce the teaching and accreditation
| functions bundled in the modern university. There is a
| clear conflict of interest.
| WindyLakeReturn wrote:
| >My complaint about these reforms is that the root cause of
| the issue is not being addressed.
|
| It becomes a question of how do we ensure every child has
| access to a dedicated adult willing to tutor them and push
| them in education matters. Once a child begins to fail in a
| class, unless someone is there who can help them back onto
| the route of succeeding, they risk developing learned
| helplessness around education. Maybe a single subject,
| maybe education in general. It takes a lot of time for
| someone to work with a kid, find out what the root cause of
| the problem is, help them overcome that, and then build up
| on the topics they have fallen behind on. It helps greatly
| when that person isn't just there for teaching/tutoring but
| also invested in the child in other ways so the child
| values their input.
|
| When parents either don't have time, ability, or desire to
| do this, there is rarely a backup. Teachers try to fill the
| gap but they are spread too thin over too many students and
| rarely are with a student long enough to make a significant
| impact. Some teachers may even avoid it because it can
| quickly become an issue of favoring certain students over
| others. As for parents, while some parents will be able to
| fix the problem by having more time available, some parents
| lack enough education to keep helping their child past a
| certain point. Both finding how to give parents more time
| and how to educate parents enough to help their children
| are hard problems. As for the parents who don't have a
| desire to help, there might not be any solution at all.
| [deleted]
| csee wrote:
| > My complaint about these reforms is that the root cause
| of the issue is not being addressed.
|
| The root cause is well outside of the scope of schools to
| address. Perhaps they can help to a small extent through
| things like lunchtime meals. But curriculum reform itself
| will never narrow the gap more than a tiny amount.
|
| Childhood nutrition, single parent households, health of
| mother during pregnancy, culture/respect towards education
| as a virtue in the community and household, education level
| of parents and the time they have to play and talk with
| their kids.
|
| All these things are going to impact the capabilities of
| young school children and feed into outcome gaps between
| various groups (Black vs White, poor vs rich).
|
| I believe most proponents of "math equity" actually know
| all this, and are just maliciously virtue signalling either
| because they're jealous that their own kids aren't doing
| well, or for social credit.
| Delk wrote:
| > Childhood nutrition, single parent households, health
| of mother during pregnancy, culture/respect towards
| education as a virtue in the community and household,
| education level of parents and the time they have to play
| and talk with their kids.
|
| I'm not American, and I don't claim to know the
| environment and the issues people face there, or their
| root causes. I may not be fully understanding the extent
| of nutritional differences or family dynamics.
|
| I am, however, absolutely certain that affluence feeds
| affluence and that misfortune feeds misfortune, on
| average. Even if you had all of the above equal except
| for the education levels and socio-economic status of the
| children's parents, you'd end up with statistically
| different outcomes.
|
| I live in a fairly egalitarian country, and if I remember
| correctly, there's an average income gap of ~30 percent
| or so between people whose parents were in the highest
| quartile in income and those who were in the lowest
| quartile. While ethnicity may play some role in the
| statistical gap nowadays, I don't think it explains the
| statistical difference; ethnic minorities are
| disadvantaged here but they make up a small enough
| minority that I expect the bulk of the difference to be
| simply due to socio-economic differences within the same
| ethnic group.
|
| Basically, if your parents and their social in-group got
| highly educated, I believe you perceive that as the norm.
| If they didn't, it's not as likely that you do.
|
| Add in some practical stuff such as whether your parents
| can afford to finance or support your education, and the
| gap's already there. The rest just amplifies it.
|
| Sure, physical health, nutrition etc. can have an effect,
| and they certainly do if the differences are great
| enough. I'm sure ethnicity or race has an effect,
| sometimes due to racism, and sometimes because people
| perceive their own opportunities or expectations
| differently depending on social roles, and for various
| other sociological dynamics. The latter is true even if
| you remove ethnicity or race from the equation. Racial
| stereotypes and images probably emphasize things but I
| don't think you can pin it all on that.
|
| Considering how much worse off African Americans are
| socio-economically, on average, than white Americans,
| it's a no-brainer that their kids end up worse off on
| average as well. I'm not saying you should just shrug and
| accept that, and I'm sure actual racism exists as well,
| but the point is that some of it would happen even
| without racism, either overt or covert, or any
| "structural racism" that could include a whole spectrum
| of things.
|
| That means any real solution is going to be hard and
| slow, unfortunately. Changing the subject matter in the
| name of equity really doesn't sound like one.
|
| > I believe most proponents of "math equity" actually
| know all this, and are just maliciously virtue signalling
| either because they're jealous that their own kids aren't
| doing well, or for social credit.
|
| It could also be that people take an easy non-solution in
| preference to working towards improvements and solutions
| that could take time, great patience, tolerance of
| morally and socially undesirable situations (one might
| have to accept that you can't achieve perfect equity, or
| at least not quickly, and be able to withstand social
| judgement for that), and are all around a lot harder to
| accomplish.
| dr_dshiv wrote:
| The poverty achievement gap is close to twice that of the
| racial achievement gap.
|
| I don't understand why we are so arrogant about
| everything that we don't even try to teach 5th graders
| how to use spreadsheets and generate graphs. So much of
| math education is useless punishment.
| golemiprague wrote:
| Interesting that you don't include genetics in your list,
| maybe it is a waste of time to try changing all those
| other things and instead we should focus on directing
| kids to aspire for their natural talents rather than
| trying to push them into something that doesn't suit
| them. To do this we will need to change the economy in a
| way that the market compensate other talents, not only
| the ones decided by the US coastal elites. We can do it
| by blocking illegal immigration and banning imports from
| countries that don't play by the same rules as western
| countries. Bringing back the power to the working class.
| cm2187 wrote:
| And the irony of course is that these anti-racism policies
| that are based on the assumption that minority students
| aren't smart enough to pass the tests and therefore the
| tests need to dumbed down to achieve social justice, are
| fundamentally racist.
| dgs_sgd wrote:
| I've read a term for this: the bigotry of low
| expectations.
| commandlinefan wrote:
| > minority students aren't smart enough
|
| Well, that's not _quite_ what they 're saying -
| essentially what they're saying is that they're a
| _different kind_ of smart. Not that I agree with the
| logic, but essentially what they 're saying is that the
| tests - along with the whole curriculum - were designed
| and written by white people, so they're unintentionally
| biased in a way that non-white people (except, I guess,
| asians) can't understand them. The implication being, of
| course, that if black people had designed the entire
| curriculum and the tests, they would be similarly
| impenetrable to white people. Of course, I don't think
| that makes much sense either, but that is the essence of
| what they're trying to assert.
| laichzeit0 wrote:
| Mathematics is arguably (besides perhaps logic) one of
| the most pure, unbiased sciences one could imagine.
| Unless perhaps you take issue with the fact that notation
| borrows a lot of Greek symbols. It's a difficult subject
| that requires struggle. Hand holding and dumbing it down
| is literally the worst thing you could do to make people
| better at mathematics. You must struggle or you will
| fail. Don't think so? Let's talk again when you hit real
| analysis.
| magicalist wrote:
| > _Mathematics is arguably (besides perhaps logic) one of
| the most pure, unbiased sciences one could imagine._
|
| But teaching math absolutely is not. It is a very human
| process, helping students find handholds in what they
| know to make the next conceptual step. Absolutely
| breaking their minds with a new topic, then returning to
| it a month later and they find it obvious now. There are
| no platonic math lesson plans out there to tap into, and
| finding more effective ones has been one of humanity's
| jobs for at least as long as there has been written
| language.
|
| (FWIW, real analysis is generally considered one of the
| easier courses in a typical math degree)
| pseudo0 wrote:
| > (FWIW, real analysis is generally considered one of the
| easier courses in a typical math degree)
|
| Quite a few colleges seem to use it as a filter class to
| determine who has the requisite aptitude and interest in
| pure math. At my college, the material wasn't
| particularly bad, but the evaluations were designed to be
| pretty challenging and grades weren't curved at all.
| jeegsy wrote:
| > Well, that's not quite what they're saying -
| essentially what they're saying is that they're a
| different kind of smart
|
| I'm pretty sure that is exactly what they are saying. The
| 2021 version of it anyway
| akomtu wrote:
| What's "equity", btw? I mean, how is it defined by the
| administration of colleges these days?
| spurgu wrote:
| This is a worrying trend across the board. Everything has
| to be equal and politically correct, because if _not_ then
| it _has_ to be racism or something else evil.
| gorwell wrote:
| What do they say when confronted with the fact that Asians
| are the top performers in this system?
| 6f4f06c00484d34 wrote:
| then they revoke Asians' minority status, see "BIPOC" and
| racial quotas for college admissions
| logicalmonster wrote:
| I'm curious for both an accurate and/or socially
| acceptable explanation too.
|
| Some have suggested racism is cause for inequality, yet
| Asians do well in America where they're a small minority.
|
| Some have suggested culture: certain parents promote
| education more.
|
| Some have suggested examining IQ more closely (though
| thinking along these lines is a doubleplusungood thought
| crime)
| akomtu wrote:
| There's a trivial explanation. If you're Chinese, you
| gotta be really smart, the top 1% smart, to immigrate
| into the US. This is also why Nigerian immigrants do so
| well here. The original European immigrants passed a
| similar test, as it takes a lot of courage and ambition
| to move across the ocean in a big wooden boat. But as you
| know the history, on one occasion, the admission process
| was violated, and since then America has been paying the
| price. The price has to be paid in full, for every cause
| has to be compensated with a result. Call it nation-scale
| karma, if you want.
| viro wrote:
| oh on avg. they completely dismiss it based on current
| immigration policy self selecting rich Asian families.
| -\\_(tsu)_/-
| eslaught wrote:
| Did you take geometry in a California public school? I did
| about 20 years ago, and my impression was that it's an
| extremely fluffy course that would absolutely benefit from
| being condensed, or at least rewritten.
|
| California math education (again, at the time I took it) was
| already extremely oddly paced. The Algebra 2/Trig class I
| took was extremely aggressive, and then the year of pre-calc
| that followed it [1] had about 2 weeks of novel content
| spread over a year's worth of teaching. I was initially a
| year behind most of my classmates (starting in junior high),
| then skipped ahead to do Calculus BC alongside everyone who'd
| been a year ahead of me---and aced it. On the other hand, the
| people who were really advanced had already gone on to
| college courses at that point and basically hadn't bothered
| with anything in the system for many years.
|
| In short, it's a mess and has been for decades. If they can
| clean it up a bit and make the pacing more even and
| integrated, I think that would be a net win.
|
| [1]: "Introduction to Analysis", I think they called it.
| fastaguy88 wrote:
| I took geometry more than 50 years ago. From my
| perspective, it was useless then as well. As far as I can
| tell, its goal was to illustrate the importance of
| mathematical proofs. Perhaps they are important to
| mathematicians, and I suppose they would be important if
| lots of high-school and college mathematics were
| potentially incorrect, so we needed a proof to reassure
| ourselves, but for most of us, even those who actively use
| mathematics, proofs are a waste of time. It would be better
| for students to become more comfortable with abstractions
| beyond multiplication.
| naasking wrote:
| Real geometry is more important these days since computer
| graphics, photo and video editing and such are so common.
| ben7799 wrote:
| Interesting thing with the integrated approach is my high
| school had that approach. That was private school, and I
| entered high school in 1990. I wonder how long European
| countries have been using this approach. The curriculum at my
| high school very deliberately blended all the mathematical
| subjects across the first 3 years with Calculus becoming
| dominant by the end of the 3rd year.
|
| However the entire goal of the integrated program was to
| maximize the amount of Calculus students could get through. I
| got not one year but two years of Calculus effectively by the
| end of HS and had no problem passing the AP calc exam. Probably
| only 10% of my HS class did that though, and that was already
| at a selective private school.
|
| Integrated is great as long it gets students to the same
| place.. it's still really important to get as many talented
| students into Calculus before HS graduation.
| 6f4f06c00484d34 wrote:
| >They are not taking algebra out of the curriculum, although
| they are cutting geometry a bit, which doesn't make as much
| sense today as it did 100 years ago when far more people grew
| up to be farmers or ranchers.
|
| this blurb alone invalidates everything else you have to say.
| you have absolutely no idea what are you talking about.
| abecedarius wrote:
| > manufactured outrage
|
| Have you ever seen Terence Tao signing up for a manufactured
| outrage? Alan Kay? If you're the type to read technical papers
| you'll recognize a bunch more names on the list of signers.
| Furthermore the language in the post was calm and measured.
| commandlinefan wrote:
| > Terence Tao signing up for a manufactured outrage? Alan
| Kay?
|
| Or Scott Aaronson. Scott Aaronson is about as social-
| justice-y as you get. When _even he_ thinks the equity types
| have gone too far, it 's _really_ time to step back and see
| if you 're making sense, even to yourself.
| krastanov wrote:
| There is another comment in this thread that addresses this
| very well:
|
| > I find it interesting with many of these criticisms that
| subject matter experts on maths, sciences, etc think that
| they are also subject matter experts on the pedagogy of
| maths, science, etc especially at a high school level.
|
| The people you mentioned are my idols, same as the authors
| and hosts of this blog post. But there is a world of
| difference between being a great scientist and being a great
| K12 teacher.
| crackercrews wrote:
| > But there is a world of difference between being a great
| scientist and being a great K12 teacher.
|
| Very good point. K12 teachers know a lot, but they may not
| know much about the path to becoming a world-renowned
| scientist. The signers of this letter know that path from
| their own experience and the experience of their
| colleagues. They may not be educators but they have
| intimate understanding of the education process of bright
| children.
| krastanov wrote:
| Oh, this is a good point that did elude me. As long as
| some form of gifted programs continue existing (which,
| given my flawed reading of this document, they will
| continue existing, just by virtue of demand), I do not
| see it being a problem. You will raise the bottom
| significantly while not really changing the top.
| threatofrain wrote:
| Gifted programs are largely not a thing in Californian
| math. When we're talking about children who opt to take
| Algebra in middle school, or children who opt to take
| Calculus in high school, we aren't talking about gifted
| programs. We're talking about alternative pathways in
| math.
|
| A central pillar of Equitable Math is that all children
| of any given grade ought to be in the same math class,
| and that there ought not be any standard specification
| for, say, taking Algebra "early" in middle school. The
| explicitly stated reasoning by the program authors is
| that this disparity sustains White Supremacy in math.
|
| A child who is ready for Algebra would be best served by
| opting into a classroom where a teacher has been
| polishing a year-long discourse on Algebra, as opposed to
| creating an ad-hoc gifted program. A return to gifted
| programs would be a return to administrative opacity.
| abecedarius wrote:
| My comment left out this aspect only because the names
| aren't familiar to me:
|
| > The signatories include ... educators with decades of
| experience teaching students at all levels ... people
| vested in mathematical high-school education, such as ...
| krastanov wrote:
| That is a well-intentioned but simply wrong statement in
| the blog. One of the letter authors is what I would call
| a professional educator in some way (a non-profit). The
| rest are university professors and a few are industry
| scientists. They are certainly not "people with
| experience teaching at all levels" even if they believe
| that. Same with the signatories. The vast majority are
| university professors. These people are generally great
| at what they do and frequently terrible at teaching,
| *especially* when teaching K12 students. I have seen it
| first hand as I have been organizing K12 events (not for
| "gifted" kids) and have been tutoring gifted students
| competing in the international physics Olympics over the
| last 8 years while working at Yale, Harvard, and MIT (as
| a graduate student and postdoc). Teaching competitive
| physics, teaching college students, teaching K12
| students, and doing research are 4 completely different
| things. The signatories are certainly amazing at the
| research, but I have seen first hand how that type of
| professionals are just terrible at teaching K12 students
| while thinking they are doing great. Even worse, we
| usually pat ourselves on the back for having a single-day
| event with cool math organized for the K12 students, but
| never bother with the year-long battle to actually lift
| all boats.
|
| Obviously this is just my personal anecdote, but I do
| claim I have been very invested in exactly this type of
| education and have seen how well-meaning crazy-smart
| professors are failing to teach K12 students (in their
| once-a-year charity event) while patting themselves on
| the back for a job well done.
| abecedarius wrote:
| The letter isn't saying that all of them teach at all
| levels. It's true that I'm a lot more familiar with tech
| reputations than education reputations. OTOH education is
| an unusual field in that practically everyone has decade-
| plus full-time intimate first-hand experience with it;
| and more in the case of parents.
|
| What do you think of the claim that the policy will
| increase inequality of preparation because better-off
| parents will bypass public education more? It sounds like
| you might have more light to shed on that.
| krastanov wrote:
| I am hesitant of having an opinion. These are luminaries
| that I look up to, but I fundamentally disagree with
| their opinion on this topic. Probably partially because I
| have been very frustrated with snobbish and
| disconnected[1] attitude towards K12 education among
| scientists.
|
| But to actually answer your question. Better-off parents
| already bypass public education, even if not completely.
| If this new program works (not a given), the problem will
| not be exacerbated, rather more students will be prepared
| to reach for these "gifted programs" (which in many
| cases, even if expensive, usually have good fee-waivers
| as this gives them more credibility).
|
| [1] Obviously just a personal opinion. But in the
| interactions I have had in this context I feel I have
| seen a lot of inflated but unsubstantiated sense of
| competence.
| abecedarius wrote:
| Thanks. I guess I can see this working out if the classes
| end up being taught better on average (aiming for deeper
| understanding instead of faster advancement along a
| standard track to "advanced" math), and if the better-off
| parents generally appreciate this. If we did successfully
| get better teaching then it'd be natural for a greater
| proportion of the disadvantaged to discover they're
| interested in real math, too.
|
| (I wouldn't bet on it, personally, and I don't think the
| infusion of wokeness is mainly about helping more people
| to understand math better. Hopefully I'm too cynical. The
| Common Core math stuff seems like progress, for
| instance.)
| throw10920 wrote:
| Just because Terence Tao is a genius at (and world-leading
| researcher in) mathematics, and Alan Kay is programming
| pioneer, doesn't mean that either of them understand the
| implications of the CMF, or are knowledgeable about
| children's education - they could merely be taking the word
| of someone else who is misinformed or not acting in good
| faith (perhaps through a telephone game mechanism).
| abecedarius wrote:
| I went looking at the names because "manufactured outrage"
| connotes politics or culture war. It's the sort of
| accusation you'd expect to see if the list was full of
| names like Jordan Peterson. Instead I see Tao who on his
| blog comes across as apolitical, mild-mannered, even
| humble. Not the kind of guy who's into culture fights. Or
| Kay whose book recommendations had a kind of 60s lefty
| flavor, as far as any political leaning came across to me.
|
| There's a bigger argument here, but I'm just addressing
| this one unmerited accusation in this thread.
| AlanYx wrote:
| It's not fair to talk about Alan Kay this way. Alan Kay
| actually did a ton of pioneering work in children's
| education, and in an applied (real-world) empirical way,
| not just in a theoretical sense.
|
| He and some of his collaborators were among the earliest in
| applying Piaget and Bruner's learning models to programming
| education, mainly for learners under age 15.
| threatofrain wrote:
| Talking about "testing out" and "gifted" programs is a complete
| distraction here, since very few students "test out", and
| taking Algebra in middle school is not considered a "gifted"
| program. With regards to math in California, gifted programs
| are largely _not_ a story.
|
| A pillar of Equitable Math is that _all_ students should be at
| the same level up until the last year of high school.1 The re-
| arrangement of subjects is _not_ the hotspot of contention, and
| neither is the disagreement over "deepness".
|
| The contention is over whether or not there ought to exist a
| faster track which, for example, permits students to take
| Algebra in middle school. This has been specifically derided as
| a sustainer of white supremacy under the Equitable Math
| discussion.
|
| A return to gifted programs as the way to deal with students
| with differences in math preparation and ambition would be a
| return to administrative opacity. A failure to specify tracks
| which allow students to take Algebra in middle school would be
| a solid win for private schools and after-school programs like
| RSM.
|
| Under Equitable Math, the last year in high school is the only
| year of differentiation.
|
| [1]: https://equitablemath.org
| naasking wrote:
| > A return to gifted programs as the way to deal with
| students with differences in math preparation and ambition
| would be a return to administrative opacity.
|
| I mean, if they're going to eliminate gifted programs for an
| advanced academic students, then they should eliminate sports
| teams for advanced athletic students by parity of reasoning.
| Isn't the star quarterback just as unfairly advantaged by
| family and genetics as the smart math geek?
| gautamdivgi wrote:
| Does it really help though? I mean parents with resources will
| always put their kids through private math courses which can be
| more rigorous and give their children an advantage in AP
| Math/Calc/etc. I don't think the disparity in math learning is
| from school.
| cperciva wrote:
| _they are cutting geometry a bit, which doesn 't make as much
| sense today as it did 100 years ago when far more people grew
| up to be farmers or ranchers._
|
| The point of high school Geometry was never to compute areas of
| fields. Trigonometry is far more useful for that anyway.
|
| The point of high school Geometry is that it is the first
| introduction to rigorous mathematical proof -- and has been,
| ever since Euclid's Elements.
| heyitsguay wrote:
| As someone who did a BA and PhD in math, went through high
| school geometry proofs, taught geometry proofs to math
| students and math education students:
|
| Geometry proofs are a _terrible_ way of introducing rigorous
| mathematical proofs to students. Seriously. I cannot
| overstate how misleading they are. I remember my first
| abstract algebra class in college, after the first HW I got
| called in by the TA because I tried to structure my proofs
| like I learned in geometry class - a sequence of symbols and
| references to hard-coded lists of axioms and prior
| deductions. I thought that 's what proofs are, but they are
| not, at least not as humans do higher math. High school
| geometry tries to distill this process down to a symbol
| manipulation game that students can memorize and regurgitate,
| and in the process loses the essence of the thing it was
| meant to capture in the first place.
| bradleyjg wrote:
| If you wrote everything like a high school essay, you'd be
| a pretty terrible writer. In real life you don't need a
| topic sentence for every paragraph and sometimes an
| infinitive needs splitting. Nonetheless, high school essay
| writing is a pretty good way station to good writing.
| Perhaps high school geometry proofs are similar.
| lupire wrote:
| That's like saying teaching arithmetic algorithms is bad
| because you can do arithmetic in your head.
|
| You have to know what logical rigor is before you can take
| defensible shortcuts.
| OccamsRazr wrote:
| It's funny, I also think Euclidean geometry is a bad way to
| introduce proofs, but my reason is different from what you
| just said. I think what you just said is primarily about
| "writing proofs", which is certainly important, but I'm not
| sure it's the fundamental issue with Euclidean geoemtry
| (and I know that not everyone learns Euclidean geometry and
| comes away from it writing proofs as you did). It sounds
| like you came out of your highschool Euclidean geometry
| experience with good logic skills but poor communication
| skills (?).
|
| The issue with Euclidean geometry as an entrance to proofs
| and logic is two-fold. First, the definitions and axioms of
| Euclidean geometry are incomplete in many ways. Many
| definitions, such as that of a line, cannot be understood
| from what is written in Euclid but require a significant
| amount of intution pumping to be able to know how to
| properly work with them. Thus, the fundamental definitions
| in Euclidean geometry are bad examples of what a definition
| in math _should_ be, and we are already starting on very
| rocky footing. Moreover, the axioms, as they are presented
| in Euclid or common modern educational sources, are not
| sufficient to do what is claimed. For example, the proof of
| postulate 1 already has a logical gap because there is no
| axiom which guarantees the existence of a point lying at
| the intersection of the two circles one has drawn. Again,
| the argument relies crucially on a figure, which is the
| intuition pump used in all of Euclid, but the picture is
| not based on any of the axioms, so it is reinforcing a bad
| way of thinking about proofs that is intuitive and not at
| all focused on carefully using definitions and axioms. (Of
| course, one can fix Euclidean geometry to be rigorous by
| adding many extra axioms, but the resulting axiomatic
| system is much more complex and is not at all suitable for
| highschool students, except possibly the brightest.)
|
| The second, somewhat more minor, issue I have with
| Euclidean geometry, related to the first, is that the way
| arguments are phrased, and the use of figures to
| illustrate, often hides many logical steps that are only
| implicit. In particular, I am thinking of the implicit use
| of qunatifiers in statements that are proven in Euclidean
| geometry. This is an issue because as soon as one moves on
| to proofs in any other context encountered by students,
| e.g. in first year undergrad, it becomes much more
| difficult to do things correctly while only thinking about
| quantifiers implicitly.
|
| It would be much more beneficial, in my opinion, to have
| the first introduction to proofs be a topic that is much,
| much simpler (such as integers) where the focus can be
| purely on how statements are formed with quantifiers, how
| strategies of proof are determined based on the form of the
| statement and which quantifiers are involved, and how the
| (much shorter and simpler, and not requiring an intuition
| pump to use correctly) definitions and basic properties of
| that topic can be applied in a proof.
|
| The root of all of this is the importance in proofs of
| properly using the definitions and axioms. Students in
| highschool, except the most talented, just are not careful
| thinkers and will revert to their preferred lazy way of
| thinking (such as pictures and vague ideas) as soon as you
| give them the opening. In my experience, the only way to
| force students to understand how to properly prove things
| is to pull out the rug of their intuition, even briefly,
| for just long enough so that they learn how to do things
| without it. Then later, once they have properly adopted the
| mindset of using the definitions, you can let the intuition
| back in.
|
| For context, I don't know if any of what I just said
| reflects how Euclidean geometry is taught in, say,
| Caifornia. I only know this from the perspective of having
| tried to incorporate Euclidean geometry in an undergraduate
| proofs course (in Canada where Euclidean geometry hasn't
| been part of the grade school curriculum for some time).
| cperciva wrote:
| I would agree that proofs as introduced in high school
| Geometry have more in common with formal axiomatic logic
| than the vast majority of "real-world" mathematical proofs;
| but a large part of that is just clumsy notation.
|
| The fundamental concepts
|
| 1. We have axioms which are things we accept without proof
| because we all agree that they're obvious;
|
| 2. Everything else should follow logically from things
| which come earlier;
|
| 3. Don't skip steps!
|
| are extremely important and apply regardless of the field
| you're in.
| joshuamorton wrote:
| But geometry is sort of badly suited to teaching this
| because it's very hard to justify. We're good at thinking
| geometrically so things look "obvious" unless you do bad
| things like explicitly mislabel images (I remember some
| geometric problems where clearly unequally drawn line
| segments were labeled as equivalent).
|
| Like you end up having to reteach proof in university
| discrete math or stats classes anyway!
|
| Using motivations that we know to be true (or can see
| empirically are true) but don't feel trivial because "duh
| those lines are the same length" is a lot more
| compelling. You actually feel like you've learned
| something, not just a dumb formalism for something you
| could already intuit (and I mean if that's all proof
| does, let you formalize things you already know, what's
| the point?)
|
| You're of course not the audience of these changes,
| because I expect that my last statement made you gag a
| little bit. But that's the way a lot of people are, and
| we shouldn't restrict ourselves to teaching the way they
| did 2500 years ago[0] unless there's still good reason to
| do it that way.
|
| [0]: I'll admit that I think "look they were able to
| prove these things in this way 2500 years ago prior to
| the conceptualization of zero" is a compelling way to
| teach this stuff, but we don't do it that way either.
| cperciva wrote:
| I disagree: It's precisely when things _are_ obvious that
| it 's useful to teach formal proof. You can't teach the
| critical part of "don't skip steps" if nobody is even
| tempted to skip steps.
| joshuamorton wrote:
| Why? "Do as I say without clear motivation except that
| I'm telling you it's supposed to be done this way" is
| maybe the worst way to teach. Is that justification going
| to keep a group of 15 year olds engaged? It certainly
| didn't for me.
| darawk wrote:
| I think the point is to teach people that apparently
| obvious things are not always actually true. This is
| extremely important in math as you move on, as i'm sure
| you know. Many "obviously true" things are not actually
| true when you get really serious about formalization.
| Teaching kids that "seems true to me" isn't good enough
| is a critical step along that path.
| cperciva wrote:
| Exactly. You can't teach people that sometimes their
| intuition is wrong if they don't have any intuition to
| begin with.
| joshuamorton wrote:
| I see this in theory, but I'm having a hard time thinking
| of geometric problems that violate intuition and that are
| appropriate to teach people who have no calculus and
| limited algebraic skills (admittedly this limits
| statistical problems too). I'm actually curious if you
| have any good examples, because I don't.
|
| And I think that's where my objection comes in: if you
| spend the entire first year just developing that
| intuition but forcing a rote procedure, you'll have lost
| the majority of people already. Proof isn't arithmetic
| and we shouldn't teach it in the same way. Sure develop
| the process on the easy method first, but then show
| people why it's important to not skip steps.
| amalcon wrote:
| I think a large part of the problem is just that it's
| poorly integrated into the larger curricula[0]. By the
| time a typical student reaches geometry class, they have
| incorrectly learned that math consists of memorizing
| things, pattern matching onto things they've memorized,
| and making at most minor adjustments. The kind of logical
| inference and objective-based reasoning that is necessary
| for a rigorous proof is covered more in writing class
| than in math. Some of the kids I've seen adjust well to
| it have dabbled in software and pattern-matched proofs
| onto that (which has its own pitfalls, but better than
| nothing). The remainder had parents who taught this kind
| of thinking from a much younger age.
|
| For those not so lucky, they need to spend probably about
| a semester un-learning what math _is_ before they can
| really start.
|
| [0]- In the arbitrary parts of the US that I know
| anything about
| AlanYx wrote:
| One advantage of geometric proofs is that they seem to be
| more accessible to some kinds of learners (visual/spatial
| thinkers) than proofs of purely symbolic results.
| BeetleB wrote:
| For quite a while I thought I'd never be great at math
| because I struggled with geometry. Fortunately, I ignored
| that voice in my head and went on to do lots of advanced
| math (analysis, abstract algebra, computational methods),
| ranking in the top 10% of Polya, etc.
|
| I still suck at geometry.
|
| Geometry is a really poor representation of whether one can
| do proof based maths.
| jacobmartin wrote:
| It is interesting to me that you didn't encounter problems
| with the rote geometric method before abstract algebra. I
| went to a so-so public school in the American South, so I
| don't think I exactly had a stellar introduction to math or
| even school/academics in general, but beginning in
| trigonometry, we had to structure our proofs with more
| words and 'connective tissue,' and less explicit
| axiomatization/symbolization. Calculus continued this
| trend, and by the time I took linear algebra (at a local
| university while I was still in high school), the proofs
| were exactly like the proofs I would write throughout
| college. But there were several 'stepping stones' away from
| the original geometric proof.
|
| Though admittedly I only got an SB in Math, I think
| geometric proofs were an okay _introduction_ to the idea of
| the proof and of logic. Of course they are not
| representative of professional math. There are many things
| we learn as an introduction which don 't turn out to bear
| that much resemblance to the more advanced form. I don't
| write 5-paragraph essays with clear thesis sentences
| anymore either. But it helped me to learn to write that way
| as a way of clarifying that I was stating my arguments
| effectively.
|
| Sometimes, for my homework, I tried to state very
| explicitly in my proofs which axiomata I was using, both as
| an intellectual exercise and to see, e.g., where I might
| have gotten my logic backwards or where I used the axiom of
| choice (which constantly surprised me). I wouldn't turn
| these overexplicit proofs, but it helped to clarify that I
| was doing things correctly. If anything, when I was in
| college, the trend was _away_ from 'informal' language.
| When I took, e.g., Discrete Math, for more complicated
| proofs, we were encouraged to write out a DAG for the
| dependencies of the proofs/lemmata so that it was
| exceedingly clear what depended on what and that we had in
| fact proven what we set out to prove.
| akomtu wrote:
| What are those "geometric proofs"? I've never seen this
| term before. Geometry is really just numbers in disguise,
| e.g. a circle is really numbers that define its center
| and its radius, and sometimes those numbers are defined
| implicitly, e.g. when its a highly complex curve that's
| not reducible to simple circles and lines. In this sense,
| all proofs are about symbols and numbers, geometry is
| only there to guide our intuition.
| jjoonathan wrote:
| Agreed. Personally I think we should swap our high school
| curriculum: Geometry -> Proofy Linear
| Algebra Trig -> Computational Linear Algebra
|
| I think the heydey of Trig was in the age of navigation and
| the heydey of Geometry was in the age of machines.
| Meanwhile, today, linear algebra has supplanted both of
| them, runs the world besides, and it seems to only be
| getting started.
| monocasa wrote:
| Rather than geometry or linear algebra, I'd love to see
| logic and set theory taught that early as more than a
| passing topic.
| lstodd wrote:
| Can only up this. Not teaching set theory is just an
| abomination. And logic. That year of Prolog taught me so
| much.
| lstodd wrote:
| Which would be utterly useless.
|
| Math, and specifically Geometry aren't about useful
| skills, they are about understanding the world.
| jjoonathan wrote:
| Linear algebra has geometry flat out beat in that arena,
| too. This isn't to say that Geometry doesn't help you
| learn about the world, but it _is_ to say that Linear
| Algebra should be prioritized above Geometry if your goal
| is to understand the world.
|
| I can't remember a physics class where LA _didn 't_ pay
| heavy dividends -- in particular, differential equations
| are the language of physics, and you'd be hard pressed to
| find either an analytical or computational diff eq
| technique that didn't have a core of linear algebra.
|
| Meanwhile, the last time Power of a Point gave me
| dividends was on math contests.
| lstodd wrote:
| LA is a very useful tool.
|
| But imagine that you never heard of concepts behind it.
|
| It'd just become a more-or-less useful artefact. And in
| no time it would devolve into a useless ... thing so to
| say, a decoration, as you lose knowledge how to apply it.
| jjoonathan wrote:
| Yes, Geometry makes the funnest puzzles :-)
|
| Believe me, it pains me to suggest bumping it back.
| Introductory proofy linear algebra just hits a quadruple
| home run: it's astonishingly useful, it's getting moreso,
| it's simple enough to remain age appropriate, and it can
| serve as an intro to proofs. As much as I enjoy geometry
| puzzles, I just don't see how they compete with that.
|
| For the true fans, of course, the answer today & in this
| hypothetical future is still to learn both.
| BeetleB wrote:
| > I think the heydey of Trig was in the age of navigation
| and the heydey of Geometry was in the age of machines.
|
| Sorry, but this is crazy. If you're in physics,
| electrical engineering, mechanical engineering, or civil
| engineering[1], then trigonometry appears in so many
| problems - including ones that have little to do with
| triangles and geometry.
|
| Calc II is heavy on trigonometry for a good reason. So
| many integrals that show up in the "real world" are
| solvable if you know your trig identities. These show up
| in semiconductor theory, mechanics, electromagnetics,
| quantum mechanics, etc.
|
| Trig is the one thing I'm glad I was taught well in high
| school. Used it all the time for over a decade.
|
| [1] And probably many other disciplines.
| kevin_thibedeau wrote:
| _Trigonometry_ has little to do with triangles. It 's
| more appropriately titled circleometry.
| taeric wrote:
| I'm curious on how you structure proofs, then? That is, how
| do you recommend?
| maire wrote:
| > Geometry proofs are a terrible way of introducing
| rigorous mathematical proofs to students
|
| You might be right, but they are the only high school math
| class that teaches proofs. If you take away geometry you
| are left with nothing.
|
| Having said that - any math concept can be memorized and
| regurgitated. My kids are in CA elementary math right now
| and it seems to be better than when I was a kid. The
| emphasis is on derivation rather than memorization. It
| might just be that geometry is better now than when you
| were a kid.
| cozzyd wrote:
| At least at my school, there was a special geometry class
| that included proofs ("formal geometry"). Other than the
| handful of few people who bothered to take that class, there
| was very little way in the way of proofs in the geometry
| class that 98% of people took (ok, I tested out of geometry
| so I don't really know what was in the curriculum).
| cperciva wrote:
| This makes me sad. High school Geometry without proofs is
| indeed not worth keeping. (Except maybe as a two week
| discussion of triangles and right angles so that students
| understand what they are when they hit trig.)
| ajkjk wrote:
| Proof-based high school geometry is an absolute joke and
| should be excised as soon as possible. There is no better way
| to ruin someone's enthusiasm for math while teaching them
| nothing useful... imo.
|
| https://www.maa.org/external_archive/devlin/LockhartsLament..
| .. makes the best case for this.
| showerst wrote:
| While both are clearly important, if we only have so many
| hours in the day I'd rather a high school student have a
| grasp on basic stats than basic formal proofs.
|
| As a data point of one (heh there's that stats again...) my
| two high school geometry classes 15 years ago never touched
| any proofs. I have no clue if they still teach that way.
|
| Edit: just noticed that I'm replying to someone who is far
| more knowledgeable about math than me. I stand by my point
| though, people like Colin can seek that out in more advanced
| classes.
| jelliclesfarm wrote:
| "Lies, damned lies, and statistics"
| ghaff wrote:
| I had proofs in HS geometry way back when. I also hated it
| and it was the worst I ever did in a math class K-12.
| tzs wrote:
| A somewhat similar point is expressed in Underwood Dudley's
| article "What is Mathematics For?" from the May 2010 Notices
| of the AMS [1].
|
| Briefly, he argues that we greatly exaggerate how much math
| you actually need in ordinary life and in most jobs that
| people usually think of as needing math (and what you do
| actually need can be learned on the job), but nevertheless
| learning math is worthwhile and important because of what it
| teaches you about how to think.
|
| It's hard to imagine now, but back in the early days of the
| US similar debates played out over teaching arithmetic in
| schools. Most people didn't need more than counting and
| simple addition and subtraction, so why make everyone learn
| any more than that? Those few who meeded more could learn it
| outside of school.
|
| [1] http://www.ams.org/notices/201005/rtx100500608p.pdf
| ivanech wrote:
| I got nothing out of my high school geometry class but loved
| my foundations class in college. I would have been a lot
| better off just going straight to real proofs instead of
| those annoying pseudo-proofs. But I don't know, other people
| probably had different experiences and got a lot out of
| geometry.
| Youden wrote:
| > The FAQ is at [2] and directly responds to these
| characterizations.
|
| I don't know whether it's intentional but the FAQ reads like
| it's intending to deceive me. They answer questions with "no
| we're not doing that", then follow up with how they do exactly
| that with different words. For example:
|
| Q: "Does the draft Mathematics Framework eliminate middle
| school mathematics acceleration programs?"
|
| A: "No. The draft Mathematics Framework does not eliminate
| middle school mathematics acceleration programs (including
| programs that offer Integrated Math 1 or Algebra 1 courses to
| grade eight students). The draft Mathematics Framework
| emphasizes the importance of following the sequenced
| progression of topics laid out in the Common Core State
| Standards for Mathematics (CCSSM) and considers the latest
| research on the impact of skipping grades or undermining the
| sequences progression."
|
| They're not "eliminating", they're "emphasising" and
| "considering". Maybe what they're doing really isn't
| eliminating but it sure reads like it is. The tone reads like
| corporate damage control. 'We didn't "spill" the oil, we
| misplaced it.'
| richk449 wrote:
| > They're not "eliminating", they're "emphasizing" and
| "considering".
|
| It is almost as if words have actual meanings ...
| rahimnathwani wrote:
| "The manufactured outrage over the California math
| recommendations keep getting posted on HN. Read the actual text
| of the plans here [1]."
|
| This is not manufactured outrage. I have read the framework
| (and many of the sources cited as support for the
| recommendations), and I am outraged.
|
| If you follow the footnotes, you'll find instances where:
|
| - the framework incorrectly states the conclusion/claim in the
| paper/study/web-page
|
| - the framework relies on a claim in a paper/study/web-page,
| when the paper/study/web-page lacks sufficient evidence to
| support the claim due to poor experimental design, poor
| interpretation, or lack of evidence altogether
|
| "The FAQ is at [2] and directly responds to these
| characterizations."
|
| The FAQ does not accurately portray the implications of the
| recommendations. (I read both the framework and FAQ a few
| months ago.)
| cgh wrote:
| Thanks. The new emphasis on stats and probability is so
| important and is something I wish I'd had before taking my
| first university stats courses. There's probably no branch of
| math more important to everyday life and maintaining an
| educated discourse in society.
| SpicyLemonZest wrote:
| I've read most of the text. It's pretty misleading to say the
| guidelines don't ban accelerated courses, because they don't
| really have a concept of "banning" things in general; they're a
| vision of what the curriculum should look like, not a list of
| rules. The guidelines do make it pretty clear that accelerated
| classes are not part of the vision.
| csee wrote:
| > the framework does not forbid gifted and talented programs
|
| How do I square this with their claim that the CMF is _"
| placing obstacles (such as doubling-up, compressed courses, or
| outside-of-school private courses) in the way of those who want
| to take advanced math in higher grades."_?
| weeblewobble wrote:
| pretty easily, I think. even taking the claim as given,
| "placing obstacles" is not the same as "forbidding"
| nickff wrote:
| This is a classic tactic. How many trees do you need to
| make a forest? How many pebbles make a dam?
| sct202 wrote:
| To get around the obstacles most kids will need a very
| motivated parent who can advocate for them with admins, and
| that basically will just harm kids who's parents don't have
| the time/resources/charisma to make it happen for their
| kid.
| csee wrote:
| This is semantics, no? Couldn't the obstacles be so large
| that it's practically the same as forbidding?
|
| When I read "they're not forbidden", I take that to also
| mean that there's few new obstacles.
| crackercrews wrote:
| Unfortunate that this is the top post since almost all of the
| replies disagree with it. Would be better if another root-level
| comment were at the top.
| monocasa wrote:
| Ironically, geometry literally means "the measuring of land"
| because it's a field derived from the bronze age super powers,
| who needed to resurvey the farming plots after each river
| flood. A farmer might actually have some benefit knowing it
| really well.
| cyber_kinetist wrote:
| Also, it helps to have some intuition of geometry when you're
| actually building something (whether that be construction,
| mechanical engineering, woodcutting, papercrafting, you name
| it...)
|
| Geometry is one of those things that you can teach in the
| utmost horrible way though (make students memorize theorems
| verbatim), I understand why students can perceive it as
| incredibly boring and useless.
| legerdemain wrote:
| Math at school started losing me some time around multiplying and
| dividing fractions, and I haven't seen anything uses of math in
| any of my jobs. I, for one, am glad that schools are finally
| removing the unnecessary pressure to Take More Math Than
| Necessary. Maybe they can now focus on more practical subjects
| like CS or shop, or even just reduce the number of hours students
| spend cooped up in those kid prisons with tyrannical teachers.
| it_does_follow wrote:
| > I haven't seen anything uses of math in any of my jobs
|
| Math didn't "click" with me until well after college, when I
| eventually caught up on a lot of calculus, discrete math,
| probability and stats, to the point where I ended up doing math
| most of the day as a data scientist.
|
| Before I learned math I used to feel like you did, and would
| argue that math wasn't necessary to be a good programmer.
|
| Funny thing is that only once I learned a lot of math did I
| realize how insanely applicable it was to a wide, wide range of
| problems I was working on. Because I had to learn it late in
| life I learned math more enthusiastically than most of my data
| science peers and so find that even in that domain people don't
| realize how often they can use math to solve problems better
| and faster.
|
| I wish I had had better teachers in HS that were able to make
| me realize just how important math is to so many interesting
| and fun problems.
|
| It's sort of shocking to me, looking back at HS, how many math
| teachers didn't have a good answer to "when are we going to use
| stuff?". I wish I could take some of my friends making high six
| figure salaries with a penchant for late night partying to
| explain to HS students exactly how math is useful because it
| lets you get a job where nobody cares how much weed you smoke,
| how late you sleep, and pay your more than many doctors all
| because you can do some basic calculus tricks. Plus you get to
| work on really fun problems.
| skeeter2020 wrote:
| I learned the conversion factors approach in chemistry but it's
| really just a basic math process of starting with something in
| one unit set, having a target unit and applying conversions
| until you get to your goal. It's probably the single most
| powerful technique I took from public school.
|
| If you think we can teach CS at any sort of non-trivial level
| without an understanding of math beyond grade 7/8 you don't
| really know what computer science is. Even if you mean
| "programming", kids want to primarily build games which
| involves tonnes of HS math. Even shop courses often involve
| questions like "find the center of an object".
| nyanpasu64 wrote:
| I think units are brilliant, and use them extensively in math
| and programming. However I often get sloppy and conflate
| conversion factors (60 minutes per hour) and quantities
| (44100 samples per second). This usually isn't a problem, as
| long as I use different units for sampling rates (samples per
| second) and waveform frequencies (cycles per second) instead
| of calling them both hertz. But things get messy when you're
| converting between multiple different sampling rates,
| polyphase resamplers ("64 subsamples per sample" etc.),
| overlap-add convolution (which has like 3 different
| quantities all labeled "samples"), and such.
| jimbokun wrote:
| > Maybe they can now focus on more practical subjects like CS
| or shop, or even just reduce the number of hours students spend
| cooped up in those kid prisons with tyrannical teachers.
|
| Well that is a strong argument for separate tracks. Advanced
| math courses for those intending to study STEM in university,
| CS and shop for those intending to get a job directly out of
| high school.
|
| (And yes, CS as "programming" and not an academic discipline is
| something you could learn well enough to get a job right out of
| high school, or maybe with a couple more years technical
| education, at most.)
| tannhauser23 wrote:
| If I were a billionaire I would fund Asia-style 'cram' academies
| in disadvantaged neighborhoods and make them free. Provide a safe
| place where students can get extra-school training in music,
| writing, math, etc. Create communities of students who, yes,
| compete against each other and become motivated to succeed.
|
| Bloomberg giving $750 million to charter schools is a great
| start: https://www.wsj.com/articles/michael-bloomberg-why-im-
| backin...
| cyber_kinetist wrote:
| From my experience, the students who are truly gifted only
| needs a good environment they can study in (without worrying
| about money/work/bullying/parental abuse) but they definitely
| do not need 'cram schools'. The talented ones often have enough
| motivation to study what they like, and they can do self-study
| well with just light attention/mentoring from teachers.
|
| People who are blindly praising Asian-style cram education
| really haven't actually experienced one in their youth at all;
| it is a fucking disaster at raising actual talent, and it robs
| you so much of your adolescence.
| rahimnathwani wrote:
| "The talented ones often have enough motivation to study what
| they like, and they can do self-study well with just light
| attention/mentoring from teachers."
|
| There are many people who do not fit this category, but could
| still benefit immensely from good teaching.
|
| I know, because I was one of them.
| 908B64B197 wrote:
| > I would fund Asia-style 'cram' academies in disadvantaged
| neighborhoods and make them free
|
| Cram schools are laughably useless. Works well at a national
| level with a large enough population but they are really a side
| effect of the intense competition and pressure for the few
| decent university spots available in Asian countries (per
| capita).
|
| It's basically optimized to pass a test, not learn, and heavily
| rewards rote memorization.
| micromacrofoot wrote:
| I live in one of those neighborhoods and you would find that
| literally no one would enroll.
|
| Cram schools succeed in Asian countries because there's an
| enormous amount of pressure to pass entrance exams, in
| disadvantaged neighborhoods kids often aren't even pressured to
| the point of graduating high school at all.
| yardie wrote:
| Billionaires could do this and yet chose not to.
|
| Do you ever wonder why American schools finish at 2-3pm rather
| than run the entire day as Western Europe? So that teachers
| could get that extra 3-4+ hours of doing the administration
| side of classroom work (grading, report writing, planning,
| etc). Even when parents request it there never appears to be
| enough money for afterschool programs, school districts create
| and withdraw them all the time depending on budget that you
| can't actually make plans for them.
| donkarma wrote:
| western europe is a pretty big place dude, which country are
| you talking about?
| Gunax wrote:
| Sounds good to me--less competition!
|
| (I kid, this sounds disasterous).
| crackercrews wrote:
| I started reading the California Math Framework but stopped
| partway through the intro, when I got to the part that says:
|
| > we reject ideas of natural gifts and talents
|
| It must be nice to think about a world in which every child is an
| equally-capable blank slate. But we do not live in that world. We
| live in a world where some people are tall, and somewhat more
| likely to be successful basketball players. And some people find
| math easy, and are somewhat more likely to succeed in math.
|
| When you start out with flawed assumptions, it's not surprising
| when your prescriptions (no advanced math for anyone!) are
| foolish and counterproductive.
| Angostura wrote:
| Context is important, no? I'm not sure how you got to read that
| bit, without reading the preceding rationale:
|
| > Research is also clear that all students are capable of
| becoming powerful mathematics learners and users (Boaler,
| 2019a, c). This notion runs counter to many students' ideas
| about school mathematics. Most adults can recall times when
| they received messages during their school or college years
| that they were not cut out for mathematics-based fields. The
| race-, class-, and gender-based differences in those who pursue
| more advanced mathematics make it clear that messages students
| receive about who belongs in mathematics are biased along
| racial, socioeconomic status, language, and gender lines, a
| fact that has led to considerable inequities in mathematics.
|
| >In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues
| interviewed university professors in different subject areas to
| gauge student perceptions of educational "gifts"--the concept
| that people need a special ability to be successful in a
| particular field. The results were staggering; the more
| prevalent the idea, in any academic field, the fewer women and
| people of color participating in that field. This outcome held
| across all thirty subjects in the study. More mathematics
| professors believed that students needed a gift than any other
| professor of STEAM content. The study highlights the subtle
| ways that students are dissuaded from continuing in mathematics
| and underscores the important role mathematics teachers play in
| communicating messages that mathematics success is only
| achievable for select students. This pervasive belief more
| often influences women and people of color to conclude they
| will not find success in classes or studies that rely on
| knowledge of mathematics.
|
| >Negative messages, either explicit ("I think you'd be happier
| if you didn't take that hard mathematics class") or implicit
| ("I'm just not a math person"), both imply that only some
| people can succeed. Perceptions can also be personal ("Math
| just doesn't seem to be your strength") or general ("This test
| isn't showing me that these students have what it takes in
| math." My other class aced this test."). And they can also be
| linked to labels ("low kids," "bubble kids," "slow kids") that
| lead to a differentiated and unjust mathematics education for
| students.
|
| That _leads_ to the principals:
|
| > * All students deserve powerful mathematics; we reject ideas
| of natural gifts and talents (Cimpian et al, 2015; Boaler,
| 2019) and the "cult of the genius" (Ellenberg, 2015).
|
| > * The belief that "I treat everyone the same" is
| insufficient: Active efforts in mathematics teaching are
| required in order to counter the cultural forces that have led
| to and continue to perpetuate current inequities (Langer-Osuna,
| 2011).
| naasking wrote:
| > The results were staggering; the more prevalent the idea,
| in any academic field, the fewer women and people of color
| participating in that field. This outcome held across all
| thirty subjects in the study.
|
| This is not evidence that natural talent is not needed, it is
| at best some evidence that minorities and women maybe don't
| think they have the requisite natural talent.
|
| > Negative messages, either explicit ("I think you'd be
| happier if you didn't take that hard mathematics class") or
| implicit ("I'm just not a math person"), both imply that only
| some people can succeed.
|
| To say the evidence for stereotype threat is "weak" is
| charitable at best [1], and multiple replication attempts
| have failed entirely.
|
| Overall, the evidence that was cited is simply not sufficient
| to justify the principles you list.
|
| [1] https://replicationindex.com/2017/04/07/hidden-figures-
| repli...
| ThrowawayR2 wrote:
| > " _The results were staggering; the more prevalent the
| idea, in any academic field, the fewer women and people of
| color participating in that field. This outcome held across
| all thirty subjects in the study. More mathematics professors
| believed that students needed a gift than any other professor
| of STEAM content._ "
|
| Wait, the finest minds and educators in their respective
| fields are providing observational data that gifts are a real
| phenomenon, literally contradicting " _reject ideas of
| natural gifts and talents_ ". This is tremendous news that
| should have been a clarion call to seek out and elevate the
| gifted and invest every possible effort to nurture their
| gifts.
|
| Yet the conclusion is somehow the exact opposite: that
| "gifts" are a falsehood used to malignly, even if
| unconsciously and unintentionally, dissuade people. How is
| this possible?
| tzs wrote:
| None of that actually shows that natural gifts and talents do
| not exist or are not necessary. Their results could be
| equally well explained by mathematics success requiring both
| gifts and early encouragement and support to develop those
| gifts, with children from less well off groups receiving less
| of the latter.
| freemint wrote:
| Thanks for this. It's important to highlight that if students
| had problems with one area of math but are talented in
| another that they might never experience that they are good
| at when math is taught area by area and not in an integrated
| way.
|
| Math is not scalar is skill! When I am working with Boolean
| value function i almost always need to draw a table of all
| options while in Linear Algebra or numerics of differential
| equations I have a quiet good intuition.
| crackercrews wrote:
| FYI the first cited research is to the work of the primary
| author of the CMF. Her work appears to be very ideologically-
| motivated, and her colleagues have raised serious questions
| about her research. She also routinely misrepresents the work
| of others. Based on what I have read [1, 2 of many], I no
| longer trust anything she says without checking the actual
| source.
|
| Based on coverage I've read, the CMF does not cite,
| acknowledge, or discuss any of the critiques of Boaler's
| work. If they had good responses to these critiques, they
| probably would have spent some of their 800 pages addressing
| these serious challenges.
|
| 1: http://www.danielwillingham.com/daniel-willingham-science-
| an...
|
| 2: https://gregashman.wordpress.com/2019/03/03/jo-boaler-
| cites-...
| bsder wrote:
| > When you start out with flawed assumptions
|
| This is _not_ a flawed assumption with respect to baseline high
| school learning.
|
| People can be taught much more mathematics and science than
| they normally learn.
|
| This is not limited to STEM--people can be taught to write much
| better than they normally learn, as well.
|
| The trick with the students is getting to the students _before_
| the "I'm not a <X> person/<X> isn't for me" kicks in. That
| means you _have_ to get them in the 5th-8th grades--5th is a
| bit early /8th is a bit late.
| crackercrews wrote:
| > People can be taught much more mathematics and science than
| they normally learn.
|
| I don't disagree. But holding back advanced students is no
| way to accomplish this.
| bsder wrote:
| People talk about "holding back advanced students", but, in
| the real world, this never happens.
|
| My father (a high school teacher for almost 4 decades) used
| to say: "I can't stop an advanced student even if I wanted
| to--sheer boredom will propel them to _do something_. " For
| him, dealing with an advanced student was the easiest thing
| in the world and took practically no effort--a little extra
| work with a slight bit of focus and they're off and
| running. At that point, he could practically forget about
| them until they raised an interrupt.
|
| My own personal experiences in school also reflect this.
| Most of my teachers forced me to turn in "normal" homework,
| pointed me at something more advanced, and let me at it
| while occasionally checking in on me or offering advice.
| Sure, they did this so that they could get me off their
| plate to focus on someone else. But, to be fair, what they
| had me doing is also the essence of _learning_ --self-
| directed engagement with an unfamiliar knowledge base via
| intrinsic motivation.
|
| And, to be fair, if your "advanced" student can't operate
| in that regime, are they really that "advanced" after all?
| _Far_ too many parents think their children are "advanced"
| when they are merely a touch above average and really do
| fit inside the "standard" curriculum.
|
| The real problem in high school is motivating average to
| below-average students who want to be anywhere but in
| class. Video games, hanging with friends/dates, vaping/CBD,
| etc. is way more compelling than anything having to do with
| school. Getting through to those students is _difficult_
| and has very little to do with the curriculum.
|
| The biggest irony is that the same people who preach that
| there are intrinsic differences always seem to forget that
| concept when it comes time to hire and pay teachers. Funny
| that.
| jimbokun wrote:
| > The real problem in high school is motivating average
| to below-average students who want to be anywhere but in
| class.
|
| And that is the real problem for parents looking for an
| "accelerated" track at school.
|
| All they really want is a program that will challenge
| their kids and surround them with an equally motivated
| peer group that has a goal of getting into a selective
| university.
|
| That is what drives private school enrollment, selecting
| public schools in areas with high property tax revenues,
| and accelerated tracks within public schools with lower
| socio-economic status.
| TraceWoodgrains wrote:
| It comes from a real place of privilege to claim schools
| holding advanced students back never happens. To name one
| specific example with the most capable, Miraca Gross ran
| a longitudinal study with children scoring above 180 on
| IQ tests and found stark differences in motivation,
| satisfaction, and accomplishment depending on their level
| of academic acceleration[1]. (Terence Tao was "Adrian" in
| this study and was one of the models of successfully
| educating an advanced student). Kids might do something
| more with math out of sheer boredom, or they might just
| devote their energy to Pokemon instead--believe me, it's
| not just the below average students who feel the urge
| towards everything else you mention.
|
| Every student, no matter how capable, benefits
| dramatically from instruction tuned to their level and
| ability. Claiming advanced students will take care of
| themselves is an absolute failure in an instructor's duty
| of care towards them, an excuse to make the teacher feel
| better about not having the time, interest, or knowledge
| to provide proper instruction. There is no merit to the
| notion.
|
| [1] https://files.eric.ed.gov/fulltext/EJ746290.pdf
| bsder wrote:
| You are talking about a _4 sigma deviation_. Really? Your
| objection to a curriculum is that it doesn 't cater to
| the 1 in 50,000 child? A child that 90%+ of school
| districts _will never see_.
|
| Sorry. That's not even close to being a valid argument.
|
| > Every student, no matter how capable, benefits
| dramatically from instruction tuned to their level and
| ability.
|
| Oh, I agree. And the research supports it. However, when
| you tally up the bill for 2 teachers per every 10 or
| fewer students to make that happen, suddenly everybody
| starts screaming and objecting.
|
| And curriculum has no bearing on any of that.
| TraceWoodgrains wrote:
| Really, you're objecting to rarity after the emphasis you
| presented? I went with 4 sigma because you claimed truly
| gifted kids would take care of themselves. As you note,
| you can't get much more extreme than that. My point was
| to directly refute that specific claim of yours. The same
| principles absolutely apply for the one in a thousand, or
| one in a hundred, or one in twenty; they're just
| proportionately less extreme for each.
| seoaeu wrote:
| Really frustrating that these sorts of arguments usually
| devolve into making no distinction between "basically
| everyone can pass a high school math curriculum with the
| right resources and support" and "not everyone can be a
| world class mathematician". Those are both true!
| jimbokun wrote:
| That is very different than claiming different people have
| different innate abilities.
| itronitron wrote:
| > we reject ideas of natural gifts and talents
|
| That is not surprising to hear as it was written by people that
| have invested a large part of their careers in the educational
| system.
|
| _" Those who can't, teach. Those who can't teach, teach Gym."_
| guerrilla wrote:
| > is an equally-capable blank slate.
|
| It seems like tabula rasa idealism has made a serious
| resurgence in leftist and liberal circles and the scary thing
| is that nobody (other than extremists saying nonsense) is
| really talking about this explicitly. Somehow we went from a
| bunch of stuff being cultural constructs to literally
| everything is a cultural construct and then this somehow became
| extremely widespread in no time at all. We need to have this
| conversation out-loud.
| twblalock wrote:
| It's not just the assumption of a blank slate -- it's the
| assumption that because everyone is a blank slate,
| differences between people _must_ be the result of oppression
| or racism of some kind, and that the primary purpose of
| education is not to teach, but rather to fight that
| oppression.
|
| Even mathematics education is now being twisted by this --
| it's now seen as more important for math classes to pursue
| equality/equity than it is to _teach math_.
|
| One outcome of this is a levelling effect -- an equal outcome
| for all students, in which they all possess average
| mathematical skills, is preferred to a situation in which
| some students perform above average.
| ng12 wrote:
| Careful there, Harrison Bergeron.
| BitwiseFool wrote:
| Every single one of us has things we support in-public but
| don't sincerely support in-private. Most of the time this
| isn't a problem because the endorsements we make don't end up
| affecting our own personal lives.
|
| I have not met a single parent who didn't want to try and
| give their own children an advantage over the others. It is
| one thing to support "equity in education", but when parents
| sense that these activists are trying to dumb-down the
| curriculum, I expect significant pushback. Especially because
| this is quite literally a "won't somebody please think of the
| children" issue.
| bittercynic wrote:
| This seems inconsistent on the surface, but I think it is
| reasonable to want both. You can push for a more equitable
| world while recognizing that we currently live in a society
| that's pretty economically savage to some of its members,
| and it's understandable to want yourself and loved ones to
| not be the ones on the losing end of our society.
| csee wrote:
| Why would there be pushback if they can just send their
| kids to private schools and not bear the negative
| consequences? Virtue signalling is actually advantageous to
| them. If they handicap all the public school kids then
| their own kids will be more likely to get into the top
| schools that manufacture scarcity.
| BitwiseFool wrote:
| I suspect plenty of parents will begin the process of
| trying to get their kinds into a private school, but it
| still requires a lot of resources and effort. I sense
| that most parents would try to fight this while
| simultaneously trying to find a way out while the process
| goes on.
|
| As for the competitive advantage, I think that only works
| for the children who are already in the private school
| system.
| int_19h wrote:
| Sending your kids to a private school is already
| considered suspect these days in some circles. And,
| conversely, some people specifically send their children
| to public schools for ideological reasons.
| 908B64B197 wrote:
| It will also drop the average test score at public
| schools, thus getting the woke crowd to lower the
| standards again! The cycle repeats itself.
| VLM wrote:
| Virtue signaling is always elitist. Look at whom does it.
|
| So the "social disease" of virtue signaling will follow
| the higher socioeconomic crowd where ever they go.
| naasking wrote:
| > Somehow we went from a bunch of stuff being cultural
| constructs to literally everything is a cultural construct
| and then this somehow became extremely widespread in no time
| at all.
|
| The people who were critical of the first moves in this
| direction and explicitly said it would be a slippery slope
| were dismissed at the time. We're still moving in that
| direction. Hopefully the pendulum will swing back to
| something more reasonbale.
| cyber_kinetist wrote:
| > tabula rasa idealism has made a serious resurgence in
| leftist and liberal circles
|
| Maybe from liberals, but from what I've seen not the left.
| Marx's mantra is literally "From each according to his
| ability, to each according to his needs", it has nothing to
| do with liberal conceptions of tabula rasa idealism. I've
| never seen a leftist who asserts that people start from a
| blank state and can be "anyone" depending on the
| circumstances, that statement will get you accused of having
| bourgeois sensibilities who ignore the material forces of the
| world.
| guerrilla wrote:
| Well, I can't say the same as that's the majority of where
| I see it from right now. I don't follow MLs on twitter but
| most of who I follow are anarchists and democratic
| socialists.
| rendang wrote:
| Here is a noted leftist writer who is not necessarily
| arguing for the strongest case of "blank slatism" but is
| definitely pushing in that direction here, claiming that
| inherent differences are overemphasized.
|
| https://www.currentaffairs.org/2020/09/we-dont-know-our-
| pote...
| jonahx wrote:
| > and somewhat more likely to be successful basketball players.
| And some people find math easy, and are somewhat more likely to
| succeed in math.
|
| I wholeheartedly agree with your point, but there is no
| "somewhat" about it. The differences can be and often are
| stark, and we shouldn't shy away from saying that if we want an
| honest and productive conversation. It does not exclude the
| also-true fact that good education, practice, and other
| controllable environmental factors play an important role.
| throwawayboise wrote:
| Absolutely. Some people are gifted. Not everybody is,
| otherwise it wouldn't be called that. They are better than
| other people at certain things. It may be math, it may be
| athletic ability, it may be music or another artistic talent.
| We should be nurturing and developing individuals in what
| they are naturally best at, as that tends to also be what
| they like to do and probably leads to happier and more
| successful lives.
| commandlinefan wrote:
| > we shouldn't shy away from saying that if we want an honest
| and productive conversation
|
| What makes you think anybody wants an honest and productive
| conversation? One half is just trying to get the other half
| to slip up and say something - anything - they can cancel
| them for saying. The other half is just keeping their heads
| down and trying not to lose their job for heresy.
| BeetleB wrote:
| If we were to abandon a policy after the first objection we can
| raise over some disagreement we have with the policy, then all
| policies would be rejected. This is not an intelligent way to
| evaluate it.
|
| It's not whether gifted students exist - it's the extent they
| should be catered to. Society benefits more when you raise the
| average than when you foster the top 0.1%. Even Soviet
| mathematicians who moved to and taught in the US after the fall
| of the Soviet Union said something to the effect of "sucks for
| talented folks, but better for society" when they compared it
| to Soviet education.
|
| With that context, whether they exist or not is really a
| rounding error. Most gifted students will do well eventually
| whether we have special programs for them or not. And it's
| challenging to show strong net positives for society if you did
| have those programs. As in, actual data that supports having
| them, vs mere anecdotes.
| [deleted]
| freemint wrote:
| Not catering to the gifted is a dangerous game for society as
| an disproportionate amount of progress is made by gifted
| which are properly nurtured.
|
| > Gifted will do well regardless whether we have special
| programs for them or not.
|
| This is very much not true. Only gifted with rich or caring
| parents will do well. Others might suffer a lot. Being in a
| program for gifted for me made the difference between being
| thrown out of a school because I never did the homework and
| being invited and having my flights paid to a conference in
| Japan where I gave a presentation while in the last grade of
| school.
| BeetleB wrote:
| > Being in a program for gifted for me made the difference
| between being thrown out of a school because I never did
| the homework and being invited and having my flights paid
| to a conference in Japan where I gave a presentation while
| in the last grade of school.
|
| The state can provide this without believing you have a
| naturally innate ability in mathematics. They can still
| construct programs for people who are performing better in
| math.
|
| The discussion is about _innate_ talent, not whether we
| treat people who do well in math differently.
| skulk wrote:
| Have there been any studies separating "natural talents and
| gifts" from a privileged upbringing where education was
| prioritized from the moment of birth? I don't think enough
| attention is paid to what happens during the critical period of
| early child development (0-3 years of age).
|
| If it turns out that "natural talents and gifts" are really
| just due to a better critical period for the child, then the
| liberals here are really shooting themselves in the foot with
| this argument.
| crackercrews wrote:
| Check out "twin studies" for good evidence that nature plays
| a significant role, not just nurture.
| freemint wrote:
| Are you aware of Twin studies that also control for
| pregnancy? Meaning two quiet identical children are born
| and raised by mothers of different social class?
| csee wrote:
| Possibly but they're not perfect either. If the
| hypothesis is that discrimination post-birth is tied to
| innate characteristics, then presumably both twins will
| face similar discrimination and this will correlated
| their environment, even though they've never met and were
| raised by different people.
|
| That said, twin studies do provide substantial evidence
| that giftedness is highly heritable and probably
| significantly genetic.
| freemint wrote:
| I mean either you are aware of such studies or you
| aren't. What do you mean with you are possibly aware of
| such studies?
|
| I am well aware of how twin studies but any claim about
| the genetic component kinda falls apart for me based on
| them as the children were in the same pregnant mother at
| the same time.
| csee wrote:
| I meant they've possibly been done, just that I don't
| know either way.
|
| > any claim about the genetic component kinda falls apart
| for me based on them as the children were in the same
| pregnant mother at the same time.
|
| They do somewhat control for pregnancy by comparing
| identical vs fraternal twins, and finding a higher
| correlation in intelligence between the former, as well
| as a far more similar brain structure in regions known to
| be related to intelligence (frontal cortex).
|
| Anyway, it's impossible to get rid of all confounds via
| twin studies. But this doesn't mean that twin studies
| provide zero evidence. It just means the evidence can't
| be fully conclusive. It just strongly points in the
| direction of genetics.
| freemint wrote:
| While Twin studies can explain like 50% of the observed
| variance with heritability of IQ, genome wide association
| studies using Polygenic scores are only able to predict
| 5% of the variance from the genome itself when n=O(10^6).
| The truth is most likely somewhere between those two.
|
| Predicting IQ from genetic information alone should
| remove all the of compounding factors (except those
| introduced by IQ measurement itself) but can only serve
| as a lower bound unless predictor overfitted the study
| data.
| csee wrote:
| Where did you get 50%? Wikipedia says "Early twin studies
| [show] 57% and 73%, with the most recent studies
| [showing] 80%."[1] > The truth is most
| likely somewhere between those two. > but can
| only serve as a lower bound unless predictor overfitted
| the study data.
|
| Yes, but the truth is likely somewhere much closer to the
| upper bound (twin studies) than the lower bound (genome
| studies).
|
| Genome studies are only good for lower bounds. They're a
| new methodology that isn't good with complex traits. For
| example, they can only explain 20-30% of the variability
| in hair color even though we know that hair color is
| almost 100% genetic due to the observation that identical
| twins always have the same hair color. Intelligence is
| much more complex than hair color, so it's no surprise
| that this method has failed to explain more than 5%.
| Further, these studies often rely on weak proxies like
| educational attainment because of the difficulty of IQ
| testing at scale, and the studies that do try to IQ test
| at scale suffer from small sample sizes which impacts the
| ability to find results due to being underpowered.
|
| Also, IQ becomes more correlated with parents as you age,
| suggesting childhood environment plays a less important
| role.
|
| In addition, the jump in correlation from fraternal to
| identical suggests more role for genetics than merely a
| few %.
|
| [1] https://en.wikipedia.org/wiki/Heritability_of_IQ
| jimbokun wrote:
| Yes, I remember reading about "separated at birth" twin
| studies, too lazy to look it up right now.
|
| But I remember they found a surprising amount of
| similarities in twins brought up in different
| environments.
| bgorman wrote:
| Do you really believe that Jacobi, Euler, Gauss and Ramanujan
| were just beneficiaries of privileged upbringing?
| noahtallen wrote:
| Perhaps not, but the purpose of the public school system is
| not to turn out a couple of geniuses every year. It's to
| maintain a well-educated populace. Most resources should be
| going towards making the average student better. I can't
| tell you how many people have told me that I must be very
| smart for going into computer science, and that they could
| never do it because they're just not math/stem people. That
| negative self-talk certainly has a huge amount to do with
| whether they're capable of going into STEM.
|
| To me, it seems these changes are oriented towards helping
| everyone succeed in STEM, even those who don't think
| they're math people. Which, again, is less to do with their
| actual abilities and much more to do with their mental
| dialogue.
|
| This makes a ton of sense. Basically any skill or habit you
| might want to develop can be easily thwarted if you're
| struggling mentally with discipline, focus, self-image,
| etc. In my opinion, the "mental game" is crucial to nearly
| everything and doesn't get enough focus. (Think of how in
| sports, a bad mental game can easily loose you the physical
| game even if you're an incredible athlete.)
|
| I doubt these educational changes would ever have much of
| an impact on bonafide geniuses, because they are operating
| in an entirely different context.
| jimbokun wrote:
| > Perhaps not, but the purpose of the public school
| system is not to turn out a couple of geniuses every
| year. It's to maintain a well-educated populace.
|
| It should be both.
| naasking wrote:
| Even if it can't be both, a few geniuses could very well
| outweigh the benefits of a slightly more well-educated
| populace. Einstein arguably gave us GPS and space flight.
| I'm not sure any amount of average-person level
| mathematics could make some advances like that.
| BeetleB wrote:
| Do you really believe they would have benefited that much
| from "advanced" classes in high school?
| csee wrote:
| That has nothing to do with the question of whether
| there's such a thing as natural ability.
| BeetleB wrote:
| The wider discussion is about how to structure public
| math education. If we're not going to connect it to the
| details of said education, then it is a moot point to
| discuss.
|
| Of all the things to evaluate the policy on, this is a
| real poor proxy as whether there are gifted people or not
| usually has little bearing on the overall health of math
| education across a very highly populated state.
|
| I never disagreed with whether they exist or not. I just
| don't see why this is such a sore point for people. I can
| virtually guarantee that the existing education system in
| CA didn't really benefit the gifted folks either. If I
| were setting up the program for a whole state, whether it
| will be good for a Jacobi/Euler/Gauss is totally
| irrelevant. We're not going to make people who show up
| once every 50-100 years be a major factor in educating
| millions of people.
| crackercrews wrote:
| This is a straw man. My original point (root level
| comment) was that the authors of this plan do not believe
| there are any innate differences in math ability, full
| stop. A reply to my comment supported my position by
| showing that obviously there are examples of people who
| are extreme outliers in terms of math ability. This
| proves the point that there are differences in innate
| math ability.
|
| Your reply is that we shouldn't design a state-wide math
| program for extreme outliers. But no one said we should!
| We only said that we should design a math program that
| acknowledges a diversity in innate math ability (as
| proven by the existence of extreme outliers, and the
| many, many less extreme outliers).
| markus_zhang wrote:
| It's actually a lot better if they reject ideas of natural
| gifts and talents but at the same time admit that a lot of
| those "gifts" are given post-birth by childhood education. In
| that case we might miss a few natural gifted children but could
| raise alertness to family education (that schools simply cannot
| substitute).
| nouveaux wrote:
| How about the difference between boys and girls?
|
| "It must be nice to think about a world in which every boy and
| girl is an equally-capable blank slate. But we do not live in
| that world. We live in a world where some people are tall, and
| somewhat more likely to be successful basketball players. And
| boys find math easy, and are somewhat more likely to succeed in
| math.
|
| When you start out with flawed assumptions, it's not surprising
| when your prescriptions (no advanced math for anyone!) are
| foolish and counterproductive."
|
| This is what society used to believe. How was that productive
| and wise?
| naasking wrote:
| I must have missed the part where girls were not expected to
| do just as well as the boys if they wanted to advance, and if
| they didn't perform as well, then we just changed the
| criteria for what constitutes success so the gender outcomes
| were equal. Women proved they were just as capable, arguably
| even more capable in many subjects, so we obviously do live
| in that world where the genders are equal in this sense.
| [deleted]
| dzdt wrote:
| Here is the full context. Our current media environment
| includes a lot of cherry-picking to provoke outrage. Better to
| judge from a more complete text:
|
| Learning Mathematics: for All
|
| Introduction
|
| Students learn best when they are actively engaged in
| questioning, struggling, problem solving, reasoning,
| communicating, making connections, and explaining. The research
| is overwhelmingly clear that powerful mathematics classrooms
| thrive when students feel a sense of agency (a willingness to
| engage in the discipline, based in a belief in progress through
| engagement) and an understanding that the intellectual
| authority in mathematics rests in mathematical reasoning itself
| (in other words, that mathematics makes sense) (Boaler, 2019 a,
| b; Boaler, Cordero & Dieckmann, 2019; Anderson, Boaler &
| Dieckmann, 2018; Schoenfeld, 2014). These factors support
| students as they develop their own identities as powerful
| mathematics learners and users. Further, active-learning
| experiences enable students to engage in a full range of
| mathematical activities--exploring, noticing, questioning,
| solving, justifying, explaining, representing and analyzing--
| making clear that mathematics represents far more than
| calculating.
|
| Research is also clear that all students are capable of
| becoming powerful mathematics learners and users (Boaler,
| 2019a, c). This notion runs counter to many students' ideas
| about school mathematics. Most adults can recall times when
| they received messages during their school or college years
| that they were not cut out for mathematics-based fields. The
| race-, class-, and gender-based differences in those who pursue
| more advanced mathematics make it clear that messages students
| receive about who belongs in mathematics are biased along
| racial, socioeconomic status, language, and gender lines, a
| fact that has led to considerable inequities in mathematics.
|
| In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues
| interviewed university professors in different subject areas to
| gauge student perceptions of educational "gifts"--the concept
| that people need a special ability to be successful in a
| particular field. The results were staggering; the more
| prevalent the idea, in any academic field, the fewer women and
| people of color participating in that field. This outcome held
| across all thirty subjects in the study. More mathematics
| professors believed that students needed a gift than any other
| professor of STEAM content. The study highlights the subtle
| ways that students are dissuaded from continuing in mathematics
| and underscores the important role mathematics teachers play in
| communicating messages that mathematics success is only
| achievable for select students. This pervasive belief more
| often influences women and people of color to conclude they
| will not find success in classes or studies that rely on
| knowledge of mathematics.
|
| Negative messages, either explicit ("I think you'd be happier
| if you didn't take that hard mathematics class") or implicit
| ("I'm just not a math person"), both imply that only some
| people can succeed. Perceptions can also be personal ("Math
| just doesn't seem to be your strength") or general ("This test
| isn't showing me that these students have what it takes in
| math." My other class aced this test."). And they can also be
| linked to labels ("low kids," "bubble kids," "slow kids") that
| lead to a differentiated and unjust mathematics education for
| students. A fundamental aim of this framework is to respond
| issues of inequity in mathematics learning; equity influences
| all aspects of this document. Some overarching principles that
| guide work towards equity in mathematics include the following:
|
| Access to an engaging and humanizing education--a socio-
| cultural, human endeavor--is a universal right, central among
| civil rights.
|
| All students deserve powerful mathematics; we reject ideas of
| natural gifts and talents (Cimpian et al, 2015; Boaler, 2019)
| and the "cult of the genius" (Ellenberg, 2015).
|
| The belief that "I treat everyone the same" is insufficient:
| Active efforts in mathematics teaching are required in order to
| counter the cultural forces that have led to and continue to
| perpetuate current inequities (Langer-Osuna, 2011).
|
| Student engagement must be a design goal of mathematics
| curriculum design, co-equal with content goals.
|
| Mathematics pathways must open mathematics to all students,
| eliminating option-limiting tracking.
|
| Students' cultural backgrounds, experiences, and language are
| resources for learning mathematics (Gonzalez, Moll, & Amanti,
| 2006; Turner & Celedon-Pattichis, 2011; Moschkovich, 2013).
|
| All students, regardless of background, language of origin,
| differences, or foundational knowledge are capable and
| deserving of depth of understanding and engagement in rich
| mathematics tasks.
|
| [1]
| https://www.cde.ca.gov/ci/ma/cf/documents/mathfwchapter1.doc...
| jimbokun wrote:
| > All students deserve powerful mathematics; we reject ideas
| of natural gifts and talents (Cimpian et al, 2015; Boaler,
| 2019) and the "cult of the genius" (Ellenberg, 2015).
|
| could be replaced with:
|
| > All students deserve powerful mathematics.
|
| and still make the same pedagogical point, that all students
| should be taught with the expectation they will succeed at
| learning mathematical concepts.
|
| Putting the emphasis on believing people do not differ in
| natural ability, is obviously false and therefor detracts
| from the overall goal.
| gorwell wrote:
| Read Chapter 2: Teaching for Equity and Engagement
|
| https://www.cde.ca.gov/ci/ma/cf/documents/mathfwchapter2.doc...
|
| Why are they integrating and layering the religion of social
| justice and gender ideology onto math? I would be just as alarmed
| if Christianity or any other religion or dogma or ideology was
| embedded with math and how it's taught. This document is pushing
| evangelical-level indoctrination and is certainly less about
| teaching math than our current system. At the very least it's
| orthogonal to learning how to add and subtract.
|
| "Teach Toward Social Justice"
|
| "Teachers can take a justice-oriented perspective at any grade
| level, K-12"
|
| "teachers need to work consciously to counter racialized or
| gendered ideas"
|
| "Students are able to take what they noticed and named - in this
| case, how gender played out in the problem"
|
| "Learning is not just a matter of gaining new knowledge--it is
| also about a change in identity. As teachers introduce
| mathematics to students, they are helping them shape their
| identity as people"
| lacrosse_tannin wrote:
| what does this have to do with the article?
| kristjansson wrote:
| There's a critical distinction to your complaint - the linked
| doc addresses how one teaches math, not the math one teaches.
| It's not unreasonable to suggest that curricula authors maybe
| choose not to make all the $PREDOMINATELY_MALE_OCCUPATION
| characters in their word problems males etc. etc. Using the
| 'defaults' in construction of narrative problems and lessons is
| itself a choice, so why not take the one that tends toward
| equity, equality, and inclusion?
|
| The subsequent exercise suggesting a close reading of the
| gender roles in said word problems ... doesn't seem to have a
| lot to do with learning math, I'll grant.
| gorwell wrote:
| They could handle that by providing a simple solution:
| Randomize names.
|
| This isn't about avoiding stereotypes though. This is about
| pushing a belief system and an agenda. A dangerously
| misguided one at that. Equity is about equal outcomes. Which
| you can only get through force because people have different
| preferences, different abilities and make different choices.
| Choices necessarily lead to different outcomes.
|
| Equality and equality of opportunity, yes, please. Equity,
| absolutely not.
| pas wrote:
| Because now it's the idea of the times and it's making its way
| into various spheres of life.
|
| Do we have data that it helps/worsens?
| deltarholamda wrote:
| >Do we have data that it helps/worsens
|
| We've been playing games with education in the US for a while
| now. This identity stuff is the newest, but you can go back
| every decade or so for some 60 years and find some fad that
| was really big at the time.
|
| Now look at the test scores over time. Up? Down? Flat? Break
| it out into race, socioeconomic class, religion, however you
| want. Check again. Up? Down? Flat?
|
| We pretty well know how to teach things like math. It's a lot
| of drills. It's a lot of homework. It's word problems. It's
| all the things that both teachers and students hate, because
| it's annoying to do and annoying to check. But math is more
| or less like learning a language. You have to immerse
| yourself in it and do a lot of practice.
|
| And, in the end, you have to accept that some people are just
| not going to cut it. They will top out at about 8th grade
| basic Algebra. And that's okay! Cramming some kid who can't
| cut Calculus into a Calculus class just because you need to
| count a certain number of different colored noses is daft and
| unproductive. School should educate people to their maximum
| ability, and everybody's maximum ability is different.
|
| It doesn't matter if it makes you feel better to attribute
| somebody's poor performance to some vaporous societal ill.
| That's not helping. That's trying to shoehorn your preferred
| reality into actual reality. The hell of it is that it
| completely shafts those who really did earn their way into
| the top ranks. There is always the spectre that they're there
| because some administrator needed enough $IDENTITY to make
| their Powerpoint presentation look good.
| a9h74j wrote:
| FWIW, a few years ago I read an article with short
| discussions of "100 Good Ideas in Education." The article
| was written by a well-qualified educational journalist.
| Again, FWIW, I'd estimate that at least 10% of the
| discussions essentially concluded with: But we can't do
| this because it would increase disparities.
| joshuamorton wrote:
| What among these is "indoctrination"?
|
| > "teachers need to work consciously to counter racialized or
| gendered ideas"
|
| Is this wrong? Is it indoctrination?
|
| > "Are there word problems that challenge gender stereotypes?"
|
| I don't see the issue here. Should all word problems reflect
| 1920s America and ask about the challenges with the dust bowl
| harvest and how many bathroom stalls you need to serve a
| particular crowd, accounting for segregation? No that's silly.
| We want word problems to reflect the world we live in today,
| which means sometimes having physician Alice and nurse Bob.
|
| > "Learning is not just a matter of gaining new knowledge--it
| is also about a change in identity. As teachers introduce
| mathematics to students, they are helping them shape their
| identity as people"
|
| There's _lots_ of discussion about how women especially, but
| also lots of minorities, seem to leave STEM after primary
| school. To me, this seems to be reminding educators that they
| should make an effort to keep these classes engaging and
| inviting for people who leave, in case the cause has
| historically been something in how we do math education.
|
| > "Students are able to take what they noticed and named - in
| this case, how gender played out in the problem"
|
| This is talking about teaching critical analysis (in the "how
| do I analyze a text" sense, not the "race theory" sense), where
| the teacher uses a math word problem as one of a number of
| places to do this. There's nothing wrong with this, in fact its
| actually really good to read critically in all contexts!
| ryan93 wrote:
| According to Joshua Morton black kids have low math test
| scores because 2021 schools use segregated bathrooms in math
| word problems.
| cortesoft wrote:
| > layering the religion of social justice
|
| You can argue the best technique to accomplish the goal, but
| `social justice` just means that you believe every person
| deserves an equal opportunity to thrive. That is not a
| religion, that is the American dream.
|
| Social Justice is simply the idea that we actually need to work
| towards providing the American Dream to everyone. That
| shouldn't be controversial.
| BitwiseFool wrote:
| From my perspective, the term "Social Justice" is more of a
| rhetorical tool than a cohesive ideology. Yes, I know I can
| google "define social justice" but if you look at the results
| there is no agreed definition. You will instead see dozens of
| different think-thanks, universities, and NGOs 'define'
| social justice use very flowery feel-good language that is
| almost impossible to disagree with. And yet, the details
| about how to achieve such positive things _are_ what people
| would actually disagree with.
|
| Your statement "That shouldn't be controversial" encapsulates
| this perfectly.
| jimbokun wrote:
| The article pointed out that:
|
| > ...the National Society of Black Engineers (NSBE), which
| set in 2015 a goal to double the number of African American
| students taking calculus by 2025.
|
| Which would be a step towards improving educational
| opportunities for everyone.
|
| The new California standards are arguably going in the
| opposite direction.
|
| I find this to be a trend, that many pushes for "equity" in
| education seeks to achieve this by reducing the success of
| high achieving groups to match that of the low achieving
| groups, instead of figuring out how to get the low achieving
| groups to the level of the high achievers.
| [deleted]
| twofornone wrote:
| >`social justice` just means that you believe every person
| deserves an equal opportunity to thrive. That is not a
| religion, that is the American dream
|
| No. That is the surface level definition which insidiously
| hides the conflation between opportunity and equity that
| underlies the politicized restructuring of our institutions.
| Equality of outcome is only possible by hindering high
| achievers.
|
| In part it is the purely faith based belief in the tenet of
| tabula rasa that makes this movement resemble a religion.
| There is no quality science which suggests that all people
| are equally capable given identical environments; in fact
| such an assertion would completely deny the realities of
| genetics and culture.
| kardianos wrote:
| a. That isn't "simply" what Social Justice is. Not by a long
| shot, not in practice.
|
| b. It sounds like you are arguing for Equality based on
| merit, allowing each person a chance to thrive. I agree, that
| would be great. But what is actually happening is different:
| equity, where in practice most implementations stunt growth
| and paper over achievement gaps.
|
| c. I want a equal opportunity to thrive. But "social justice"
| is also extra-judicial justice. It sounds nice, but isn't
| waht I want.
|
| See also "motte and bailey".
| dwater wrote:
| When I searched for the definition of indoctrination I get
| this:
|
| "The process of teaching a person or group to accept a set of
| beliefs uncritically."
|
| What I see in your examples does sound like teaching a set of
| beliefs, but there is nothing that I see where it is done
| uncritically. For example, there are stereotypes in our society
| about what genders and races are good at STEM and which are
| not. If a word problem reverses those stereotypes, do you think
| that encourages or discourages the reader to think critically
| about their own biases?
| TeeMassive wrote:
| > but there is nothing that I see where it is done
| uncritically
|
| And you yet you immediately say:
|
| > there are stereotypes in our society about what genders and
| races are good at STEM and which are not
|
| Your post is a good example for why it is very difficult to
| make any critique of the DIE "teachings" in a public /
| classroom setting. DIE only makes sense if front of a mob.
|
| If you disagree, you are against the DIE (diversity,
| inclusion and equity) virtuous teachings. Unlike other
| theoretical fields, to understand is to agree with DIE and
| its apparent virtues.
|
| And DIE should stay away from any serious academic setting,
| especially young students, because it's a widely discredited
| field: https://areomagazine.com/2018/10/02/academic-
| grievance-studi...
| loeg wrote:
| > DIE
|
| Usually spelled DEI, for the obvious reason that "dei"
| isn't an English word meaning death.
| TeeMassive wrote:
| Dei also means God in some context, so who cares.
| gorwell wrote:
| That's also about not calling attention to its cult-like
| characteristics. DIE is a little too on the nose for a
| group that demands conformity and unpersons those that
| dissent.
| autokad wrote:
| there is nothing one would see where the teacher is doing it
| critically either. you just assumed they were because it fits
| your worldview. "yes, I believe this so children should be
| brainwashed at an early age to push the agenda that suits me"
|
| This is childhood rape. Those teachers are in a position of
| power and students are rewarded for believing what ever the
| teachers say as the truth. This is wrong.
| Manuel_D wrote:
| It's hard to say whether the teaching is uncritical without
| actually being present in the classroom. If to "counter
| racialized or gendered ideas" is implemented by insisting
| anything other than 50/50 representation across all
| occupations is evidence of discrimination and that any
| suggestion to the contrary is sexism, then yeah that's
| definitely uncritical. I'm not sure how prevalent those kind
| of simplistic teachings are, but they do exist.
| pishpash wrote:
| I would suggest this not be done in math class, lest you go
| down this path [1]:
|
| "Before the Great Proletarian Cultural Revolution there were
| 48 students in class one in Qunli Elementary: During the six
| years of obliteration by revisionism on the educational
| system, 13 students dropped out. All 13 students were from
| the worker or poor peasant families. Compute how many
| students from the worker or poor peasant families dropped out
| and how many were retained due to the obliteration by
| revisionism?"
|
| [1] https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1
| .98...
| AlanYx wrote:
| Wow -- your example is real (page 12). Thanks for that
| fascinating article.
| loeg wrote:
| > "The process of teaching a person or group to accept a set
| of beliefs uncritically."
|
| > there is nothing that I see where it is done uncritically.
|
| I mean, how is it going for those criticizing CRT-ification
| of education? It doesn't seem like its advocates are actually
| interested in criticism of the dogma.
| asoneth wrote:
| > how is it going for those criticizing CRT-ification of
| education?
|
| From what I can tell in our local area it seems to be going
| about as well as they hoped.
|
| First they rail against about some weird graduate-level
| field most people have never heard of that isn't related to
| anything taught in our elementary schools. Then they
| interpret the eyerolls from the other parents and patient
| administrators attempting to keep the conversation focused
| on relevant topics as attacks on their freedom and they get
| to play the martyr.
| [deleted]
| [deleted]
| whymauri wrote:
| >"Learning is not just a matter of gaining new knowledge--it is
| also about a change in identity. As teachers introduce
| mathematics to students, they are helping them shape their
| identity as people"
|
| I don't get it... what about this is so scary to you? Is it the
| word 'identity'? Because as a standalone statement, I actually
| think this is a healthy approach to education.
|
| I get that "social justice" and apparently now "justice" are
| loaded terms in our modern political discourse, but countering
| racialized ideas and framing education as a part of our
| identity as people/citizens... I mean, that hardly seems like
| objectionable to me.
| jimbokun wrote:
| It's meaningless pablum taking away class time from actually
| teaching mathematics to promote political ideology.
|
| What does it mean that learning mathematics changes your
| "identity"? You are still the same person you were before,
| but now you know some math and can do and can understand some
| things you couldn't before.
| cscurmudgeon wrote:
| Please explain how objectivity in Math is white supremacy:
|
| From: https://equitablemath.org/wp-
| content/uploads/sites/2/2020/11...
|
| > As a visual indicator, we italicize the terms used to
| identify white supremacy characteristics as defined by Jones
| and Okun (2001). They are as follows: * Perfectionism * Sense
| of Urgency * Defensiveness * Quantity Over Quality * Worship
| of the Written Word * Paternalism * Either/Or Thinking *
| Power Hoarding * Fear of Open Conflict * Individualism * Only
| One Right Way * Progress is Bigger, More * Objectivity *
| Right to Comfort
| krastanov wrote:
| Come on, this is such a willfully ignorant reading of this
| text. Check the FAQs, interviews with the authors, or
| simply the rest of this very document. Sure, it could have
| been written better in order to not trigger and scare
| people, but the meaning is pretty trivial if you read it
| without being primed, especially in the context of all the
| other words around it.
|
| First, they are listing words cited in an academic study,
| to set up the language used for the rest of the document.
| Claiming they are saying "objectivity in math is white
| surpremacy" is like saying "critical race theory is taught
| in high school".
|
| Second, the overall message is that "roteness" is a bad way
| to teach. Sure, they link it to how "my way or the high
| way" authoritarianism is linked to how the downtrodden have
| been treated in America and make a parallel between that
| and rote memorization style of teaching. How is that
| unreasonable in a document talking about the experience of
| black people in highschool?
| cscurmudgeon wrote:
| > Come on, this is such a willfully ignorant reading of
| this text.
|
| Maybe you are the willfully ignorant one here?
|
| I understand roteness is bad. But please explain:
|
| 1. How roteness is linked to white supremacy.
|
| 2. How objectivity is linked to roteness. They are not
| related at all. You can be objective and creative. E.g.,
| Ramanujan.
|
| 3. Asians are well known for rote learning. I am Indian.
| I know how rote it can get and I agree it is bad. But
| stop conflating that with objectivity.
|
| 4. > Claiming they are saying "objectivity in math is
| white surpremacy" is like saying "critical race theory is
| taught in high school".
|
| Did you read the document? That is exactly what they say
| and imply in multiple places. Roteness is different from
| objectivity. You are defending a straw man. Words have
| meanings. If they mean't roteness, use that.
| robotbikes wrote:
| If you look at the source of these terms they aren't as
| inflammatory and include a number of antidotes to how these
| can manifest in organizations -
| https://www.thc.texas.gov/public/upload/preserve/
| museums/files/White_Supremacy_Culture.pdf
|
| I would personally say that this is sort of a manifestation
| of hierarchicalism which can be predominantly connected to
| white people in the United States but really transcends the
| racial dynamics and instead focus on accepting and
| promoting social structures that make those who have power
| over others feel like their power is justified and that
| those who question it or don't accept it are wrong.
|
| For instance here is how they define paternalism:
|
| decision-making is clear to those with power and unclear to
| those without it
|
| * those with power think they are capable of making
| decisions for and in the interests of those without power
|
| * those with power often don't think it is important or
| necessary to understand the viewpoint or experience of
| those for whom they are making decisions * those without
| power understand they do not have it and understand who
| does
|
| * those without power do not really know how decisions get
| made and who makes what decisions, and yet they are
| completely familiar with the impact of those decisions on
| them
|
| Here they present some antidotes:
|
| make sure that everyone knows and understands who makes
| what decisions in the organization;
|
| make sure everyone knows and understands their level of
| responsibility and authority in the organization; include
| people who are affected by decisions in the decision-making
|
| Is this directly related math, not necessarily and should
| it be tied exclusively to white supremacy culture, I would
| argue no but it can certainly be the case that the
| corporate culture of our hierarchical society has a lot of
| these problems. I just wouldn't lump it under a racial lens
| because I feel like that misses the mark.
|
| I also agree that the short list included is sort of a
| disservice/reductionist as it doesn't explain how these are
| problems or how they can be overcame whereas the source
| document at least provides context and explanation.
| jimbokun wrote:
| > I would personally say that this is sort of a
| manifestation of hierarchicalism which can be
| predominantly connected to white people in the United
| States
|
| I find this an absurd and utterly indefensible statement.
|
| You cannot find any examples of "hierarchicalism" outside
| of white people in the United States? Seriously?
|
| You put the weasel word "predominantly" in there, but I
| think most human civilizations through out history have
| featured these kinds of dynamics.
| TeeMassive wrote:
| Identity has nothing with math.
| seoaeu wrote:
| There's plenty of people who consider "bad at math" to be
| part of their identity. I think HN of all places would
| recognize that's a bad thing
| astrange wrote:
| https://en.wikipedia.org/wiki/Identity_function
| whymauri wrote:
| It's not that identity defines math from a correctness
| point-of-view, it's that math can become a part of and
| enrich your identity. Countered with the perspective that
| math is a chore or 'useless', this instead posits that you
| can make education a part of your identity.
|
| And what is academic passion if not a combination of
| identity, desire, and education? I think it's a nice
| framing, one that engage students more than 'you will learn
| math because we say you must learn math.' One that ensures
| teachers are aware of their role in shaping the identity of
| students.
|
| If you trace back the history of math, it's not uncommon to
| make math a passion, a part of your identity (think of the
| Pythagoreans, for a historical example). When you become a
| mathematician, is math not then a part of your identity?
| That's what I interpret from:
|
| >As teachers introduce mathematics to students, they are
| helping them shape their identity as people.
|
| So the idea is to have teachers be aware of the impact of
| math and education on people's identity. It is a
| consciousness thing.
| TeeMassive wrote:
| Everything we do is part of our "identity". That doesn't
| really bring anything new to the conversation.
|
| Math deal with concepts, forms and quantities and their
| relationships and their abstractions, not personal
| identity. There are more proper academic fields for this
| (such as language and art), although it doesn't remove
| the fact that DIE is a discredited field and should be
| done away with anyway.
| jimbokun wrote:
| Why is making math a part of your "identity" preferable
| to seeing math as a tool you can apply to accomplish your
| goals, or something you can do for fun?
|
| The vast majority of high school math students will not
| become mathematicians.
| whymauri wrote:
| >So the idea is to have teachers be aware of the impact
| of math and education on people's identity. It is a
| consciousness thing.
|
| It's not a question of preferability (one view is not
| mutually exclusive of the other), and I didn't claim high
| schoolers should all become mathematicians (where did
| that come from?). In either case, I fail to see how
| training instructors to be aware of their teachings'
| effect on identity can be harmful. I'm not particularly
| scared nor threatened by the idea of it, and the idea
| that there's no connection between education and identity
| doesn't make sense to me.
|
| That's all I have to say.
| lapetitejort wrote:
| Culture and identity have always been present in math.
| Starting words problems with "Bob makes $50,000 a year" or
| "Alice needs 10 onions from the store" helps frame men as
| workers and women as home-makers. Taken by themselves they're
| fairly innocuous. Combined with every other social signal
| children hear every day, they can perpetuate out of date and
| harmful stereotypes.
| danachow wrote:
| Lord jesus what a strawman. You have any good evidence that
| math word problems in elementary ed are systematically
| biased in this way - and the plural of anecdote is not
| data, so don't waste our time.
| commandlinefan wrote:
| They were working overtime _not_ to allow any of this
| into the curriculum even when I was in elementary school
| back in the 80 's. Usually it was worthy of an eyeroll
| from all of us: "John and his friends Jamal, Carlos and
| Akira are on the bus..."
| jimbokun wrote:
| So write a script to randomize the names in the textbook
| and be done with it.
| Out_of_Characte wrote:
| My experience with those story driven math problems is that
| dyslexic people fail them despite doing well on pure math.
| freemint wrote:
| Yet being able to map real world problems into math
| problems and solve them is an essential skill. In my
| class in Europe story driven problems were read aloud.
| syspec wrote:
| So randomize the names, problem solved without getting rid
| of word problems.
|
| Word problems are pain in the butt, but they teach the
| skill of converting an abstract problem math symbols which
| can be solved
| BitwiseFool wrote:
| "Starting words problems with "Bob makes $50,000 a year" or
| "Alice needs 10 onions from the store" helps frame men as
| workers and women as home-makers."
|
| This is one of those statements where part of your brain
| goes "well, I guess there might be atom-sized kernel of
| truth to this". But in reality, I doubt anyone is tangibly
| affected by the congruent use of Male/Female names in word
| problems that map to traditional Male/Female gender roles.
| I believe this is a result of a hypersensitive social-
| justice filter which results in an astonishingly large
| false-positive rate.
|
| Quite frankly, I just fail to see how gendered language in
| word problems not only 1) reflects math being inherently
| cultured and identity-based, 2) harmfully reinforces
| malicious stereotypes (people can just as easily write
| Alice makes $50,000 a year, Bob needs 10 onions from the
| store), and 3) are odious enough to justify a substantial,
| near fundamental, change in math education.
| lstodd wrote:
| The whole of your reply is scary.
|
| I guess it's just I think that the pursuit of knowledge shall
| have nothing to do with any one 'identity' or 'ideology'. It
| is orthogonal to that, or it just doesn't work and then why
| teach something that does not work.
| tokai wrote:
| It sounds much in line with the notion of bildung. It's a
| key concept in teaching and pedagogical theory.
| seoaeu wrote:
| So surely you're on board with fighting any racism or
| sexism in the classroom, right? Specifically that any
| "racialized or gendered ideas" have no place in a math
| class, and that "teachers need to work consciously to
| counter" them if they do come up? In other words, exactly
| what the the original report said to do...
| hnaccount141 wrote:
| I don't think the person you're replying to is saying that
| the pursuit of knowledge has anything to do with any one
| identity, they're simply saying that the pursuit of
| knowledge inherently changes the way we conceive of
| ourselves, which seems pretty universal.
| robotbikes wrote:
| I think your interpretation of the word identity in this
| case is wrapped up in political discourse. Encouraging
| students to identify as an educated people for whom
| pursuing knowledge is both important and desirable seems
| like a net positive goal. Understanding that there are
| cultural and psychological hurdles that can stand in the
| way of this when people don't see themselves as math people
| is part of solving the problem.
|
| I can also agree that it is very difficult to do and learn
| Calculus when your understanding of Algebra is limited or
| out of practice as someone who went back to get an
| undergraduate degree after almost 2 decades of not doing
| math. Is Calculus actually essential for critical thinking
| ? No and it does serve as a stand-in for this in many STEM
| degrees and if someone is lacking in understanding of the
| basic principles of algebra then it is going to feel like
| torture to solve calculus problems even if you can
| understand the concepts.
| SpicyLemonZest wrote:
| It's this metastasized concept of identity that scares
| me. The traditional response to "I'm not a math person"
| was to reassure students that, hey, you don't have to be
| a math person to learn and get value from math. (This is
| where culturally responsive education was understood to
| come in - it helps students realize that math is useful
| for them no matter who they are and where they come
| from.)
|
| Now the conventional wisdom seems to be that you _do_
| have to be a math person, and teachers had better work
| hard on cultivating a "math person" identity, because
| otherwise there's no way their students can learn math. I
| think this is a false belief that will make education
| quite a bit worse if acted on. I would never have learned
| to write well if teachers told me I needed to identify as
| a writer first!
| glerk wrote:
| Because the adults in the room are too afraid to speak up.
| seoaeu wrote:
| Ah yes, the "silent majority" that won't stop screeching
| about any social change
| mizzack wrote:
| That's because those adults don't want an EDUOFFICIALS flag
| on their FBI file.
| octernion wrote:
| Because social justice and gender ideology are universal,
| important concepts that apply in mathematics and science as
| well?
|
| I fail to see how it is "clearly" indoctrination as it is
| taught critically (as is well evidenced in the link) unless you
| are some sort of "anti-SJW warrior" against any sort of
| modernization of our curriculum.
| jimbokun wrote:
| > Because social justice and gender ideology are universal,
| important concepts that apply in mathematics and science as
| well?
|
| Then you are doing mathematics and science wrong.
|
| The whole point of those disciplines is to eliminate human
| bias in favor of objectivity in order to accurately
| understand the world, or to make correct conclusions or
| predictions based on axioms, observations, and data.
|
| If you introduce biases like gender ideology into those
| subjects, you are defeating the purpose.
| octernion wrote:
| The whole point is to remove biases -- did you even read
| any of the source material?
|
| Right now there is tremendous societal pressure and varying
| outcomes depending on _who_ you are (race/gender/other
| socioeconomic factors) and the entire point is to remove
| that from the equation to lead to better outcomes overall.
|
| To do that, you need to be aware of those factors and
| control for them. That is very basic science.
|
| You seem to be advocating putting ones head in the sand and
| saying that those factors don't matter and should be
| removed.
| itronitron wrote:
| Why do educators always fail to effectively communicate with a
| non-captive audience?
|
| The author needs to re-work this so that the first paragraph
| tells me everything that I need to know, and the rest of the
| essay/letter/memo can elaborate on things that I should or might
| want to know.
|
| If they aren't willing to do that then they are going to continue
| to remain out of touch to most people.
| bstockton wrote:
| I'm confused, what is the proposed framework supposed to fix, or
| how is it better? Is the goal really to reduce achievement gaps
| by limiting the advancement of top students? Surely, that can't
| be the goal...that's crazy. Furthermore, that has the possibility
| to exacerbate the problem by forcing advanced students to augment
| their math education in the private sector, something only
| available to wealthier families.
|
| Also, the shifted emphasis on data science stuff is a joke. The
| very courses they're talking about minimizing are the building
| blocks of data science and there's no shortcut.
| didibus wrote:
| Not sure, from other comments I gather the goal is to de-
| emphasize the idea that you need to be gifted to be good at
| math, which studies apparently have shown that this idea tend
| to discourage other students, often girls or racially
| disadvantaged boys, which do have the ability to succeed at
| math, to pursue math or be interested in it.
|
| I don't think anything is changing for truly gifted students,
| they should still have the ability to be fast-tracked or
| options to take more advanced topics. It seems more that it's
| about focusing on students who don't see themselves as gifted
| or who aren't yet showing signs of it.
| TraceWoodgrains wrote:
| This is incorrect. Their explicit goal is to remove fast
| tracking and options to take more advanced topics for gifted
| students. The vision is for uniformly paced classes for all
| same-aged students.
| tzs wrote:
| Some interesting stats from ed.gov [1].
|
| Only 59% of schools offer algebra in 8th grade.
|
| There's a map showing percent of schools with 8th grade algebra
| by district. There's another map farther down shown percent of
| 8th graders who took it by school district. (The maps can be slow
| to load).
|
| Overall 80% of students have access to algebra I in 8th grade.
| Breaking that down by type of school it is 88% in magnet schools,
| 81% in traditional schools, 60% in charter schools.
|
| It is 86% in suburban schools, 75% in urban schools, 75% in rural
| schools, and 76% in town schools.
|
| That is access. Enrollment is another matter. 24% of 8th graders
| actually take it. By gender that is 25% of the females and 22% of
| the males. By race 34% of the Asians, 24% of the Whites, 23% of
| the two-or-more race students, 14% of Pacific Islanders, 13% of
| the Hispanics, 13% of the Natives, and 12% of the Blacks.
|
| [1] https://www2.ed.gov/datastory/stem/algebra/index.html
| ec109685 wrote:
| I don't understand why there is so much effort put onto cramming
| math into high school. I took calculus in high school and then
| repeated it in college. There is plenty of time in college
| (especially if some of the less useful elective requirements were
| taken away) to catch up on your math requirements, so whether you
| are ready for Algebra in 8th grade or not should have no barring
| on whether you are able to pursue a STEM major in college, let
| alone be successful in your career.
|
| I think we lane people out of STEM way too early, which is what I
| believe some of these curriculum changes are trying to redress.
| ucm_edge wrote:
| Math is one of the pure foundations for liberal arts so getting
| it done early is better. We should be focusing on getting high
| schools teaching it so well that colleges don't feel the need
| to rerun it not saying you can do it later. High school grads
| should be able to pass the AP Calc and AP Stats exams to the
| level colleges feel they can totally ditch the 100 level
| courses for those subjects.
|
| If you don't have students repeating basic math (and chemistry)
| in college, they can do deeper on an elective track involving a
| STEM because because their STEM credit hours aren't spent
| getting a rerun of Calc I.
| jimbokun wrote:
| So you were perfectly willing to pay for an extra semester of
| college to learn something you could have learned in high
| school for free.
| thepasswordis wrote:
| The wealthy are going to send their kids to private schools, and
| homeschool coops.
|
| People might talk a lot of woke on twitter, but nobody is going
| to willingly handicap their own children in the name of some
| nebulous greater good.
|
| It's _exactly_ the same as liberal NIMBYs. Preach tolerance and
| acceptance until somebody who doesn 't look, talk, and think
| exactly like you, wants to live in your neighborhood and alter
| your precious neighborhood aesthetic.
| cm2187 wrote:
| What is worrying though is that universities preach the same
| wokeism and seem to apply it to their recruitment. Whatever
| value they add or not, the top universities form a very
| effective cartel and gatekeeper to the most prestigious and/or
| lucrative careers. This can efficiently cancel the benefits of
| taking your kids out of public schools.
|
| I think long term, wokeism will kill those universities. A not
| insignificant part of the population isn't impressed with
| slogans like "decolonise maths", and the perception that they
| are handing over diplomas in the name of social justice, rather
| than skills, inflates away the value of those diploma. My own
| modest contribution to their demise is to give equal
| consideration to CVs of candidates from less prestigious
| universities. And I have seen enough idiots graduating from top
| universities to think that this credentials system was broken
| even before wokeism.
| freemint wrote:
| Wokeism will kill universities? Kill institutions that have
| been around longer than the USofA?
| cm2187 wrote:
| At the end of the day what makes a top university is its
| reputation, its brand. Any other measurable metric (SAT
| scores, quality of research, size of endowment fund, etc)
| is a consequence of that. There is no better way to hurt
| their brand than what they are doing now. And by "kill" I
| don't mean "close", I mean kill their reputation.
|
| And I think it's a good thing. I much prefer the German
| system which, as I understand it, doesn't rely on a small
| number of elite universities, and where you have to
| evaluate the candidate rather than its credentials.
| jkhdigital wrote:
| The irony is that this same logic is twisted beyond recognition
| to justify these "alternative" curricula: just because these
| math classes don't look like yours (algebra is "white" math, I
| guess) doesn't mean they aren't just as valuable.
| felistoria wrote:
| Teaching Pod start up is seeming like a better idea everyday.
| [deleted]
| rdtwo wrote:
| You think private schools aren't teaching woke ideologye? You
| are wrong. The future rules are are getting schooled in proper
| wokeness so they can run hr department and navigate proper
| corporate norms.
| tannhauser23 wrote:
| The difference is that private schools teach
| math/reading/writing at high levels. Otherwise parents would
| not put up with the political stuff that also gets packaged
| in.
| tinyhouse wrote:
| Exactly. Every time it's the same thing. They come up with
| stupid rules for the sake of equity, just to realize they made
| things worse cause everyone who could afford it moved to
| another town, or private school, etc. My town one day decided
| to cancel so many school traditions like the halloween parade
| for the sake of equity. Then they didn't allow in-person
| learning during the entire year. Then they did many other
| stupid things like that. Everyone I know who could afford it
| moved. They just have no clue what they are doing, they are
| just trying to look good, but in practice are doing more harm
| than good.
| nateburke wrote:
| While very much different in terms of the number and financial
| size of directly-applicable job prospects, American pre-
| collegiate math and musical training share a very important thing
| in common -- there is a step-function proficiency gain to be had
| from trained parents living in the same house as the child.
|
| Yes, primary and secondary curriculum matters, but in the same
| way a church musician parent will politely nod approval at the
| elementary school musical show knowing full well that real
| musical development for children usually happens in the home with
| parental involvement -- a mechanical engineer or e.g. actuary
| parent living in a small or under-schooled town will also
| politely acknowledge the child's remedial math homework
| assignments, yet know enough to be able to seek out quality
| instruction for the child, even if it means utilizing community
| college or other nearby resources.
|
| Given the same family and upbringing, something tells me that
| Scott would still excel in math as a HS student in today's
| California, were he there and that age now.
| indymike wrote:
| Father of five, and husband of teacher here. Math is a problem
| for middle school teachers because they often don't understand
| algebra, trigonometry, calculus or geometry well enough to teach
| it. When you add to that common core style arithmetic where
| parents and family can't help (because they do not understand how
| to do common core-style math), teachers are struggling to even
| teach math at all.
|
| Additionally, many professions pay better than being a teacher,
| and unfortunately, that includes package handling for FedEx and
| UPS (just drove by a sign promising $24/hour starting) in some
| areas.
| dorchadas wrote:
| > Math is a problem for middle school teachers because they
| often don't understand algebra,
|
| _Thank you_ for saying this. I am /was a high school math
| teacher and this was always the biggest problem when we got
| students in. The teachers at lower levels just don't understand
| it well enough to teach it. And, sadly, the same can even be
| said to be true for some of my coworkers. Our calculus teacher
| hasn't retired yet because there's nobody she trusts enough in
| the math department to understand pre-cal/calculus well enough
| to teach it (I'm on a leave of absence and have switched to the
| science department, though I've been asked by her and admin to
| teach those if I return).
|
| To me, common core math makes perfect sense. It's how I do math
| in my head. But it's also because I feel like I understand
| math. If I'm subtracting 26 from something, I'm going to
| subtract 30 and add back 4. It's just quicker and simpler.
| That's what I've seen parents struggling with, and even
| teachers struggle with it too! Because they don't get how
| numbers work. It's really frustrating and harms the kids. I
| wish I could overhaul how elementary school teachers are
| trained as in my state they're not even required to do _well_
| in math, or take any upper level math courses, before teaching
| math.
| julienb_sea wrote:
| This is a huge problem. I have friends who are teachers and
| have never taken anything past trig at a high school level,
| and certainly have no understanding of calculus. I think this
| results in a fundamental understanding gap, since the main
| application for algebra is really cemented in higher math
| (calculus).
| dorchadas wrote:
| I sadly don't know how to fix it without reworking the
| entire teacher education system, sadly, but I do believe
| it's _the_ problem affecting primary schools especially.
| How many times are you taught to read and the 'importance'
| of reading by a teacher who doesn't like to read
| themselves? Or 'science' by a teacher who has no grasp of
| what science is and just reads the slides (I distinctly
| remember having to correct my 5th grade teacher becasue the
| notes she used were so old it said Saturn was the only
| planet with rings...I was that kid, but at least it was
| after class!).
|
| We need teachers who have trained in those areas, _and
| then_ wanted to become teachers. And it needs to go all the
| way up through middle and high schools, but I truly think
| the focus should be on primary first. It 's why we get so
| many kids who don't understand multiplication when they get
| to high school, let alone division -- their teachers don't
| either and they just give them calculators at a young age!
| And it all boils down to _how_ teachers themselves are
| trained.
|
| Back to math at the school I taught at, there are two there
| who understand it. Funnily enough, they both came out of
| retirement to teach again (one has been doing it for 15
| years, and the other just retired from her VP job a few
| years ago), and they're related. The older one married the
| younger one's uncle. It's funny how it stays in the family.
| The younger one's dad was also a math/chem/physics teacher,
| and was an amazing teacher until he just got too old. They
| were the only teachers I know or had at that school when I
| was there who truly knew math, and it showed in how they
| taught and the general outcomes of their students -- A "C"
| student in the accelerated algebra II class made an easy
| "A" on college algebra when they got there two years later,
| simply because it had been imparted to them that well.
| rahimnathwani wrote:
| "Additionally, many professions pay better than being a
| teacher, and unfortunately, that includes package handling for
| FedEx and UPS (just drove by a sign promising $24/hour
| starting) in some areas."
|
| In California, teachers' retirement benefits include defined-
| benefit pensions, with some inflation-protection. They also
| don't work the same hours as package handlers. Total
| pay+benefits for teachers in SF is about 50% higher than base
| salary.[0]
|
| [0]
| https://transparentcalifornia.com/download/salaries/school-d...
| throwawayboise wrote:
| I'm never heard of a middle school offering trigonometry or
| calculus. The rare kid who is ready for those topics by age 13
| can be accommodated by allowing him to attend that class at the
| local high school.
|
| A middle school algebra teacher should of course understand
| middle school algebra. This is not an unreasonable expectation
| for a job that requires a college education. If a teacher lacks
| the ability to master middle-school algebra, how on earth did
| he get into college?
| ben7799 wrote:
| It's not that the students need to be taught high school or
| college math in Junior high.
|
| It's that a teacher which did not master high school and
| college math is not necessarily a good candidate to teach
| high school or advanced middle school math, and it absolutely
| occurs when the primary focus of the teacher's college career
| was teaching and not Math or another STEM field.
|
| The model in the US seems to have become that the Teaching
| degree is the most important degree for a public school
| teacher regardless of the subject that is going to be taught.
| At some point that breaks down in a big way in the STEM
| fields in the range of middle or high school. Certainly you
| are not going to be taught Math at the College level by
| someone who does not have a Math degree. But in public school
| they've decided at some point that a math teacher doesn't
| need to have a math degree.
| yakkityyak wrote:
| > But in public school they've decided at some point that a
| math teacher doesn't need to have a math degree.
|
| For anything pre-high school that would seem sort of
| overkill. A "good" teacher in the earlier grades is more of
| a function of how well they work with children.
| ben7799 wrote:
| This discussion is mostly about 8th grade and up though.
| indymike wrote:
| > A middle school algebra teacher should of course understand
| middle school algebra.
|
| Yes. Exactly.
|
| > If a teacher lacks the ability to master middle-school
| algebra, how on earth did he get into college?
|
| Knowing a subject well enough to pass a class or pass a test
| is not the same as knowing it well enough to teach. STEM in
| schools is a real problem because, well, non-education jobs
| pay 3-5x what teaching jobs do for math, CS, and robotic.
| maniflames wrote:
| Honest question from someone from the Netherlands: when are
| kids in the states old enough for these topics?
|
| Me and all of my friends were thaught the fundamentals of
| algebra & trigonomatry (admittedly not calculus) at 13 years
| old. I had no idea the wasn't the case in the US and it
| honestly kind of blows my mind.
| eitally wrote:
| In some US public schools, the "advanced math" curriculum
| puts 7th graders in algebra. In more, though, algebra isn't
| available until 8th grade (and that is still treated as
| accelerated). "Normal" math progression has standardized on
| algebra as the first high school course, followed by
| geometry, then trig, then precalculus/analysis.
|
| The first level of math acceleration moves that high school
| progression up a year and has seniors taking calc 1
| (limits/derivates & single variable integrals. The second
| level of acceleration has calc 1 in 11th grade and calc 2
| (multi-variable) in 12th grade.
|
| There are a handful of schools, mostly private, that move
| faster or have more diverse math curriculum offerings, but
| this is the most common.
|
| So, when do American kids his algebra?
|
| Standard curriculum: 9th grade, ~14yo
| Izkata wrote:
| Very roughly, subtract 6 from age to get grade. For
| example, barring being held back, jumping a grade, or
| unusual things around birthday timing, you'd usually finish
| 12th grade at age 18.
| scruple wrote:
| I came through the American system, in the 1990s, in a
| rural place. At grades:
|
| 7: Algebra I
|
| 8: Algebra II
|
| 9: Geometry
|
| 10: Trigonometry/Pre-Calculus
|
| 11: Calculus
|
| 12: Calculus-based Physics
| ecshafer wrote:
| My school was rural and that is way more advanced than
| mine was.
|
| 8: Algebra I 9: Algebra II 10: Geometry 11: Trigonometry
| 12: Pre-calculus
|
| Advanced class was -1 year. This was Upstate New York
| 90s/00s. Though I guess to be more specific these courses
| were actually combination. So it was 3 years of mixed
| algebra/geometry/trigonometry. Math A, B I think New York
| called it. Until Pre-calculus Which was actually year and
| a half courses of mixed topics.
| scruple wrote:
| I should've added that I was on the advanced track and
| was a year ahead of most of my peers, though we had full
| class of > 20 students (in a graduating class of, I wanna
| say, ~100-ish) who were in this track. IIRC, it was a
| toss up what most students did for Math in the 11th and
| 12th grade. I do believe that the school offered a
| dedicated Trigonometry and Pre-Calculus course that many
| students took in the 11th and 12th grades, and there was
| also an Algebra-based Physics class that students could
| take, but I want to say that they were not necessary for
| graduation.
| indymike wrote:
| The norm for exposure to basic algebra is 5th (10-11 years
| old) grade in most US states. Not sure what the standards
| are exactly, but each grade after that does progressively
| more, with 14 year olds expected to complete a full year
| course.
| jimbokun wrote:
| Maybe we need a reformed "Teach for America" style program,
| where the government gives scholarships to students getting
| double undergrad major in Mathematics and Education, if they
| agree to teach in inner city schools for X years after
| graduation.
| tannhauser23 wrote:
| We all know what initiatives like California's leads to. Parents
| from middle to upper class families will send their kids to
| private schools or invest in extracurricular math programs. This
| will be especially true in immigrant and tech-worker parents who
| know the value of a strong STEM education. Only people who suffer
| will be kids from families without the means or the desire to go
| beyond public education - most likely the same people that these
| initiatives purport to help.
| 908B64B197 wrote:
| > This will be especially true in immigrant and tech-worker
| parents who know the value of a strong STEM education. Only
| people who suffer will be kids from families without the means
| or the desire to go beyond public education - most likely the
| same people that these initiatives purport to help.
|
| Short term schools like Lowell are switching from using test
| score to a lottery based admission. And so are UC schools! So
| the smart kid interested in learning but who doesn't have
| parents in tech to send him to private tutoring better be lucky
| at the lottery or have the correct "holistic" attributes his
| target school will admit on!
| nouveaux wrote:
| "We all know what initiatives like California's leads to.
| Parents from middle to upper class families will send their
| kids to private schools or invest in extracurricular math
| programs."
|
| Are you saying it's not happening now?
| julienb_sea wrote:
| Whether or not it's happening now, doesn't preclude
| opposition to policy choices that actively accelerate the
| process.
|
| People with money and wherewithal are always going to have
| alternative options available to them, such as private
| education or moving to expensive neighborhoods with strong
| schools. The problem is when public school policy results in
| actual degradation of education for everyone else.
| twblalock wrote:
| A lot of high-earning parents in California send their
| children to public schools, and they are willing to pay extra
| money to buy homes in the best school districts in order to
| do so.
|
| School district quality has a significant impact on home
| values in California, and that wouldn't be the case if the
| majority of high earners sent their kids to private schools.
| itronitron wrote:
| Just do Khan Academy for Math, they have very succinct and
| clear math education videos. IXL is also very good for
| practice.
| astrange wrote:
| What value is there in a strong STEM education? A weak one
| might be fine too.
|
| Just because tiger moms think there is one doesn't mean there
| is. You'd have to believe students actually remember or use
| everything they learn in class, vs it being signalling you're
| conscientious enough to do the homework.
| the_optimist wrote:
| Here's a little paper on just this: - STEM education is
| associated with better problem-solving capability - better
| problem-solving capability leads to higher earnings - higher
| earnings (to a point) lead to greater happiness
| https://files.eric.ed.gov/fulltext/ED531752.pdf
| tinyhouse wrote:
| The US unfortunately has lost its direction. Everything is so
| political, including education. They don't try to improve equity,
| just to look good from the outside.
| felistoria wrote:
| I'm as red blooded American as they come but I believe we are
| on a downward slide with little to no hope for recovery.
| Outside sources have so successfully utilized technology to
| drive a wedge between two sides the country that I don't see
| how it can ever be brought back together. The wedge pushes
| further every single day it seems like.
| ihsw wrote:
| There is hope for America yet:
|
| > Michael Bloomberg: Why I'm Backing Charter Schools
|
| > The public school system is failing. My philanthropy will
| give $750 million to a proven alternative.
|
| Source: https://www.wsj.com/articles/michael-bloomberg-why-
| im-backin...
| nopinsight wrote:
| From the post: "The report states that while 80% of all students
| have access to Algebra I in middle school, only 24% enroll."
|
| A solution is to enroll all students in schools that offer the
| course by default, but let some opt out if they have a very good
| reason to do so (ie, nudging in behavioral economics term.) A
| potential problem is the pressure to water down the course for
| unwilling students but many countries have already solved that by
| having different streams/versions of the course.
|
| Another objection is that it could be too hard for some students.
| I'd say it should be possible for a majority of students to
| understand Algebra I if they are taught properly, as in the case
| of many countries with high PISA Math score. In these
| countries/regions, to my knowledge, much of Algebra I is taught
| in math courses compulsory for ALL middle school students.
|
| PISA 2018 results: https://www.oecd.org/pisa/PISA-
| results_ENGLISH.png
|
| I grew up in Asia, taught math there for several years, and have
| run a tutoring school specializing in math tutoring there for
| over a decade. I was quite surprised when I saw how easy the
| American math curriculum/textbook is for a given grade. (I'd say
| 1-3 grades easier than Asian counterparts) Others in Quora have
| expressed the same sentiment.
|
| Math is a skill that requires a great deal of time to master.
| Those who start properly sooner tend to have an advantage. US
| schools should offer more advanced math courses to all students
| at a younger age, rather than the reverse.
| A4ET8a8uTh0 wrote:
| Eh, watching all this makes me only more willing to properly
| research homeschooling ( it is not yet apparent whether we will
| be able to afford private school.. so I am assuming we won't be
| ).
|
| Still, the pattern is hard to miss. I think my current favorite
| is biology and its treatment of race (
| https://www.nytimes.com/2019/12/07/us/race-biology-genetics....
| ).
|
| Quote directly from the article:
|
| "We basically decided, no, race is still a social construction,
| it's not a biological thing," Ken Miller, an author of the widely
| used Prentice Hall biology textbook, told the science magazine
| Undark of the decision to omit mention of race.
|
| I guess what I am saying is not new to anyone. Public schools
| will continue to degrade. There is no benefit to any of the
| groups other than the parents to ensure kids learn things (
| administrators, their lawyers, your congressman, my congressman,
| teachers, teacher's unions, book publishers ). Sure, they pay lip
| service and some individual teachers care, but each of those
| groups have goals beyond kid's education.
|
| edit: I was gonna add Apple and Microsoft in that list, but I
| removed them, because, as flawed as their reasoning is, at least
| they pretend they want to teach kids basic coding, which is not
| horrible.
| leephillips wrote:
| I don't understand your comment. Why is your current favorite
| biology "and its treatment of race"?
| A4ET8a8uTh0 wrote:
| Because, and I don't think that is questioned, race as a
| biological concept exists and, as Prentice Hall quote
| demonstrates, the publisher unilaterally decided on a lie of
| omission, while attempting to teach. It is not a good look if
| the goal is teach kids basic biology.
|
| Unless, naturally, it is not the goal; or even a goal.
| mabub24 wrote:
| You're really referring to genetic ancestry, which is
| regularly used in biology without any issue. The term
| "race" is really not used anymore, except in a
| social/historical/statistical (population) context for
| humans. It's only informally used in human biology.
|
| > Because, and I don't think that is questioned, race as a
| biological concept exists
|
| This is questioned constantly, and is far from the standard
| or consensus opinion for human biology. In reality, most
| scientists and biologists don't use the term "race" often
| or at all precisely because of it's historical connotations
| and social uses. Removing the term "race" from a science
| textbook does not change anything really, beside clarify
| that race _in the context of racial essentialism in
| biology_ is a useless concept. Understanding how the
| concept of race was used to abuse science, and in turn
| abuse large swathes of the population, is more important,
| and likely has a role in learning about the ethics and uses
| of biology.
| WindyLakeReturn wrote:
| Race is better replaced by populations. Populations are
| groups of people who grew up in a region back when travel
| between regions was restricted enough that genetic
| differences appears. As our world become more connected,
| populations were grouped based on similar phenotype (not
| similar genotype) into races. Races do exist in that they
| are phenotypically similar groupings of population, but
| they have little value in comparison to populations at
| the biology level. Sociology level race has more
| importance because of how society reacted once those
| races were created (which also means it has an importance
| in the fields dealing with the history of science). And
| as the world becomes more globalized, the effects of
| populations decrease. It isn't gone and has a long way to
| go before it is gone, but as long as the world stays
| globalized it will happen. Far into the future, assume
| humanity achieves long distance space travel, it will
| likely result in new populations emerging and potentially
| even different species evolving. But that's so far away
| that it is best left to science fiction.
| A4ET8a8uTh0 wrote:
| Hmm. I like the explanation and I appreciate some of the
| concern.
|
| I would personally argue its absence says more than its
| presence given race is used in other contexts you listed.
| You simply can't get away from it when discussing
| demographics, so I question a little your statement that
| the term is not used in biology or other sciences.
|
| Could you share an example of a paper that follows that
| 'no race' ( "at all" ) approach? I may very well be
| wrong. I am pretty ancient.
|
| << This is questioned constantly, and is far from the
| standard or consensus opinion for human biology.
|
| You clearly are more immersed in it than me. Could you
| elaborate a little bit and link to two recent opposing
| papers? Sorry for all the questions. I am genuinely
| curious now.
| mabub24 wrote:
| To be clear, the term is used and has been used. But the
| idea that it's a concept that everyone agrees on, or that
| everyone agrees _must_ be used, is not at all true. The
| debate is alive and well in philosophy and in the
| sciences. Personally, I don 't really see any use for the
| term in science, beyond referring to a social/informally
| named group.
|
| For a philosophical discussion see a good summary here:
| https://ndpr.nd.edu/reviews/what-is-race-four-
| philosophical-...
|
| And for a very extensive summary of relevant scientific
| and genetic findings, see the wikipedia page on Race as a
| system of human categorization: https://en.wikipedia.org/
| wiki/Race_(human_categorization)#Bi...
|
| The key quote from that article is:
|
| > Even though there is a broad scientific agreement that
| essentialist and typological conceptions of race are
| untenable,[12][13][14][15][16][17] scientists around the
| world continue to conceptualize race in widely differing
| ways.[18] While some researchers continue to use the
| concept of race to make distinctions among fuzzy sets of
| traits or observable differences in behavior, others in
| the scientific community suggest that the idea of race is
| inherently naive[7] or simplistic.[19] Still others argue
| that, among humans, race has no taxonomic significance
| because all living humans belong to the same subspecies,
| Homo sapiens sapiens.[20][21]
|
| You can clearly see a number of competing views,
| including constructivist, essentialist, and anti-
| essentialist, the idea that the concept of race is
| irrelevant to the study of biology.
| leephillips wrote:
| I assure you that it is questioned. How do you define race,
| biologically? How would you test, say, former president
| Obama to determine his biological race?
|
| EDIT: To be more precise: of course there is no question
| that the biological concept "exists". The biological
| concept of Lamarckian genetics exists, too. The question is
| whether race is meaningful, useful, and whether it should
| be taught in the textbook.
| A4ET8a8uTh0 wrote:
| How do you test for things if you can't see them?
|
| Does God exists? Does wind? We look for effects.
|
| No. I am not going to go that route, because helpfully
| Webster dictionary defines race as:
|
| "any one of the groups that humans are often divided into
| based on physical traits regarded as common among people
| of shared ancestry"
|
| But that is not biological race definition. Fair enough.
| From biologyonline ( https://www.biologyonline.com/ ):
|
| "(1) A group or population of humans categorized on the
| basis of various sets of heritable characteristics (such
| as color of skin, eyes, and hair)."
|
| Now, I get that it is a touchy topic in US, but what
| heritable characteristics does Obama possess that are
| visible to the naked eye?
| leephillips wrote:
| So different people look different. Why is that an
| important principle of biology that needs to be developed
| in a textbook? How does it help us to understand
| anything?
|
| And I persist: if you can't measure it, and tell me what
| someone's "race" is in a way that biologists in general
| would agree with, the concept is too wobbly to be of any
| scientific interest. Finding definitions merely shows
| that the word exists. It doesn't support the idea that
| it's a meaningful or useful categorization.
| A4ET8a8uTh0 wrote:
| Because, and I do not think I can stress that enough,
| science is not a religion. It is not a movement or a
| cause. And I am concerned that you are worried more about
| the 'good' derived from uhomitting a bad word might cause
| than about exploring and describing reality for what it
| is.
| yjftsjthsd-h wrote:
| > So different people look different. Why is that an
| important principle of biology that needs to be developed
| in a textbook? How does it help us to understand
| anything?
|
| Race strongly correlates with other things; for instance,
| per https://www.cdc.gov/heartdisease/facts.htm "White
| (Non-Hispanic)" men are most at risk of heart disease,
| and "American Indian or Alaska Native" are winning by
| several percentage points. That is _deeply_ of scientific
| interest.
| leephillips wrote:
| In order to apply these supposed correlations, we would
| need to be able to determine the patient's race. How do
| we do that?
|
| (It seems to me that there is at least a hint of
| tautology in your comment. How can we talk about these
| correlations with race unless we're assuming that racial
| categorizations are meaningful in the first place?)
| [deleted]
| oh_sigh wrote:
| How do you define dog breeds, biologically? How would you
| test, say, a Goldendoodle for its biological breed?
| leephillips wrote:
| Interesting question. I have no idea.
| freemint wrote:
| Race as biological concept exists but there are no human races
| in the biological sense. Humans are able to interbreed and were
| not selected by their environments for long enough to develop
| significantly different cognitive abilities. If we use the word
| race for human being it can only mean cultural or other such
| societal concepts meaning it is a social construction. I hope
| that helped.
| leephillips wrote:
| It didn't really help. Why do you mention interbreeding? Are
| you confusing race with species?
| freemint wrote:
| Because partial but not complete genetic isolation is a
| criteria in the IMHO applicable (or rather not applicable)
| definition of race here.
|
| I am not confusing race and species.
| burnished wrote:
| No, there is just history to the word you might not know,
| some extra meaning. Race fundamentally refers to the idea
| that there are different kinds of people. Which is why
| 'interbreeding' comes up, because some people used to
| believe that a black person and a white person having a
| child was more like crossing a horse and a donkey than say
| a person with light hair and a person with dark hair.
|
| There is some real ugly history here.
| lliamander wrote:
| That's not really a good argument for the thesis that
| "there are no human races in the biological sense". Even
| if there were misconceptions embedded into the definition
| of the word "race", that doesn't mean there's no
| underlying biological reality to the differences between
| human populations that are identified by categories of
| race.
| leephillips wrote:
| No kidding?
| lliamander wrote:
| Even if there wasn't enough time for selection to act on
| cognitive abilities (citation needed), the fact of the matter
| is that patterns of population genetics do correlate highly
| with self-identified race.
| VLM wrote:
| > patterns of population genetics
|
| Which then result in patterns of race related medical
| diseases and similar topics. Sickle cell anemia, etc.
| rendang wrote:
| Seems like a weird false dichotomy - even in the olden days
| of pseudoscience on race, obviously people didn't believe
| that races couldn't interbreed, as they observed such
| themselves.
|
| The fact remains that if you run PCA and clustering on
| genetic data as in https://en.wikipedia.org/wiki/Human_geneti
| c_clustering#/medi... you will get groups that generally
| correspond with Caucasian/SS African/East Asian/Amerindian.
| You can call those "races" or something else, but they are
| not just artifacts of society/culture.
| astrange wrote:
| It's remarkable that whenever I read a blog post by either
| Scott, there's someone in the first comment thread complaining
| society won't acknowledge that black people have genetically
| lower IQs.
|
| This is the third time this week it's happened to me.
| ambrozk wrote:
| I cannot tell you that this has never happened to you, but I
| can inform you that the person you are responding to did not
| say a single word about either black people or intelligence.
| naasking wrote:
| Or "genetics" even, although it does appear in the url they
| posted.
| itronitron wrote:
| >> whether we will be able to afford private school
|
| Private school is not necessarily better than public school,
| especially for high school. If you are in a good public school
| district then it is unlikely that a private school will give
| your children a better education.
| teeray wrote:
| Everybody hates it to different degrees, but grinding Algebra I &
| II problem sets hard for a few years was a dramatic advantage in
| college calc & physics. Some classmates were still struggling
| with special right triangles where it was completely intuitive to
| me at that point.
|
| The applications of math that everyone clamors for in high school
| eduction became far more apparent once I got to college.
| tomohawk wrote:
| I took an informal poll of foreign students at the US university
| I went to. Regardless of major, they all took Algebra in 6th
| grade. This was quite some time ago.
|
| I was interested as I was ready for Algebra in 6th grade, but was
| unable to take it until 8th grade. If you don't get into Algebra
| before high school, there is no chance of taking a reasonable
| calculus class before college, which puts you way behind the
| curve if you get into an engineering program.
|
| I went to a state university that had a strong engineering
| program. The students that I knew who were having difficulty and
| eventually dropped all had first seen calculus at the university.
| These were smart, talented people, but they were not given the
| chance to succeed.
| jelliclesfarm wrote:
| they are screaming Fire!!..no one is listening. The only solution
| is to split public schools into two streams STEM and liberal arts
| studies(I don't know what it's called).+ more vocational/trade
| schools. We can't cater to the lowest common denominator in math.
| endisneigh wrote:
| This makes no sense - stem and liberal arts aren't mutually
| exclusive things you can just separate. In fact math itself is
| generally thought to be part of the "liberal arts", along with
| logic, which could be said to be the precursor to computer
| science.
| leetcrew wrote:
| liberal arts may include parts of stem, but stem and
| humanities are pretty much disjoint, which is probably a
| better way to have this discussion. I think there's an
| argument for not forcing people who are interested/capable in
| stem to suffer through perfunctory humanities courses (and
| vice versa).
|
| is something lost when someone learns about propositional
| logic and set theory without learning about the vienna circle
| and logical positivism? yes. does it matter very much
| practically? probably not, and stem people who are interested
| in that kind of thing can probably pick it up on their own.
| jimbokun wrote:
| My take on the core skills for any educated individual:
|
| Be able to write well to communicate your ideas clearly and
| persuade people to your position.
|
| Be able to apply math to a variety of practical problems.
|
| I think that prepares you to specialize in any field later.
| NoSorryCannot wrote:
| They're not disjoint. At an advanced level, subjects like
| linguistics and psychology heavily cross displines with
| mathematics, logic, and neuroscience at least.
|
| Students probably shouldn't be falling hard on one side or
| the other any earlier than they already do lest even more
| of them believe they are completely unrelated.
| sokoloff wrote:
| > not forcing people who are interested/capable in stem to
| suffer through perfunctory humanities courses
|
| I hated my humanities courses all through middle and high
| school and college. I took as many advanced math/science
| courses as my high school had. I graduated from a well-
| regarded technical university.
|
| My humanities courses have probably had more positive
| impact on my career earnings than my tech courses. I feel
| like I should find my old English teachers and apologize to
| them.
| panzagl wrote:
| You hated them for the reason most STEM track students
| do- because they're hard.
| Anechoic wrote:
| I read that as "stem & liberal arts" as one stream and
| "vocational/trade schools" as the second stream.
| bluGill wrote:
| We don't need more trade schools though. Over here on
| hacker news many of us have day jobs eliminating those
| jobs. While we won't succeed (and trades are still a better
| job than many artistic degrees) there are a lot of kids
| going into them. Most trades are also taught on the job.
| Want to be a carpenter - you can start tomorrow morning at
| 7am in any large city. From there you can branch out if you
| want.
| jimbokun wrote:
| The majority of programming jobs, DevOps jobs, etc. could
| be learned in a trade school. Only a minority of
| programming jobs really require a four year CS degree.
|
| Also, is that true that most trades can be learned on the
| job without prior training? I thought you needed a decent
| amount of training to be a plumber, electrician, etc.
| jaywalk wrote:
| See "Modern usage" in:
| https://en.wikipedia.org/wiki/Liberal_arts_education
|
| "The modern use of the term liberal arts consists of four
| areas: the natural sciences, social sciences, arts, and
| humanities."
|
| So no, math is not "generally thought" to be part of the
| liberal arts.
| aaaaaaaaaaab wrote:
| How can you do natural sciences without math?
| blibble wrote:
| there is little science without mathematics
| caconym_ wrote:
| If you read the whole "Modern usage" section rather than
| just the first line, you will see that mathematics is
| listed prominently there (and also logic, CS, physics,
| etc...).
| etchalon wrote:
| So you're of the belief that Physics, which is considered a
| natural science, does not require "math"?
|
| Interesting.
| imoverclocked wrote:
| I had two different Physics teachers/classes in high
| school.
|
| One was almost entirely conceptual and provided a
| fantastic base with which to reason about the world.
| Everything was explained completely without math and then
| a little bit of math (usually no higher than basic
| algebra) was used to describe what we had just developed
| to fulfill basic requirements of the curriculum. People
| had wonderful conversations about how things worked and
| understanding was developed from observation and
| intuition.
|
| The other was almost completely the opposite direction
| and calculus based. I often found errors in the
| application of math and reasoning about the subject.
| There was a moment where the teacher couldn't be
| convinced that something he said was wrong because of the
| math he was looking at. Years later, in a college Physics
| course, a similar core concept was covered and I was
| internally vindicated.
|
| Einstein/Feynman were known to be highly conceptual and
| the math was often worked out after a thought experiment.
| A famous quote by Einstein, "Do not worry too much about
| your difficulties in mathematics, I can assure you that
| mine are still greater."
|
| It all depends on how it is taught.
|
| All of that being said, Mathematics is an excellent tool
| to sharpen ones ability to reason.
| MrsPeaches wrote:
| It then goes on to say:
|
| Academic areas that are associated with the term liberal
| arts include:
|
| Life sciences (biology, ecology, neuroscience)
|
| Physical science (physics, astronomy, chemistry, physical
| geography)
|
| Logic, mathematics, statistics, computer science
|
| Philosophy
|
| History
|
| Social science (anthropology, economics, human geography,
| linguistics, political science, jurisprudence, psychology,
| and sociology)
|
| Creative arts (fine arts, music, performing arts,
| literature)
| [deleted]
| anonnyj wrote:
| Such fixes are obvious, but they're "racist", and as such won't
| be resolved in a sane manner.
|
| We've got molten lava in our mouths that we can neither spit
| nor swallow.
| felistoria wrote:
| In my local school district there is a dedicated Arts School
| (Art, Music, Dance, etc.) for grades 6-12 and a dedicated STEM
| school for grades 6-12. Kids within the district have to apply
| to get accepted to either of them otherwise they just go to the
| traditional middle/high schools.
|
| A neighboring district has a similar school geared towards
| Healthcare.
|
| These schools obviously teach all necessary subjects but have
| more advanced classes geared towards those subjects than your
| average school would have.
| zwieback wrote:
| Effectively most high and even middle schools are already split
| in the sense that students can take more or less math based on
| interest and skill. At my daughters' middle school there were
| three tracks: low, medium and high. My kids were in medium and
| high level and the curriculum was different for each. By the
| time they were in 11 or 12 grade they had maxxed out math
| (including calculus) and could have taken college math (but
| chose not to).
|
| I think the complaint from the left is that minorities don't
| end up in the higher math offerings because they are either not
| offered at certain schools or, for whatever reason,
| unattractive to those students. That's the problem that needs
| to be fixed. Whether any public school can do that is
| questionable.
| jaywalk wrote:
| I don't think they're complaining about the programs not
| being offered, since their "solution" is to stop offering
| them completely.
| zwieback wrote:
| Not exactly, it sounds to me that the idea is to push out
| Algebra I and offer the data-sciency, more "equitable"
| option earlier. Nerdy kids would still go through the
| Algebra-Calc-AP track but on a slightly different schedule.
| [deleted]
| pwthornton wrote:
| But liberal arts includes math and science. They are two of the
| cores. Maybe you are thinking of humanities?
| nitwit005 wrote:
| I suppose this is a new trend, but there's constant pressure to
| lower the standards here in California. We genuinely graduate
| some students who can't multiply as-is.
|
| I went to Sonoma State, which at the time had at least 3
| semesters of remedial math you could take, plus a tutoring
| program, trying to fill in the knowledge a high school graduate
| was supposed to have. The state got mad about all those classes
| because the high schools were supposed to cover the material.
| dorchadas wrote:
| Not just California. I'm from the South and it's the same.
| a9h74j wrote:
| To my reading the posted article makes only passing reference to
| the California recommendations, and gives positive emphasis to a
| number of focussed initiatives or programs.
| Hermitian909 wrote:
| I think many of the commenters posting that this step will
| necessarily lower mathematical achievement are unlikely to have
| taught math to small children (or at least to a large number of
| them). The change has tradeoffs, but I think we'll likely end up
| a more numerate state for the change.
|
| It's important to remember that children are not tiny adults. At
| an early enough developmental stage, a child may be physically
| unable to learn algebra. The number of such children is much
| higher in middle school than freshman year of high school. Note
| that developing later doesn't mean you're not very smart nor that
| you have aptitude. A student I had many years with this issue now
| has his PhD in mathematics.
|
| By delaying algebra, you give a large chunk of students time to
| move forward developmentally so they can engage in the material.
| The current system ill suits them for a few reasons. One is that
| curriculum (somewhat necessarily) assumes high mastery of pre-
| requisite concepts, when it turns out this isn't the case
| students tend to not understand the material and get very
| frustrated. That frustration and anger often causes lasting
| damage that may never be undone.
|
| My mother was a math educator during the years when Algebra first
| moved into middle school fought heavily against it. According to
| her the push came mainly from professors of Mathematics (with no
| educational training) who wanted better trained students. I think
| this has worked out for some of the top schools. If you're smart
| _and_ a little precocious algebra in 8th grade is good, but I
| think net we lose out on a lot of talent.
| threatofrain wrote:
| Under the Common Core as specifically implemented in
| California, children who are ready for Algebra in middle school
| may take it, and children who benefit from a delay may opt for
| delay.
|
| A central pillar of Equitable Math is that this disparity
| sustains White Supremacy in math, and thus _all_ children
| should _always_ be in the same class, up until the last year of
| high school.1
|
| This is the central point of contention, and not whether some
| children benefit from a delay of Algebra past middle school,
| and nor whether all children ought to learn Calculus.
|
| [1]: https://equitablemath.org
| stakkur wrote:
| Public education in the US sits at a difficult nexus of political
| will, cultural ideology, public opinion, and educational
| 'theory'. It rarely goes well, because everyone vehemently
| believes they know the 'purpose' of public education.
|
| And so, we get posts like this: public ed as a 'pipeline to STEM
| careers'.
|
| The reductionist view of public education-as-career-training is
| one of those contentious topics. I myself find it absurd. An ed
| system driven by vocations and political/ideological nation-state
| goals has been so genuinely harmful to people it's hard to know
| where to begin.
| mherdeg wrote:
| I don't understand how you can remove algebra from middle-school
| curricula without exacerbating inequality.
|
| Supplementary math education in our area costs about
| $1500-$2500/year (looking at Russian School of Math list prices).
| The exemplary private schools in the area I grew up charge
| $30k-$35k annual tuition (with financial aid available for some
| families). And you can DIY home instruction -- I've been working
| through the Moebius Noodles play with our 4yo, and I guess you
| could try to see if there's a Math Circle to sign up for.
|
| But not every household can afford the time or money to
| coordinate extracurricular instruction. The kids whose parents
| are hyper-prepared and able to spend the time and money will end
| up with better math background, maybe a better shot at the
| AHSME/AIME/USAMO, and I guess _maybe_ better career outcomes,
| versus their peers. Is that a fair outcome? Is it a good thing to
| do?
|
| I'm very willing to be wrong here ... I just don't understand how
| this plan promotes equity.
|
| p.s. saw this in the news and tried introducing algebra to the
| 4yo. We're not quite ready yet.
|
| "Hey kid -- if I have four of something but I want to have six of
| them, how many do I need to add?"
|
| He holds up a fist, empty. "Four." Then he starts counting out
| fingers. One finger: "Five!". Two fingers: "Six!". He says,
| "Two!"
|
| "That's right, kid. Sometimes we say 4+x=6, so x=2."
|
| He gives a sly grin. "But _I_ know my numbers so well that I don
| 't need to use x!"
| ucm_edge wrote:
| Related, I also have a hunch that the UC system dropping the
| SAT is going to promote inequality. I don't want to defend
| standardized tests as flawless, but the SAT has been around
| forever, you can go to basically any public library and get a
| prep book, one of the librarians can probably help explain it
| to you, most teachers are familiar with the strategies to
| improve score on it, resources exist on the internet, etc. So
| there exists a multitude of paths toward showing proficiency on
| it.
|
| Now that we're not doing standardized tests and turning
| admission into high school transcript plus additional material
| it's really going to help the kids whose parents can organize
| and pay for the most extra circulars.
| tzs wrote:
| > I don't want to defend standardized tests as flawless, but
| the SAT has been around forever, you can go to basically any
| public library and get a prep book
|
| That's great unless there are a few other kids in the same
| area that also need to the book and also think to get it from
| the library.
| WindyLakeReturn wrote:
| Most people have smart phones and getting free resources
| online are easy enough.
|
| The larger overall point is that acquiring SAT prep
| resources is easier to do than acquiring resources for
| volunteering or extra curricular activities. While the
| former may be difficult in some situations, in those same
| situations the latter has even greater difficulty.
| financetechbro wrote:
| What about the kids who can afford to pay for top tier
| college consultants and tutors to maximize their standardized
| test scores? Doesn't that also exacerbate inequity?
| durovo wrote:
| I am not from the US but I did appear for the SAT. The
| books are more than enough to get a very good score on the
| SAT. In my opinion, SAT is not difficult enough for
| coaching to make a very big difference.
| nickff wrote:
| > _" Related, I also have a hunch that the UC system dropping
| the SAT is going to promote inequality."_
|
| My guess is that it will reduce racial inequality, but
| increase inequality based on parental income (class).
| Eliminating SAT scores will result in greater affirmative
| action, and the richest people of each race will be able to
| sculpt a compelling resume for their child; there will be no
| way for those with poorer parents to compete on the holistic
| measures.
| Izkata wrote:
| I actually remember worksheets in first grade (around age 7)
| where we had problems exactly like that, but with an empty box
| instead of a letter and we wrote the answer in the box.
| jkhdigital wrote:
| This should be the foundation for all teacher training: spend
| most of your time sitting with small groups of kids at various
| ages and try to teach them concepts that are obviously beyond
| their current knowledge. Take copious notes. Patterns will
| emerge, and you'll develop an intuition about what sticks and
| what doesn't.
| xwdv wrote:
| Meh, you're asking too much. For many teaching is just a
| steady paycheck and generous time off. It's not a calling.
| yjftsjthsd-h wrote:
| > For many teaching is just a steady paycheck and generous
| time off.
|
| A tiny paycheck and... I'm sorry, I have no idea how to
| read "generous" time off; are you referring to summers when
| they don't get paid, or something else? My impression is
| that most teachers are working significantly over 40h/wk
| and either don't know that they're victims of wage theft or
| somehow don't care.
| yellow_postit wrote:
| There is no "generous" time off if talking about public
| primary education in the US. Curriculum development and
| continuing education most frequently happen outside the
| "day job hours".
| earleybird wrote:
| Piaget - stages of cognitive development?
| AlanYx wrote:
| Moebius Noodles looks fantastic. Would you happen to have any
| other resources you'd recommend for DIY home instruction for
| early childhood learners?
| julienb_sea wrote:
| I don't have kids but I keep seeing https://www.kiwico.com/
| recommended all over the internet and it seems like a great
| way to get projects and learning infused into early childhood
| play and exploration.
| wott wrote:
| > I just don't understand how this plan promotes equity.
|
| Well, it can turn every one into a bad pupil :-)
|
| I wish people would take a look at what happened in other
| countries which followed a somehow similar path of dumbing down
| courses and lowering requirements.
|
| Here is what 25 years of dumbing down achieved in France:
|
| https://3.bp.blogspot.com/-xHQ532qyiek/XJ8kH-PnVTI/AAAAAAAAH...
|
| This extremely telling graph about the level in the end of
| primary school is taken from an official note from the Ministry
| of Education itself:
| https://www.education.gouv.fr/media/22373/download
|
| It is about maths (calculus) but we have somewhat similar drops
| in other matters, notably in French language.
|
| You can easily see on the graph how the above average pupils
| from now perform as bas as the below average pupils from 30
| years ago. Only a small part of pupils perform as the average
| pupil used to perform. You can also note that the 'excellent'
| pupils have basically disappeared: there is no bump (and no
| long tail) on the right of the curve any more.
|
| Furthermore, every social category performs much worse:
| http://centre-alain-savary.ens-lyon.fr/CAS/documents/documen...
|
| Not a single category got something positive about it. The
| lower social classes for which this dumbing down was intended
| actually suffer badly from it; the upper classes didn't find
| ways to escape it either.
|
| It is estimated that when they reach the end of high school,
| pupils' level is late by 1 or 2 years (depending on the matter)
| compared to what it was in the last two decades of the XXth
| century (when high school access was already expanded
| massively, we're not talking about the 50s-60s-70s). And yet
| the high-school pupils are basically automatically all given
| the degree: 95% success rate compared to 75% in the 90s (and in
| those days that was after many had repeated 1 or more years,
| which they don't any more, they almost all pass all classes
| automatically, even though they didn't assimilate the necessary
| knowledge and understanding to follow next classes ).
|
| Another troublesome consequence is that it propagates. Very
| recently, universities, which for a long time tried to keep the
| same level as before, started to dumb down their courses an
| lower their requirements for passing years too, because the
| first years of university had become a slaughterhouse for a
| mass of students who were coming with a completely insufficient
| level (the high-school graduation serves as an automatic entry
| ticket for universities, there is no entrance exam). So the
| same effect as in primary and secondary education is about to
| happen, and selection is pushed to the Master level, but that
| last barrier will probably very soon break too (we already hear
| complaints about it).
| somethoughts wrote:
| For those interested in understanding what it looks like on the
| flip side - from the generally underserved side of things -
| here's an interesting article.
|
| Middle-school students embrace endless summer ... of linear
| equations
|
| https://edsource.org/2017/middle-school-students-embrace-end...
|
| The Effects of the Elevate Math Summer Program on Math
| Achievement and Algebra Readiness
|
| https://www.wested.org/resources/effects-of-elevate-math-sum...
|
| Khan Academy in 7th Grade Math Classes: A Case Study
|
| https://www.wested.org/resources/khan-academy-7th-grade-math...
___________________________________________________________________
(page generated 2021-12-03 23:02 UTC)