[HN Gopher] Math Academy pulled me out of the Valley of Despair
___________________________________________________________________
Math Academy pulled me out of the Valley of Despair
Author : gmays
Score : 206 points
Date : 2025-03-03 13:27 UTC (3 days ago)
(HTM) web link (mikelikejordan.bearblog.dev)
(TXT) w3m dump (mikelikejordan.bearblog.dev)
| ChuckMcM wrote:
| Always great to hear from people on the far side of the valley of
| despair. I don't think it is pointed out enough that people who
| fall off of "mount stupidity" can sometimes get really really
| stuck. In my experience when they do that at work it is quite
| traumatic.
|
| Another good book for the author and others is "5 Elements of
| Effective Thinking" by Burger & Starbird. It thinks _about_
| thinking which can sometimes side step the depression of suddenly
| not thinking you know anything about anything that accompanies
| that big drop off mount stupid.
| financypants wrote:
| what do you mean by falling off mount stupidity, especially at
| work?
| brm wrote:
| Mount Stupidity relates to section two of the blog post where
| it references a concept related to the Dunning-Kruger effect.
| ChuckMcM wrote:
| It was discussed in the article, but to be more explicit,
| sometimes a person who is sure of their understanding of
| things learns a new thing and that new thing opens their eyes
| to a _huge_ amount of complexity they were missing. They go
| from feeling like they knew everything there was to know
| about a thing to feeling like they know little to nothing
| about the thing. (this is the "Falling off Mount Stupidity")
|
| Depending on how senior they are at work, that can be quite
| traumatic. A lot of people in tech sort of base their self
| image on how smart they perceive themselves to be with
| respect to their peers. When that perception inverts their
| own world model makes them feel worthless.
|
| In the two cases where people I was managing this occurred
| (that I knew of) their productivity dropped like a rock and
| they became seriously depressed. One I managed to get back on
| track, the other left tech and I have lost track of where
| they ended up.
| mikelikejordan wrote:
| Mount Stupidity is the peak of overconfidence greatly
| outpacing your competency level. So, falling off is
| essentially being humbled by expreiences that make you
| realize you do not know as much as you think you do, and your
| confidence takes a major dive as a result.
| mikelikejordan wrote:
| Thanks for reading my blog post! I'm going to pickup that book
| today and make sure to start reading it!
| shermantanktop wrote:
| For child, being precocious in a subject is usually a curse.
| Being bright and a generally fast learner is also a trap. Hitting
| the wall is inevitable for almost everyone, but until that point
| your self-image is built on forward velocity, and especially
| relative velocity -- you're just faster than your peers. Turns
| out there are faster kids, they just aren't at your school.
|
| Parents can make this worse but it's pretty hard to prevent it.
| tippytippytango wrote:
| Yep, we all have to hit the wall and that's where we find out
| what we're made of. It can be a valuable experience with the
| right people around to help.
| skyde wrote:
| Can you give more detail on what you mean by it can be a
| valuable experience with the right people around to help.
|
| My son (7 years old) is gifted in Math and as a parent I find
| it extremely hard to decide how much I should push him
| (register him to math competition, weekend math club ...) and
| how much I should just let him get 100% on exam and not
| accelerate the learning.
| thfuran wrote:
| I guess how easy it is to do depends heavily on the
| district, but why not have him skip some math courses and
| leave extracurriculars for if he's really interested in it
| rather than just good at it? I ended up skipping three
| years of math by the end of high school, though I never did
| any club or competitions.
| sebg wrote:
| It really depends on how much your son wants to do math.
|
| As you can imagine, there is a whole world of kids like
| your kid who love math and want to do nothing more than
| math.
|
| If you're interested I can chat with you or recommend
| resources here if you decide to help your kid do more math.
| dbcurtis wrote:
| In my experience as a parent, you can provide the resource
| but don't need to push. Love of math will happen if it has
| the right environment. For a 7yo I might suggest looking
| onto Epsilon camp, and Art of Problem Solving (which is on
| line).
|
| My own kid went to MathPath (middle school camp by same
| people as Epsilon Camp). Loved it. "Yes, dad really, I want
| to spent a whole month of my summer doing math." The social
| experience is great for kids to be with other kids that
| like math.
| gunian wrote:
| rich people stuff is so fascinating to me my family went
| on one vacation my whole life i wonder why jesus made us
| poor because i loved school so much
| mezzie2 wrote:
| If you're 'good' enough/identified a certain way as a
| kid, they'll bend over backwards to get you in things
| like that even if you're not well off. I wasn't from a
| well-off family, but test scores in the top 0.1% meant
| _somehow_ there were scholarships to make camps and
| programs accessible once /if I expressed an interest.
| Whatever amount was required to make it affordable.
|
| I'm a thoroughly useless adult, so it was a waste of
| money on their part, but it does happen. Or at least it
| used to.
| in_cahoots wrote:
| This might be the first time in my life I've seen someone
| with a similar experience. As a big fish in a small pond,
| opportunities just present themself to you. Free summer
| camp that provides college credits? Going to
| national/state competitions just because? It's all second
| nature once you're 'that kid'. Even bullying goes away
| because everyone knows you have the ear of the teachers
| and administrators and/or wants your help on homework.
|
| Of course you still hit the wall later. But I see all the
| reports of how terrible it is to be gifted and am so
| grateful that my experience was different.
| mezzie2 wrote:
| You get away with _so much_ , it's a terrible adjustment
| to be 'normal' after that. I still struggle frequently,
| and have to take a lot of steps not to come off as an
| arrogant prick. Luckily, I have a fair amount of
| charisma, and I used to be an attractive young woman,
| which conceal a lot of social sins, but it's still one
| hell of an adjustment.
|
| If I'm honest, I never ran into an _intellectual_ wall. I
| did choose a comparatively 'easier' path, but that was
| more because I had a wide breadth of interests and
| choosing something easier meant I'd have more time to
| indulge my various interests. I was still getting
| interviews for tenure track positions out of grad school
| and when I did try to work post-graduate school, my first
| position was at an Ivy where I was the only one on staff
| who _didn 't_ come from an Ivy League school. (I was too
| lazy/too absorbed in my own things to do what was
| required to go to one.)
|
| I ended up disabled in my last semester of graduate
| school - the 'wall' in my case is my body being unable to
| accommodate the social/networking demands of an academic
| or high powered private research career rather than my
| running into a topic I felt was beyond me. Particularly
| combined with being on my own in a HCOL area as that
| lifestyle required: Doing all your life management on
| your own with no safety net _along_ with running at that
| high of an intellectual level is near impossible when you
| have a severe disability. (I have MS.)
|
| I've been 'stuck' intellectually once in my life, and it
| was the result of a medication we tried for symptom
| management, and I found the feeling horrifying, if I'm
| honest. It was the first time I'd run into a problem
| where I had to sit there and think and still couldn't
| come up with a way to proceed, versus running into a
| problem and just being too damn lazy to bother. (Being
| able to see what I would do to solve the problem is very
| different from being _motiviated_ to do so.) Apparently,
| most people feel that way fairly often? It made me way
| more sympathetic to people who didn 't like school or who
| don't like learning.
| dullcrisp wrote:
| You...have a PhD and you never encountered a research
| problem you didn't immediately know how to solve?
| whatshisface wrote:
| They mean a problem they didn't immediately think of
| something to try for.
| mezzie2 wrote:
| Yes, this. And I don't have a PhD, I have a Master's. I'm
| not saying the wall doesn't exist - that's why I
| specified I chose an 'easy' path. I'm just saying in my
| case the wall wasn't intellectual.
| popularonion wrote:
| I got put into some "smart kid" activities in grade
| school, but as a poor kid with zero advice from parents,
| I really had no idea what to do with it.
|
| No one told me that math is really 90% about writing
| proofs, all those homework problems I did were just the
| weed-out stuff, the academic equivalent of Leetcode.
|
| So when I got put into some "real" academic math as a
| teen, I crashed and burned hard. I didn't have a tutor
| and it never would have occurred to me to ask for one, so
| that was that.
|
| When I was 18 years old in my first year of college,
| after my first semester grades came in, a guidance
| counselor set up a 1-on-1 with me to talk about the
| Rhodes Scholarship process and what my research interests
| were.
|
| My response was: 1) what the heck is a Rhodes Scholarship
| and 2) how could I possibly have "research interests" as
| an 18 year old college freshman.
|
| That was the final chapter of society considering me
| "gifted", but it was just as well, I couldn't imagine any
| greater success beyond getting a job and being able to
| afford my own apartment.
| mezzie2 wrote:
| I'm curious how old you are?
|
| Mostly because a lot of my personal interests/ability to
| self-develop was related to Internet access. (My parents
| made VERY QUESTIONABLE financial choices and opted to pay
| for Internet access instead of food or clothing so I
| might have been freezing and my clothes all had holes in
| them but I could go online to talk to other smart kids.)
|
| Also because I remember me + my parents being sat down
| when I was in elementary school and having my options
| talked about. In middle school once I was proven to have
| programming and math aptitude during the dot com boom,
| educational experts came to us and discussed specific
| gifted learning options (including things like private
| schools, skipping grades, or even pulling me out of
| school altogether for private instruction). None of this
| was initiated by my parents - it was brought to us. This
| was in the 90s.
| popularonion wrote:
| I was born in 1985, we got dialup around 1996 I think?
|
| I did teach myself programming in the 90s, after my
| friend loaned me his floppy disk with all his QBASIC
| stuff. Then dabbled in PHP, MySQL, etc.
|
| We had one computer programming class in high school and
| I never got to take it because I had too many other
| electives. I don't think it would have done much for me
| by the time I could have taken it.
|
| It never really occurred to me as a teen that I could use
| the internet for getting really good at academics or
| broader "self-development" - I guess I just cared about
| video games and making money. Parents' attitude was as
| long as I was getting As and going to college they didn't
| need to do anything.
| tippytippytango wrote:
| He needs to learn grit and how to ask for help. He needs to
| learn some things are hard and that he can't always lean on
| his intelligence.
|
| The best way to guarantee a gifted kid wastes a lot of
| their potential is to be in an environment that is too
| easy. It creates a devastating mental habit that won't
| trigger until later in life, like college. Whenever they
| try to do something that doesn't come easy, their brain
| will try to shut down out of a kind of frustration. They
| won't know how to overpower it. It will cause depression,
| anxiety, shame and low self worth later on. Because the
| gifted kid will know they are wasting their potential, but
| blame themself for not being good enough to deal with it.
| It feels like being broken.
|
| All of this is created by being rewarded for maxing out the
| rewards of a trivial environment. Someone needs to
| patiently and compassionately teach them to value
| overcoming appropriately sized challenges. To find and
| operate on the edge of their potential and ask for help to
| operate beyond those limits.
|
| So yeah, grit and asking for help. Intelligence is mostly
| wasted without it.
| theodric wrote:
| Hey, stop describing me accurately, that's mean.
| GardenLetter27 wrote:
| It's just like exercise - if you just stay lifting
| weights you can manage easily, you never really progress,
| even though it still feels easy.
| shermantanktop wrote:
| I faced the same problem. Some analysis in retrospect,
| having kids who have now graduated college:
|
| - your child has a wall. At 7 he is not hitting that wall.
|
| - that wall is probably mostly related to the pure math
| concepts, and probably less to his actual age when he
| encounters them. This is my assertion and I cannot prove it
| but let's assume it is true. Precalc or calc is a typical
| wall moment, but for others it might be geometry or trig.
|
| - one response to an eager math learner is to move them
| through the curriculum faster. They are happy, because
| everything is fun prior to the wall! You get to be the
| parent of that kid who is great at math! Let's put the
| pedal to metal!
|
| - what acceleration means is that your kid will hit the
| wall at 13 instead of 15, or 14 instead of 16, etc.
|
| - those two years can make a big difference. Accelerating
| might be positive, in that they hit that at an age where
| you can support them better. It might be negative, in that
| they now have a crisis that their peers can't relate to.
| Not accelerating might mean that they respond to the wall
| by pouring their energies into age-appropriate activities
| instead, like listening to loud music or being grumpy.
|
| So no easy answers here. We did not think ahead clearly,
| and pushed forward, and had some decisions to make later.
| In retrospect I think it turned out fine, but I wish I had
| known that I was pulling the wall forward in time.
| zozbot234 wrote:
| If you're hitting a hard "wall" either some concepts are
| not being taught effectively, or there are some
| undetected gaps in your previous learning that make some
| things difficult to understand for you. There's nothing
| specifically about precalc that makes it inherently
| harder than, e.g. Algebra II or whatever if the teaching
| is effective. So being able to access alternate sources
| of understanding, such as Khan Academy or the Math
| Academy OP talks about, can be especially important.
|
| Moving through the curriculum faster is a common approach
| but it's also risky, because that's how the gaps are
| created that can then hinder your understanding later. Of
| course if you have reached true mastery of a given topic,
| moving forward is preferable to being bored to death, but
| assessing whether that applies can also be difficult at
| times.
| erikerikson wrote:
| The gifted programs we have liked most focus on depth over
| acceleration. Finding someone who can open the deeper views
| of things might be more supportive of his joy and longevity
| in the subject.
| moi2388 wrote:
| You shouldn't push him. You should encourage him.
|
| If he likes to do math you make it available, if he would
| rather play with legos instead of doing math you let him do
| that in his free time.
|
| You can encourage learning and problem solving without it
| having to be math, or pushing.
| thechao wrote:
| My youngest is not gifted in math. She's still in the top
| 1/3 of her class, through diligent study, repetition, and
| review. Over the last year she's gone from dreading to
| loving math. Please keep an open mind about your kiddo's
| interests and don't push too hard.
| Swizec wrote:
| > Turns out there are faster kids, they just aren't at your
| school
|
| Moving from Slovenia to SFBA in my mid 20's (~2015) was ...
| super fun like that. Sooo many people here are that most
| brilliant super talented engineer/founder/whatever from their
| home locale. But here we are just the norm.
| zdragnar wrote:
| We've got an idiom for that: being a big fish in a small
| pond.
|
| Then you move or have some experience that opens your eyes
| and you see that there are so many people out there that
| you're not actually as special / smart / talented / athletic
| etc as you thought.
|
| I've had the experience a few times myself, and it's always a
| bit of an existential wakeup call.
| wholinator2 wrote:
| Yeah, i was the best physicist the tiny impoverished state
| school had seen in years. I'm_significantly_ behind
| everyone else in my PhD program. But then, i tell myself if
| i can't be the best prepared, i can be the hardest worker.
| But realistically... nah. I'd rather stay _inside_ the 5th
| story window of my office. It's not a race, unless you're
| losing
| whatshisface wrote:
| Erdos could learn as much in five minutes as the average
| person can in five years, but there are more things to
| study than he had five-minute intervals.
| yapyap wrote:
| What
| recursive wrote:
| Erdos learn a million time faster than Grug. But Erdos
| still not learn everything.
| tornadofart wrote:
| If topics infinite: Knowledge of Erdos bigger than
| knowledge of Grug, but ignorance of Erdos as big as
| ignorance of Grug: both infinite :)
| com2kid wrote:
| My first job at Microsoft fresh out of college, my office
| mate had 2 PhDs, one in chemistry and one in physics.
|
| Related - About 10 seconds into my first job I decided that
| staying quiet for a bit and listening to people around me
| would be a very good strategy throughout life.
| hinkley wrote:
| Being in the 99.9th percentile for intelligence just means
| that there are 8 million people in the world who are smarter
| than you. And a few more every day.
| jjani wrote:
| > Moving from Slovenia to SFBA in my mid 20's (~2015) was ...
| super fun like that. Sooo many people here are that most
| brilliant super talented engineer/founder/whatever from their
| home locale. But here we are just the norm.
|
| Very similar story here! Grew up in the Netherlands, joined
| an SV company in my late twenties. Huge mix of imposter
| syndrome and sadness that I hadn't been able to experience
| such brilliant people earlier.
|
| Very much regret not choosing different educational paths
| that could've let me surrounded by them a decade earlier. I
| would've enjoyed life much more. On the other hand, I don't
| think either of us could've realized it before experiencing
| it first-hand, so no reason to beat oneself up over it.
| FuriouslyAdrift wrote:
| Accelerated advanced math at Purdue as a freshman flung me into
| that wall at high velocity. Nothing like a competitively graded
| class to make you hate a subject for life.
| hinkley wrote:
| The 'experimental' accelerated calculus program run by
| Stephen Wolfram had a similar effect and is why I decry
| trying to learn CS using AI and also why I don't like
| Mathematica or Wolfram. Fuck that guy. I loved math more than
| almost anybody I knew before that.
| progmetaldev wrote:
| As someone who tried to learn CS properly, as far as deep
| fundamentals, I was told by advisors that me being terrible
| at math would stop my career. I switched to a CIS degree,
| which at my local university was learning networking and
| Microsoft Office mostly. I dropped out of school and went
| into sales, while still having an interest in software. I
| started to pick up software development on my own, and
| found that I loved it even more without worrying about
| math. I ended up going to a "career" school, which would
| have turned out terribly, but I had a professor that taught
| all of the important programming and CS classes (there
| weren't too many CS classes, just fundamentals of OOP/data
| structures and algorithms).
|
| All of this to say I have been writing software
| professionally since 2006, and while I do struggle with the
| thinking behind functional programming and math-heavy
| subjects like graphics programming, I have written lots of
| business software that has brought me personal
| satisfaction. I would really like to understand calculus
| better, but I'm not sure if it would actually do anything
| for my skills in programming. If math is holding you back,
| think about whether you need the full breadth of CS
| knowledge, or if you just enjoy writing software.
|
| I became better at code organization, making code
| maintainable and simple enough to understand unless
| performance was an issue, and general people skills. I can
| understand why math and software are so close to each
| other, but at the same time, I don't think it needs to hold
| you back unless you really want to go into a topic that is
| deeply intertwined with math. It took me four times to get
| past pre-Calculus, and once I did, I realized that I just
| did not enjoy that type of math and didn't need it to build
| useful software (as in makes people's lives easier and/or
| generates profit for business) that I also find fun to
| create.
| hobs wrote:
| You think that's bad? :) I went to the University of
| Minnesota Talented Youth Mathematics Program and they
| assigned a fourth grader (me) about 50 hours of math homework
| a week.
|
| It genuinely wasn't until I was in my mid twenties that I
| wanted to look at anything mathematical again :)
| HPsquared wrote:
| The really bad thing about being precocious or a fast learner
| is it allows terrible working habits to develop in school - if
| you can max out the standardised tests by doing almost no work,
| this develops awful habits for life in general.
| GardenLetter27 wrote:
| Yeah, this is why IMO there should be more project-based work
| and just move faster and harder for skilled students in
| general.
|
| Get students to build their own drone with MCUs - so they're
| forced to overcome challenges and practical trade-offs.
|
| Introduce algebra in primary school, and calculus much
| earlier - so Green's functions, etc. can be taught in high
| school to those who want to study mathematics, and they feel
| what it's like to struggle to master concepts early on.
|
| Hopefully with more of a shift to online courses and AI, this
| will be possible. Unfortunately the majority of schools just
| act more like a daycare centre / prison.
| tonyhart7 wrote:
| "Introduce algebra in primary school, and calculus much
| earlier"
|
| algebra and calculus is college level century ago, we
| already bring it on HS level in some part of the world
| (Asian country) we already learn it earlier than most of
| the world but that's not sustainable
| zelos wrote:
| Calculus is 16-18 (A level, years 12-13) in the UK, 15-16
| for kids who do advanced maths.
| dominicrose wrote:
| Very true. Before working for a company I expected it would
| be OK or didn't give much thought about it. Meanwhile school
| was easy and I didn't put anything close to 40 hours per
| week. Plus the school was close. The first months working for
| a company were OK but then I was thinking oh damn I'm going
| to have to work 40 years like this?
|
| And then after a few years you learn that you can accept the
| workload but it's not enough to guarantee everything will be
| OK. In school everything is handed to us, really.
| nyeah wrote:
| This may be a great article.
|
| As an aside, all Dunning and Krueger showed is that everybody
| thinks they're in the top 1/3 to 1/4. (At least everybody in
| undergrad school at Cornell.)
| dahart wrote:
| Oh it's much worse than that, and it wasn't everybody in
| Cornell undergrad, it was a grand total of like 45 undergrads
| at Cornell who signed up for extra credit (which I imagine is a
| pretty big confounding factor - the A students don't need it,
| and the F students don't bother, on top of the massive
| confounding factor of only measuring undergrads from Cornell -
| they didn't measure any people who are truly incompetent or
| unskilled).
|
| The DK experiment depends on people _ranking_ themselves
| against the cohort, other people who they _don't know_. The DK
| effect probably doesn't exist, it has been argued compellingly
| that the paper does not demonstrate what it claims to.
|
| "To establish the Dunning-Kruger effect is an artifact of
| research design, not human thinking, my colleagues and I showed
| it can be produced using randomly generated data."(!!!)
| https://www.scientificamerican.com/article/the-dunning-kruge...
|
| "the asymmetry reported by Kruger and Dunning actually goes
| away, and even reverses, when the ability tests given to
| participants are very difficult."
| https://talyarkoni.org/blog/2010/07/07/what-the-dunning-krug...
|
| "The Dunning Kruger Effect is probably not real"
| https://www.mcgill.ca/oss/article/critical-thinking/dunning-...
| nyeah wrote:
| If you are downvoting, I hope you've read at least one of
| D&K's papers. Or at least looked at the plots. Not meta-stuff
| pro or con, but what Dunning and Krueger wrote.
| philips wrote:
| I have enjoyed the challenge of relearning mathematics with Math
| Academy as well. I find the format and reviews extremely helpful-
| it is so refreshing to end a lesson or review early if you are
| getting all the answers right compared to the drudgery of my
| schooling experience where you are getting question after
| question that isn't introducing a new mental challenge.
|
| My only desire is that their site worked on my phone- it would be
| nice to do a lesson when I have some free time and some paper.
| Exoristos wrote:
| That is known as "drill," and is vital to math success.
| dleeftink wrote:
| I'd wager there are not many skills or occupations were drill
| isn't vital to success.
| chrsig wrote:
| I'll call out 3b1b and khan academy for me. Especially over
| covid. Made math fun again.
|
| My middleschool principal thought it'd be a good idea to skip me
| over pre-algebra into alg 1.
|
| Turns out that doesn't work great, and I still have confidence
| issues because I have a hard time remembering the properties of
| addition & multiplication _by name_. I know the rules.
| rahimnathwani wrote:
| My middleschool principal thought it'd be a good idea to skip
| me over pre-algebra into alg 1.
|
| Next time you read a novel, try this:
|
| 1. Read each sentence at half your normal reading pace
|
| 2. Skip every other chapter.
|
| Sounds ridiculous, right?
|
| That's my reaction when people propose grade skipping as the
| only solution for a child whose natural pace is 2x the
| 'standard' pace at which math is taught in school.
| harrison_clarke wrote:
| a lot of school is redundant, and the courses are often non-
| sequential
|
| skipping chapters of a novel doesn't work very well, but it
| works great for the encyclopedia, and pretty well for a lot
| of textbooks
|
| it's also not that hard to use khan academy or wikipedia to
| fill in the gaps, if you did miss something
| rahimnathwani wrote:
| I'm thinking specifically about the USA math curriculum.
| It's pretty sequential until 8th grade or so.
|
| Filling in gaps is fine for people with good study skills,
| but that excludes the vast majority of elementary school
| students.
| harrison_clarke wrote:
| the "smart" kids do seem to have those skills, though.
| either that, or they're being tutored on the side, or
| they just require fewer examples to get it
|
| whatever the case is, i think the idea behind skipping
| grades is that the kid isn't learning much in the classes
| they're in. they may not learn much in the next level
| either, but it allows the school to test that they've
| learned what they were supposed to (from class or
| elsewhere), while wasting less of the student and
| teacher's time
|
| that said, testing out seems like it'd be better than
| forcing the kids to sit through yet another math class,
| even if it's one level higher. more time to touch grass,
| or read in the library, etc.
| rahimnathwani wrote:
| Yeah the smart kids may need fewer examples or fewer
| practice reps, but very few kids can skip entirely, say,
| 4th grade math, and not struggle to catch up. It seems
| unnecessarily painful, when instead they could be taught
| smoothly at double the pace.
| eitally wrote:
| The best solution is to offer accelerated math classes in
| public schools, in both elementary and middle. Mostly in
| middle school because elementary math can usually be
| handled through differentiated instruction by the teacher,
| unless the child is exceptionally advanced.
|
| I really like the way my kid's middle school does it:
| accelerated 6th grade math covers the entirety of the 6th,
| 7th, and 8th grade standard math curriculum, which sets the
| kids up for algebra in 7th grade and geometry in 8th.
| Because the standard middle school math curriculum is
| essentially just advanced arithmetic, it's pretty
| straightforward to bundle this way. It also makes it easy
| to inject 7th graders who missed 6th grade accelerated math
| into the accelerated track _if they pass the algebra
| qualifying test before 7th grade_.
|
| When I was growing up the G&T program started in 4th grade
| and cohorts from multiple schools were pulled into a school
| that ran the "gifted" program. Essentially all the kids
| were tracked from 4th grade through high school graduation
| and there was no real possibility for non-G&T kids to get
| into the "gifted" classes in middle school. In HS that just
| transitioned into APs and college dual-enrollment; by the
| time I graduated HS in '99, I had 22 credit hours of
| college classes banked, including dual-enrollment bio and
| calc 1 + 2, plus a bunch of humanities APs.
|
| Today -- at least in our bay area public high school --
| there's no tracking outside of math and the vast majority
| of classes can contain students in multiple grades. That
| absolutely was not the case when I was in school, and imho
| it's an improvement.
| djeastm wrote:
| Yes, it's ridiculous. They should really only grade-skip in
| math after giving the student take-home exercises during the
| current year that will serve as a replacement for the skipped
| grade. It's irresponsible to do otherwise, imo.
| rahimnathwani wrote:
| Agreed, but I'd rank the choices in this order. #3 is still
| better than #4.
|
| 1) Allow the child to go at their natural pace.
|
| 2) Grade skip every 2 years, with take-home exercises.
|
| 3) Grade skip every 2 years, without take-home exercises.
|
| 4) Force the child to go at the same pace as the rest of
| their same-age peers.
| chrsig wrote:
| I a missing component is a plan for recourse if the
| student doesn't take to the new pace/material.
|
| That was my biggest problem, that and I wasn't actually
| on-board for the skip. Educators need to learn how to
| admit when they fucked up and learn how to improvise a
| new strategy.
| whatshisface wrote:
| A noun that only refers to one thing isn't a real word, so if
| you want to cure yourself of "the associative property" being
| meaningless, you could study other algebras where the rules are
| different.
| chrsig wrote:
| this was actually one of the things that really turned things
| around for me actually. it took probably 25 years in between.
| abstractbill wrote:
| Congrats on your progress!
|
| Over the past few years, while homeschooling my daughters, I've
| come to see the way math is usually taught as horribly
| pathological. In the US, where we live now, it's often seen as a
| competitive activity -- almost like a sport. In the UK, where I
| grew up, that wasn't the case but still it was taught as this
| huge body of knowledge and skills with almost no motivation.
|
| My daughters are so advanced in math and I really don't believe
| it's even mostly due to innate ability. It's because, just to
| take an easy random example, when we studied geometry our very
| first lesson was me pointing out that the word "geometry" just
| means "earth measuring", and it was useful for farmers to be able
| to do that. Or, when we proved the irrationally of sqrt(2), of
| course I entertained them with the tale of Hippasus being thrown
| into the sea by the Pythagoreans. For basically everything we've
| learned there are so many fun stories. It makes me sad that most
| students of math never get to hear them.
| pipes wrote:
| As a b and c grade student, who messed about, stumbled through
| a not very good info technology degree at university I
| definitely agree with this. The stories and lore are what makes
| me now so interested in programming and software engineering.
| I've pretty much taught myself everything programming related
| and that's what I work as too. I desperately want to learn math
| up to and including calculus as I feel like it's a hidden shame
| that I'm a programmer with not much math ability. I'm actually
| considering signing up for math academy.
| rcarr wrote:
| I really want to do Math Academy and even briefly tried it a year
| ago. It's absolutely great but it's also very expensive. I know
| that math skills are invaluable, it's far cheaper than schooling,
| and that long term the investment is likely to pay for itself but
| when you're skint $49/month is still a pretty hefty sum,
| especially if you live outside of America. For context in the UK,
| a basic gym membership (PS17/month) and a SIM only phone plan
| with unlimited data (PS22/month on a two year contract) only
| costs PS1 more in total than Math Academy (PS38/month). I can't
| help but feel that the people who would benefit from it the most
| are also the people least likely to be able to afford it.
| gen_greyface wrote:
| +1
|
| I wish there was PPP for the subscription, i tried for a few
| months but stopped the subscription recently.
| nsfmc wrote:
| my read as a US person is that math academy is optimized
| towards students who would otherwise be well served by an in-
| person supplemental math program. at the earlier grades for
| math academy (grades 4-5 etc) the main competition i've
| encountered are in person programs like AoPS, Russian Math, or
| Kumon. The prices for those range between $450-$100/mo and for
| a student or student and parent combo that may be looking to
| supplement their math classes or for somebody who needs to home
| school for a period of time, mathacademy at $50/mo is a steal.
| suncherta wrote:
| The way I come to look on such offers (monthly unlimited
| subscriptions) is not the net price itself, and not future
| supposed returns to it (who knows what they be, and they for
| sure will depend on many other things), but how many hours a
| week I am willing to spend on that service.
|
| If you can and willing dedicate on average 2 hours a day (a big
| commitment but I think I was able to hold it for several month
| with them) the cost of mastering, say, Linear Algebra will be
| ~4 less then if you subscribe and will be spending ~30 minutes
| a day.
| ohgr wrote:
| Go on eBay and buy the following Open University book sets.
| They go for around PS30-50 a pop: MU123 (basics), MST124 (more
| complex). 6 months worth of study in each book set. If you like
| it do MST125 (even more complex) and M140 (stats) after. That's
| the first year of a mathematics degree literally from the
| ground up through GCSE and A-level stuff. If you really like
| it, get a student loan and do the associated accredited degree.
|
| PS30 for 6 months is pretty damn cheap and you get to keep it
| forever!
|
| ebay example of the latest edition for sale:
| https://www.ebay.co.uk/itm/197011707080
|
| On archive.org too if you are happy with PDFs:
| https://archive.org/search?query=creator%3A%22The+MU123+Cour...
|
| First MU123 book A:
| https://archive.org/details/BookAMU1232ndedOU2014/MU123-Book...
|
| This is a proper accredited course developed over 50 years or
| so with its own textbooks and material from a respectable
| university, not a gamified subscription portal experiment put
| together by god knows who that can disappear in a puff of smoke
| at no notice.
| AntoniusBlock wrote:
| The OU maths books are indeed very good. This is the way to
| go.
| NlightNFotis wrote:
| I'm studying the Q31 (BSc Maths) on Open University.
|
| I can second this recommendation. The maths books are
| _excellent_.
|
| It's hard to explain how, but let me try: most of the maths
| textbooks I possess (plenty of them) are written with the
| assumption that you attend lectures at a classroom and use
| them for extra material/exercises/reference.
|
| The OU books are written with the assumption that you learn
| from them as the primary material, so they go a lot further
| with regard to explaining things as well as producing them
| from first principles.
| inglor_cz wrote:
| I wonder if they could charge lower rates for people who live
| in poorer parts of the world.
|
| $49/month is almost nothing to me now, but it would be
| prohibitively expensive for a 15 y.o. me in freshly independent
| Czechia.
|
| I suspect it would also be prohibitively expensive for most 15
| y.o.s in the developing world today, and these are the guys and
| gals who stand to gain the most.
| david_allison wrote:
| It's not just the price. You'll find a number of 15 year olds
| have no ability to spend money online.
| criddell wrote:
| Did you try contacting them and asking for a discount?
| Sometimes all you have to do is ask.
| eps wrote:
| > very expensive
|
| I guess it depends on where you are at in the world, but in our
| neck of the woods $50/month is an absolute bargain compared to
| using a tutor. Not to mention you get to work at your own pace
| and to practice spaced repetition consistently.
| raincole wrote:
| It is. But I don't think there is an alternative way to make it
| sustainable. There are just not that many people who are
| serious about self-education, and you won't like it to cater to
| the less dedicated customers.
|
| > I can't help but feel that the people who would benefit from
| it the most are also the people least likely to be able to
| afford it.
|
| Even if it were $10/mo, the people who would benefit from it
| the most (around the world) still can't afford it.
| mikelikejordan wrote:
| Hey everyone! This my blog. Just made an account on here so I
| could comment. Thank you all for the support and reading my
| story! :)
| pona-a wrote:
| I am currently studying for our country's version of the SAT and,
| having tried Math Academy -- having been convinced there is
| nothing anywhere as polished and developed on the market -- I
| still had to cancel my subscription after the first month. The
| price just wasn't worth it; over a single year, it translates to
| a cost greater than one-on-one tutoring.
|
| Small companies have to understand the value of local pricing --
| nobody is willing to pay above h percent of their salary for a
| service X, and there's only so much that rule can be bent. I
| understand that, at the end of the day, the company still has all
| their expenses in USA prices, but for digital services with no
| manufacturing or logistic costs, it can be better to make a
| modest profit than none at all.
| chamomeal wrote:
| Wow that's a pretty glowing review of the service. Sucks about
| the pricing though.
|
| I haven't really looked at math academy, but I was in school
| (including college) I probably learned 40% of math from khan
| academy, 40% from textbooks, and maybe 10% from lectures.
|
| How does math academy compare to Khan academy?
| pona-a wrote:
| Math Academy uses spaced repetition for skills with tiny, to-
| the-point interactive lessons (typically following "theory,
| some exercises, theory, some more exercises" formula) based
| on an initial diagnostic test, where the skills are
| structured as a graph of dependencies.
|
| I didn't, at the time, appreciate how challenging a problem
| it was until I started researching Bayesian Knowledge
| Tracing. While their definition of a skill can be a bit
| narrow, thus putting more time into reviewing things I'd
| rather move on from, it does work from what I've observed.
|
| I recall they had a course on Abstract Algebra and other more
| advanced subjects, so if you're really interested, the great
| thing about subscriptions is that you can afford to try it.
| ABS wrote:
| I decided to try it 10 days ago exactly because of the pricing.
|
| It would be impossible for me to have one-on-one tutoring for a
| year at only EUR465 ($499 but I'm in EU). And that's regardless
| of the tutoring quality
| simplegeek wrote:
| Inspiring and well written. It resonated with me for I find
| myself in a similar position. I wonder how much time did the
| author commit on weekly basis. Nonetheless, I wanted to signup on
| Math Academy immediately but doesn't look cheap.
|
| Are there any other recommended websites for learning math (apart
| from Khan Academy, Math Academy)?
| mikelikejordan wrote:
| Hey! This is my blog post thanks for reading! At my peak I
| spent roughly 4h a day on math academy because I wanted to get
| 100+ XP. I've brought it down to about 2h a day since I'm also
| teaching myself python for my goal of being a MLE in the
| future.
| BinaryMachine wrote:
| Great post! It's always interesting to see the experiences of
| fellow peers going through Math Academy.
|
| It took myself 2 1/2 months to complete Mathematics for Machine
| Learning on Math Academy last year (2024) working through reading
| material, taking notes, and completing all the exercises took all
| day everyday I loved it, this was after I completed Khan Academy
| (starting from the beginning of mathematics negative numbers, to
| the end differential equations) because I kept putting it off for
| years when I got to busy.
|
| The main thing for me was learning not to get too frustrated when
| getting an answer wrong. If I made a mistake, I focused on
| understanding what went wrong, looking up youtube videos on the
| topic if it was confusing, and then trying again.
|
| At the end of a lesson I wish I had someone to bounce questions
| off of but thats when I used chatGPT.
|
| Congrats!
| mikelikejordan wrote:
| Thanks for reading my blog! M4ML is the next course for me
| after I complete MF3. What are you doing now on math academy!
| BinaryMachine wrote:
| Yeah! Unfortunately at the time I had gotten laid of from
| work so I had extra time just not extra $ to keep paying
| monthly subscription, also some courses still said coming
| soon at least the ones I wanted to take when I was taking
| M4ML.
|
| Good Luck with M4ML its a great course! Covers a lot, I was
| impressed, wish there was some videos or more visuals but it
| doesn't hurt to use youtube. I took maybe 7 pages of notes on
| my github and each over 4000-8000 lines (I used the notes to
| do the step by step exercises it was easier for me to type
| notes and do the exercises on computer than pen and paper
| this is what I used to do).
|
| I take the notes because I will probably forget, but I think
| its key to always be learning and keep practicing even when
| your done the course.
|
| Once I get hired again I will def take Discrete Mathematics.
| In the mean time I've just read books on ML and LLMs, free
| online courses, youtube videos etc.
| mikelikejordan wrote:
| I understand the feeling. You'll get another job soon and
| be back to crushing math problems on math academy. Thanks
| I'm excited for M4ML a lot. I feel like I'll experience
| math in a way I never have before. Would you be willing to
| share your github of notes?
| jimsojim wrote:
| Could you have completed the entire curriculum on your own
| using ChatGPT without needing Math Academy?
| sn9 wrote:
| Not at all. ChatGPT can't even reliably do arithmetic.
| tptacek wrote:
| Math Academy is awesome, I'm fully hooked, but, repeating
| something I wrote elsewhere: it is a bleak existential
| confrontation with your ineptitude with fractions.
| plutosmoon wrote:
| you and me both buddy
| tptacek wrote:
| I'm signing up like, oh, I have a lot of gaps I can fill in
| with calculus, and it's like, no, you got a lot of gaps you
| need to fill in with simplifying cube root expressions. The
| best is every once in awhile it double checks to make sure I
| still know what multiplication is, with like Dick and Jane
| bought 10 apples problems. I have given it no reason to
| believe otherwise! But I trust the algorithm.
| tptacek wrote:
| Also, I go too fast through them and do stuff in my head
| that I should write down and make dumb mistakes, and when I
| get the "Incorrect" I'm like, yeah, I see exactly the dumb
| thing I did, let's move on, and it's like, no, let's do a
| next problem that's real nice and easy to make sure you get
| this and I'm like "stop patronizing me motherfucker".
| golly_ned wrote:
| I tried math academy about a year ago since I wanted to finally
| get a strong grasp on linear algebra.
|
| But I gave up during the diagnostic test. It was very, very long,
| and didn't seem to be adjusting in difficulty, and asked similar
| questions. I'm normally a fast test-taker, but after about a
| third, I figured it would take me an hour and a half or two hours
| more.
|
| I hope they've updated it by now.
| littlekey wrote:
| It's still the same and I agree it's a splash of cold water to
| sign up for the platform and immediately be put through the
| gauntlet. I would say it's worth getting through it as none of
| the actual course material is like that, it's much more bite-
| sized. But I hope they figure out a way to smooth out that
| onboarding process, maybe split the test into segments and
| weave them into the rest of the material somehow.
| cultofmetatron wrote:
| def try again. I personally absolutely bombed it. But you know
| its been 20 years since I've been in a math class. Its all to
| figure out where to start you off. It doesn't matter where that
| is, it matters where you go from there.
| zelos wrote:
| You can do the diagnostic test in multiple sittings: I think I
| split it up into 3 parts?
|
| To some extent, though, I don't think you're meant to spend
| lots of time on each question struggling to figure it out as
| it's trying to determine what bits of the course you can skip,
| so if you can't answer a question relatively easily it's best
| to just say "Don't know" and move on so you get some revision
| during the course.
| MisterTea wrote:
| $50/month? I know people with children who can't afford the NYC
| mandated trash cans which cost the same...
| bost-ty wrote:
| I read this article because I wanted to learn more about their
| Math Academy experience, but I found the preamble and backstory a
| little long, which caused me to skim.
|
| Re: Math Academy, I used the service for ~3 weeks last year from
| a post here on HN by the guy responsible for the AI/ML knowledge
| graph behind the platform (I believe his first name is Justin). I
| was "only" doing about 30-60 minutes a day (a little bit higher
| than their guidance, but low for someone not doing math otherwise
| IMO).
|
| N.B. Due to substandard early instruction combined with being
| "gifted and talented", I was placed by the test into Math
| Foundations 1 (or 2?). For example, I still don't have an
| active/working mastery of the unit circle. So if you're a real
| whiz, YMMV.
|
| I found Math Academy effective at showing me my weaknesses and
| sharpening those skills in the short term, but I probably didn't
| do it for long enough to benefit from the spaced repetition
| effects. I found the UI/UX better than Khan Academy (sans AI),
| and much less tedious (when I demonstrated understanding, the
| questions moved on or increased the complexity vs. doing the full
| problem set no matter what).
|
| When I cancelled within the first month to receive my refund (see
| other commenters mentioning the high price), I was surprised to
| see my support email and refund request email both went to one of
| the founders (or owner?), Sandy Roberts, who was emailing me
| while also attending her daughter's college orientation (or
| helping her move, can't recall right now).
|
| Cancelling was painless once I realized I was getting a response
| from someone at the platform --- so if you're interested in
| trying it, I can recommend giving it a shot. Maybe there's some
| sort of economy for them if more (adult) people sign up, because
| 50 USD still feels a bit steep.
| Nifty3929 wrote:
| "other commenters mentioning the high price"
|
| I understand that everybody has different financial
| circumstances, but personally I find it so odd how people
| prioritize their spending. $50/mo to level up your math game?
| Too much. 8x $6 lattes per month - totally worth it. $200k+ for
| a university education after which you STILL won't know basic
| math (or much else useful for most majors) - super totally
| worth it.
|
| For me I'm just willing to pay a lot more than other folks are
| to learn interesting skills. Math, sailing, music,
| leatherworking, perfume making, whatever - to me that's such a
| good use of money.
| littlekey wrote:
| I agree with your overall point but I don't think those
| comparisons are very useful. Regardless of my monthly latte
| consumption, an extra 50/month is 50/month... the only real
| comparison imo is how much you'd be saving vs hiring a tutor
| or simply going through books yourself for free. I think it
| comes down to whether you have the drive to learn from books.
| If so then that's clearly the best move. But I'm willing to
| pay the 50 because this is the only approach that's worked
| for me so far. It's worth it but it still stings.
| Nifty3929 wrote:
| Fair point. IOW, what you're saying is: If learning math is
| your goal, is this the best (or most cost effective) way to
| do it? Sure, for some it would be, but for others they'd be
| better off with books or some other alternative.
| djaouen wrote:
| A rare, insightful post from someone who _didn't_ do well in
| maths in high school. A true HN treat!
| TrackerFF wrote:
| Side note: An absolute pet peeve of mine is how the Dunning-
| Kruger paper is being misrepresented, to the point of abused,
| like the graph included in this blog post.
| Denzel wrote:
| In what specific way did this post misrepresent or abuse the
| Dunning-Kruger concept? (Btw, the graph used is the same one
| used on the Wikipedia page for DK.) If you're able to explain
| what you understand to be misrepresented, you can clear up the
| misconception for others -- like me.
| TrackerFF wrote:
| You can find the original paper here: https://www.researchgat
| e.net/publication/12688660_Unskilled_...
|
| It's a mere 15.5 pages of actual text.
| qntty wrote:
| I don't see that graph anywhere on the Wikipedia page
|
| https://en.m.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effec.
| ..
|
| I do see other graphs that tell a different story. Namely,
| that confidence is a monotonically increasing function of
| competence. If the data supports the idea that there is a
| valley of despair where confidence decreases as competence
| increases, I must be missing it.
| strken wrote:
| I am likewise baffled by this. The entire "Mount Stupid"
| theory of Dunning-Kruger is wrong, and the blog shows that
| same wrong graph for me.
|
| Maybe the author is running some kind of A/B test between
| the actual Dunning-Kruger paper graph and the fake one?
| erikerikson wrote:
| Here, from Wikipedia:
|
| https://commons.wikimedia.org/wiki/File:Dunning%E2%80%93Kru
| g...
|
| [edit: yes, it isn't currently on the Wiki page. On the
| other hand, I've seen that graph associated with that work
| before]
| tux3 wrote:
| This is Commons, not a Wikipedia article. This image is
| incorrect, has been removed from the enwiki article, and
| is in fact explicitly tagged with a disputed factual
| accuracy notice.
|
| Dunning-Kruger described a relationship between people's
| subjective opinion of their skill, and their performance
| on a test. They find the subjective curve is less steep
| than the objective one (low performers believe they are
| closer to the center than they really are, and so do top
| performers). There's no "peak of stupid", or anything
| else on that graph.
|
| Repeating vague associations you've seen on the Internet
| before is how misinformation spreads.
| erikerikson wrote:
| I dispute nothing you write. Looking at the paper that
| graph is not within it.
|
| Either my eyes skipped past it or that dispute notice was
| added after I linked the image. Regardless it belongs
| there.
|
| I have previously seen a similarly shaped graph with
| Dunning-Kruger effect discussions many times, including
| on Wikipedia I believe. Now I'm curious what the source
| of the misrepresentation is since it does not appear
| quite derivable without artistic interpretation from the
| paper's data.
|
| Regardless, I'm glad to update and add to my beliefs.
|
| Please note that despite the implication that seems to be
| in your final statement, I did not mean to say the graph
| was correct, only that it is a graph commonly associated
| with the paper's message and thus understandable for the
| author to have used. From that, the use of it doesn't
| quite come from nowhere. I'm fact, I didn't really say
| much at all. While Wikipedia is the first search result,
| the Decision Lab is next which has a similar, even more
| distorted graph on their page [0] and yet is a fairly
| well esteemed organization.
|
| Glad to improve my knowledge but that the graph is in
| common use is not misinformation even if the graph itself
| misinforms and isn't from the paper.
|
| [0] https://thedecisionlab.com/biases/dunning-kruger-
| effect
| cleandreams wrote:
| I am going through Math Academy and I like it very much. I have
| done advanced technical work in my field but my math background
| had weaknesses from my public schooling in a large urban area and
| some experimental math instruction in high school. The ability to
| do it over is oddly exhilarating.
| bbconn wrote:
| Who is building the Math Academy equivalent for other subjects
| (especially other sciences)?
| sn9 wrote:
| From listening to interviews, it seems like after completing a
| full undergrad's worth of math courses, they plan to expand to
| CS and math-adjacent fields (probably physics at least?).
| keeeba wrote:
| Nice story - I've seen you on the leaderboard a few times. Good
| luck through the rest of Foundations III
| yapyap wrote:
| This kind of started to feel like a Math Academy promo at the
| end.
| hasanas wrote:
| Thank you for sharing your wonderful story. The prelude triggered
| a lot of emotions and memories from my own past.
|
| Math Academy looks very enticing!
| danielecook wrote:
| I'm doing math academy and I have two comments. First, the value
| of this site comes from its content which is very thorough. I
| think it's a great way to learn math.
|
| Second - I love the website. It reminds me of what I think of as
| the golden age of web design where sites were mostly server side
| rendered with a little jquery / Ajax sprinkled in, and more
| information density was preferred.
| darkteflon wrote:
| I've used Khan Academy with the kid and always been impressed,
| but Math Academy sounds very promising indeed. Anyone have an
| informed view on the relative merits? I don't mind paying the
| monthly fee if there's genuine value.
| sn9 wrote:
| https://jonathanwhitmore.com/posts/2024-09-10-MathAcademy-af...
| Rendello wrote:
| Math Academy and a SQLite course pulled me out of despair as
| well. I grew up thinking I was relatively smart and being able to
| learn on my own, but only randomly and sporadically. After not
| learning much the past few years and feeling very stupid, I
| decided to look for some paid courses to take on Hacker News.
|
| The SQLite course was in a very different video format and took
| roughly 20 hours, but I learned a lot and immediately used that
| knowledge in two software projects that would've seemed
| insurmountable to me.
|
| As for MA, it's taken a lot longer and has been difficult. I'm
| now at 6000XP and halfway through Fundamentals II. I have a lot
| of thoughts, but I (kind of) plan to (probably not) write a
| review after having completed Foundations I-III, since I haven't
| talked to anyone else who's done so so far.
| bb86754 wrote:
| Any chance you remember the name of the SQLite course?
| Rendello wrote:
| It was High Performance SQLite:
|
| https://highperformancesqlite.com/
|
| The course content could all be learned from the excellent
| SQLite docs, and in greater detail. However, I think paying
| the $200 was worth it for me, since the course led me through
| a structured learning path, this is my "year of structured
| learning", after all. I had some minor complaints, but in the
| end I learned a ton and feel empowered because of it. I'd
| like to take his Postgres course too but the price is too
| high for me.
| lolu_plan wrote:
| which sqlite course ?
| harry8 wrote:
| Tried it for one of my kids, mini-review:
|
| From Parent: Expensive Alpha quality - missing absolute value
| signs, auto-marks "1./2" as wrong compared to "1/2", parental
| controls have bugs, eg you want to pause, then change the date
| won't update the date you're pausing to. Uses XP (experience
| points) as gamified motivator and then doesn't respect their
| value by docking unnecessarily or due to bugs. Emailed on sign up
| to be "personally welcomed and invited to respond with feedback,
| or any questions" So I did, because I want this kind of effort to
| succeed. Response totally ignored all content of the email and
| suggested he could delete the account for me(!)
|
| From student, who is quite a way ahead of his peers in math.
| "boring, annoying and stupid"
|
| Account is paused due to the above, if we cancel it I'll be
| pretty annoyed given the unused portion and expense.
|
| Khan Academy has very similar merit. You can donate a lot less
| than USD$50 / mth.
|
| Maybe we got unlucky and the good intentions of "personally
| welcoming and requesting feedback, inviting questions" was lost
| due to getting snowed under so response LLM happened and totally
| ignoring follow up rather than being deliberately rude? Could
| well be.
|
| Lotta hype about it, justified? I didn't see it.
| wjholden wrote:
| If anyone from Math Academy is reading: the price point just
| doesn't work for me. I'm happy to pay ~$100/year for our family's
| Duolingo subscription. $49/month is too much.
| soonyatha wrote:
| I started reading the article without paying much attention to
| the word Academy in the title, and was attracted by the single
| word 'Math'. In the first part, I found it interesting when the
| OP talked about their learning experience. In the final part, my
| interest faded when their writing turned towards a business
| entity.
|
| Reeks of a publicity stunt.
| Gimpei wrote:
| I had a similar experience where math went from being easy and
| fun to an intimidating and painful slog. My problem was just how
| focused most courses are on learning techniques for solving
| problems. I found all those endless substitutions that you learn
| in calculus to be infinitely dull and so it was difficult to do a
| good job. Ditto for the solution techniques for differential
| equations. Don't get me started on matrix inverting. I think I
| had to do a 5x5 matrix once for a homework assignment. What a
| colossal waste of time.
|
| Proof-based math classes came like a revelation to me. When I
| took Real Analysis, for the first time in over a decade, math was
| fun. You weren't just memorizing and reapplying recipes. You were
| seriously thinking about unique problems and devising solutions.
| And all the while, you were learning where all these techniques
| actually came from and how everything connected together.
|
| I don't understand why we can't have more proof heavy math in
| high school. Who cares whether you remember the arctan
| substitution or whatever in an integral; I'd always just use a
| solver for that anyway. I'd rather be learning about what an
| integral is in the first place.
| cultofmetatron wrote:
| > I don't understand why we can't have more proof heavy math in
| high school.
|
| proof based math requires critical thinking and its a lot
| harder to scale the teaching of critical thinking. We dont' pay
| enough for teachers of quality to be able to do this at the
| public school level. Its also much harder to test for in
| standardized tests.
| zozbot234 wrote:
| > Its also much harder to test for in standardized tests.
|
| You could test it using interactive proof verifiers. This
| would also make it a lot easier to teach, since proof
| verifiers can handle even very complex mathematical proof via
| the repeated application of a mere handful of rules. (The
| rules are also surprisingly similar to the familiar "plug and
| chug" workflow of school-level math, only with different
| underlying objects - lemmas and theorems as opposed to
| variables and expressions.)
| nicf wrote:
| I'm a private tutor who works with adults on proof-based math.
| I've often had a similar thought to the one you're expressing
| here --- I also found proofs pretty revelatory when I first
| exposed to them and wondered where this magical tool had been
| all my life --- but I wonder how well this experience would
| scale to the mass of students in high school math classes.
|
| After teaching proof-writing to my students for several years
| now, I've seen a lot of variation in how quickly students take
| to the skill. Some of them have the same experience that it
| sounds like you and I had, where it "clicks" right away, some
| of them struggle for a while to figure out what the whole
| enterprise is even about, and everything in between. Basically
| everyone gets better at it over time, but for some that can
| mean spending a decent amount of time feeling kind of lost and
| frustrated.
|
| And this is a very self-selected group of students: they're all
| grown-ups who decided to spend their money and spare time
| learning this stuff in addition to their jobs! For the kind of
| high school student who just doesn't really think of themselves
| as a "math person", who isn't already intrinsically motivated
| by the joy of discovering what makes integrals tick, I think it
| would be an even harder sell. High school math teachers have a
| hard job: they have to try to reach students at a pretty wide
| range of interest and ability levels, and sadly that often
| leads to a sort of lowest-common-denominator curriculum that
| doesn't involve a lot of risk-taking.
| ninetyninenine wrote:
| A wonder no one uses this for programming.
| nicf wrote:
| Uses what?
| ninetyninenine wrote:
| Proofs
| AntoniusBlock wrote:
| A more rigourous approach was tried after WW2, when Americans
| feared the Soviets were edging ahead
| mathematically/scientifically. It was called "New Math" [0].
| For an example of the type of textbook high school students
| were taught from, check out Dolciani's Modern Introductory
| Analysis (the 1960s and 1970s editions only; the later editions
| were dumbed down, especially when Dolciani died) [1], which
| starts with set theory, logic, field axioms, and proof writing
| techniques.
|
| [0] - https://en.wikipedia.org/wiki/New_Math
|
| [1] - https://archive.org/details/modernintroducto00dolc
| Evil_Saint wrote:
| I completely disagree. Proofs are very abstract. Learning to
| read them is a skill you have develop before you can learn
| anything from them.
| stared wrote:
| Dunning-Kruger effect does not look like that!
|
| Compare and contrast with actual one:
| https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
|
| Sure, novices overestimate their skills - but the relationship is
| monotonous, with no peaks or valleys at all.
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