[HN Gopher] Why don't we use the math we learn in school?
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Why don't we use the math we learn in school?
Author : enigmatic02
Score : 25 points
Date : 2022-01-26 22:12 UTC (47 minutes ago)
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| lordnacho wrote:
| This is a good question, why is it that seemingly nobody uses the
| math they've been taught?
|
| When I was in school, my math teacher used to write AMBS on the
| board before calculus lessons: Algebra Must Be Strong. What
| happens when you study calculus is you end up rehashing algebra
| over and over again until it's second nature. Consequently if you
| find someone who's done well at calculus, you can be sure they
| can do algebra.
|
| Someone mentioned this in relation to RenTech. Why do they hire
| mathematicians who have studied incredibly complex things with
| seemingly no relation to trading? One reason might be that people
| who have done that know the fundamentals very, very well.
|
| Similarly accountants don't use vectors or geometry at work
| either, but they certainly are comfortable with arithmetic and
| its application in spreadsheets.
|
| When I look at my own education, it is also the case that the
| things I'm least sure of are the deepest, latest courses that
| build on everything else. Probably if I built on top of those I'd
| be more comfortable with them. Taking this line it would appear
| that you can't just teach people the math they'll use, because
| they won't really get it until they try to do the next thing.
| ohiovr wrote:
| My school rarely ever directed mathematics instruction in
| relation to another skill or problem. Sure math might be used in
| industrial arts, or in home economics, but the instruction phase
| of the math is always 100% abstract. If people knew all the
| interesting things you can do with math they would be more likely
| to use math more often and remember what they learned. This was
| certainly the case for me and may have been the only thing that
| made me even care about math at all. I am referring to only one
| math class I took in high school which did this, and that was
| geometry. I loved my geometry teacher. He was the only math
| teacher I ever found likable.
|
| I loved the geometry class because it helped me a lot when
| thinking of practical considerations to 3D graphic arts I was
| creating on Amiga computers at the time not to mention the value
| of the discussion of area and volume. Did you know Pythagoras was
| a kind of cult leader?
|
| Geometry wasn't just abstract, it was practical. How much carpet
| do I need for a room? How much water will fit in this cylinder?
| If I have a disc that has to be one square foot, what would the
| diameter be?
|
| I had some enthusiasm for algebra one level math for solving an
| unknown variable using what is already known. I didn't learn the
| value in this at school. My dad was an electronic technician
| (Worked at Argonne Labs) and I was interested in what he did
| there. He taught me all there is to know about ohms law, finding
| resistance, conductivity, current voltage, using simple
| procedures. We did parallel circuits, tank circuits, ac theory.
| In less than a years time he gave me a complete 2 year associates
| degree understanding of dc and ac circuits.
|
| Most of us found our math teachers some of the most arrogant
| people in the school. They demanded that we show our work and
| show it going down the way they personally approached solving
| problems. If the result was correct but if they didn't like your
| preferred procedure they would lower your scores. They never
| could offer a sound reason for their demands. Perhaps they did
| have a sound reason. They just didn't bother to sell us on it.
|
| I suppose it isn't right of me to condemn all math teachers this
| way as my experience is kind of limited. This is just what I felt
| about it while being a student in high school and middle school
| 30 years ago.
| RealityVoid wrote:
| My math teacher was not like the ones you describe, he really
| let me go off the reservation if I ever wanted to approach the
| problem in some wierd zany way. IMO, that's how it should be.
|
| On the other hand, mastery of the tools and methods requires
| repeating it and spending a lot of time with them untill they
| "make sense" or rather, you get used to them. So that is useful
| as well. Most people can apply mechanical methods well, but the
| part where I see a disconnect is applying them to new problems
| and new contexts. It's like... Most people don't even realize
| you can do that. Would love to find a scalable way that
| teaching can approach that as well. It is a crucial mental
| tool.
| superfamicom wrote:
| I'm sorry you had so many less than awesome teachers. I had an
| Algebra 1 teacher in middle school (United States) that really
| made a huge difference. The way she taught was so different
| than every other teach I had up until that point. She
| approached everything in a meaningful and useful way. It really
| set me up for success then and now.
| dataflow wrote:
| > If the result was correct but if they didn't like your
| preferred procedure they would lower your scores. They never
| could offer a sound reason for their demands. Perhaps they did
| have a sound reason. They just didn't bother to sell us on it.
|
| The reason was always "because the goal is to see if you've
| learned this technique, not if you can solve this specific
| problem". Which is a perfectly fine reason that I sympathized
| with, though I agree some were poor at articulating it. Where I
| had issues was when I didn't _know_ what technique they wanted
| me to use, and then lost points for not guessing it correctly.
| That part is what always seemed unfair - if the goal is to test
| a technique, it should always be clear what the intended method
| is, and they need to explicitly specify it in the problem when
| it 's unclear. The exercise is supposed to be in math, not ESP.
| ioseph wrote:
| When I started learning woodwork I was really excited to apply
| geometry which I hadn't used much since highschool (even working
| with geospatial data vis). However as I've progressed I find
| myself using math less and less and it's often faster and more
| accurate not to measure or calculate.
|
| To give an example, making a three legged stool I needed 3
| equally spaced spaced points around a circle, I could find the
| center, draw the first point then use a protractor to find the
| other 3 points at 120 deg. But it was far far quicker to just use
| a divider, step around the circle a few times adjusting until 3
| steps takes you back to the first point.
|
| Of course this is still some form of math, but it doesn't involve
| any calculation. I feel there's a whole world of very useful
| techniques that work on a different abstraction, though I'm
| struggling to name or describe to properly.
| jcun4128 wrote:
| Heh I used cross product first time in like 9 years for a little
| robot project.
| kevin_thibedeau wrote:
| I just did some regressions to model sprinkler head flow rates
| for variable pressure and spray angle.
| imglorp wrote:
| Given the relative innumeracy of the public, some argue we should
| teach stats and probability instead of calculus, if there's a
| choice. Those things are more applicable for everyday choices
| like "should I buy a lottery ticket or invest in the market?"
| "How likely am I to die from disease X versus side effects of its
| vaccine?" "Should I buy comp insurance or pay out of pocket if I
| break my car?" etc.
| rland wrote:
| Math is incredibly useful; probably everyone here knows that. But
| it's actually fine that most people don't use it.
|
| What we really need is for every student to realize _why_ math is
| useful -- so that if they want to, they can go learn it so that
| they can make some kind of technological contribution to the
| world. The fact is, you need to be good at math to make some new
| fundamental breakthroughs in technology. Those breakthroughs
| benefit everyone, even those who don 't know any math at all. But
| you won't really get why that's the case until you know enough
| about sines and cosines to make sense of modern technological
| development.
|
| The real issue is that we just teach the math, hoping that
| students will understand on their own that it's fundamental.
|
| What we should do instead is try to instill that sense of wonder
| about the world that inspires people to study math. We don't need
| every person to know calculus, we just need everyone to
| understand _why_ calculus is useful -- then they can be inspired
| to go further. Educators say that they 're trying to do this, but
| I'm sorry "how many meters of fence does Farmer Bob need to keep
| the sheep inside the pen" is not inspiration -- it's drivel, no
| better than "find the perimeter given a=5, b=6."
|
| If every person understood _why_ math is so useful, we would have
| many more people who are motivated to work on improving the state
| of things.
| hnmm23 wrote:
| Any good resources that help instill the "why"?
| Shared404 wrote:
| > it's drivel, no better than "find the perimeter given a=5,
| b=6."
|
| Not only no better, but actually worse - if you add a word
| problem around the problem that doesn't fundamentally add
| anything or make the problem easier to understand [0] all
| you've added is another layer of text to parse through.
|
| [0] Sometimes it can be helpful. Adding a relevant layer of
| physicality to help reason about the problem can be nice,
| especially in calculus.
| netizen-936824 wrote:
| Adding the extra physical descriptions to calculus actually
| helped me better understand what the equations meant and
| represented. Definitely beneficial in some scenarios to some
| people
| Jarwain wrote:
| I think that act of translation is pretty helpful; it's not
| often irl math is presented nicely, but rather as a scenario
| that one has to solve. Translating a scenario into a math
| problem is practice for that, I think.
|
| To try and inspire people, though, maybe word problems could
| be written to be more relevant
| paulpauper wrote:
| >What we really need is for every student to realize why math
| is useful -- so that if they want to, they can go learn it so
| that they can make some kind of technological contribution to
| the world.
|
| That is what word problems try to instill.
| csdvrx wrote:
| You don't - I do (including some math only seen in uni).
|
| It all depends on your job, and since we can hardly know in
| advance, school tries to cover all bases. Drill and practice or
| the other proposed solutions won't help with that.
| jessenichols wrote:
| Because most school is forced knowledge work on problems that
| don't fit the person's problem situation.
|
| When people are free, they learn the math they need for the
| problems they are trying to solve.
|
| Traditional, compulsory school forces children to solve problems
| they don't have. See Karl Popper's idea of the bucket theory of
| mind, or David Deutsch and Taking Children Seriously.
| graycat wrote:
| Uh, there is a carpenter with a Web site that uses the "3, 4, 5
| rule", of course, the Pythagorean theorem.
|
| The first order ordinary differential equation initial value
| problem
|
| d/dt y(t) = k y(t) ( b - y(t) )
|
| can be use to model _viral growth_. Once it kept two crucial
| FedEx BoD members from walking out and saved the company.
|
| Similarly for the law of cosines for spherical triangles for
| finding great circle distances.
|
| Linear programming (LP) gets used right along for actual, genuine
| LP problems and also as a means of approximation for problems
| that are not linear. The problem of minimum cost flows is a
| special case of linear programming.
|
| If want to sort keys, e.g., for some positive integer n, if want
| to sort n numbers into ascending order by comparing numbers two
| at a time, then heap sort does that in worst and _average_ case
| in O(n log(n)) and, thus is the fastest possible -- this is from
| a cute counting argument, the Gleason bound, A. Gleason.
|
| Statistics is important and parts of it are awash in math, not
| all of it trivial.
|
| The design and operation of the Webb telescope is awash in math.
| aweofjwef wrote:
| So much of modern math education, especially once you get into
| high school, is centered around _computation_ instead of
| _reasoning_, so you get a lot of kids who spend an entire year
| doing random integration problems or charting a bunch of useless
| functions/conic sections instead of really understanding
| fundamental structures, reasoning, problem solving, etc. It's
| just rote computation, but we have computers for that now.
| syntaxing wrote:
| I can understand the average person not using the math we learn
| in school, but it's crazy to me that even the average engineer
| doesn't beyond basic arithmetic. I don't mean this in an elitist
| sense but I feel like I was the same way a couple years ago.
| Until one of my mentors kinda guided me through the thought
| process and understanding the math is extremely powerful and
| useful.
| ramesh31 wrote:
| I can remember failing math class _hard_ throughout my entire
| academic career. I never passed a math class past primary school,
| and ended up dropping out of high school. The concepts simply
| never made sense to me, and as they were presented were just
| meaningless rote exercises of memorization. Math was something I
| had completely written off as ever being able to understand.
|
| Then I took calculus and trig classes in college. Since I was
| also learning graphics programming at the time, I was able to
| actually make sense of math with a real world connection.
| Everything immediately clicked. I was able to intuitively
| visualize the trig functions and graph equations. Ultimately the
| problem for students I think is just creating this connection to
| reality.
| pthread_t wrote:
| It would be incredible if trigonometry classes had a lab
| component where students work on a 2D game, such as tower
| defense.
|
| I ended up taking a fun programming elective in college where
| my team did exactly that -- we created a 2D game. That
| experience made me appreciate trigonometry more than my high
| school teachers and Khan Academy ever did.
| paulpauper wrote:
| It is like this for all subjects. Beyond the 5th grade,
| applicability drops a lot. Knowing how to read simple sentences,
| perform elementary math is enough to get by with most tasks, but
| personal finance will be a struggle.
| jeffbee wrote:
| In my opinion serving up 2/3 cups of a semi-solid cheese and
| reserving a quarter of that demonstrates a quite excellent
| intuition about the problem of 3/4 of 2/3. Probably 3rd-grade
| children would be congratulated upon discovering this strategy.
| mlyle wrote:
| The article mentions "More drill and practice" ...
|
| I don't think this is the right way. I believe something happens
| with math to many/most students which leaves them less than
| fluent in mathematics.
|
| Somewhere along the way, they stumble for a few weeks and fall
| behind. Maybe their family took a vacation. Maybe the teacher's
| explanations don't make sense to them. And then there's a
| deficit.
|
| Pretty soon, supporting that student through math becomes a whole
| lot more about drilling and memorizing strategies and
| understanding is deprioritized.
|
| This becomes insurmountable, especially with the "layer cake"
| model of how math is taught in US schools. Pretty soon you'll
| _never_ catch up in understanding. But you probably just
| attribute it to "not being good at math".
|
| I'm working with a student right now, who is in precalc and "bad
| at math." He is actually really bright. Some missing knowledge
| and intuition about fractions has made everything since much
| harder. And the problem's never been fixed because he's
| constantly been in a survival mode.
| globular-toast wrote:
| I think I've used almost everything I learnt in maths at school
| at one point in my adult life. And not just because I'm a
| programmer. The other day I was using trigonometry to work out
| how to install a projector into a room.
|
| From what I can tell, most people don't do things like install
| projectors into rooms. They either get someone else to do it, or
| just figure out some placement that is good enough via intuition
| or trial and error. If people have jobs that require it, they
| usually remember the bare minimum for their job and aren't
| remembering general concepts to help them solve brand new
| problems.
|
| If there is causality here, I'm not sure which way around it is.
| Either they don't need maths because they don't stuff that needs
| it, or they don't do stuff that needs it because they can't do
| maths.
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