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Why don't we use the math we learn in school?

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Re: Why don't we use the math we learn in school?

#21

Post by Jarwain »

Shared404 wrote: post #18
rland wrote: post #8

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 bre…

> 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, espe…

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

Re: Why don't we use the math we learn in school?

#22

Post by mlyle »

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 in his math classes.

These students never end up doing the kinds of things that kids are ahead in math are taught to do to crack free-form problems:

- Make a good guess of the answer

- Form a mental picture and use it to select strategy

- Work a simpler problem and see how this can be extended

- Organize your givens ; use dimensional analysis for a hint as to what operations may be required or what picture should be drawn

- Look for symmetry and transformations that result in simpler cases

- Does positing an incorrect answer reveal any information about the solution?

IMO, teaching these things -- strategies-- should be more the goal than doing lots of kinds of applied math work by rote in a way that deeply depends upon previous work.

Re: Why don't we use the math we learn in school?

#23

Post by globular-toast »

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.

Re: Why don't we use the math we learn in school?

#24

Post by paulpauper »

rland wrote: post #8

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 bre…

>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.

Re: Why don't we use the math we learn in school?

#25

Post by lordnacho »

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.

A thing that needs addressing is the notion that we should only teach people things that will be useful, which seems to underlie this article. We should teach people how to explore, and math is the premier example of a large space that can be explored with very little access to resources and evidence. You can do it just in your mind, and you don't need any apparatus or conclusions from people who had such apparatus, like you do in science.

Re: Why don't we use the math we learn in school?

#26

Post by ioseph »

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.

Re: Why don't we use the math we learn in school?

#27

Post by hnmm23 »

rland wrote: post #8

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 bre…

Any good resources that help instill the "why"?

Re: Why don't we use the math we learn in school?

#28

Post by bjarneh »

jessenichols wrote: post #14

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.

> most school is forced knowledge work on problems that don't fit the person's problem situation.

Have you never been in a situation where you are about to take train going at 80 mph; wondering when you'll meet up with your friends going in the opposite direction at 90 mph?

Re: Why don't we use the math we learn in school?

#29

Post by mlyle »

graycat wrote: post #15

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. L…

> Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem.

Knowing a triplet ain't employing Pythagorean theorem.

> [lots of following examples that are moderately deep applied math used in lots of skilled professions]

Most people don't do this kind of work or analysis.

Re: Why don't we use the math we learn in school?

#30

Post by globular-toast »

jcun4128 wrote: post #5

Heh I used cross product first time in like 9 years for a little robot project.

Yeah. One underappreciated thing about education is exposure. It's not that I've been walking around every day for the past decade being capable of matrix multiplication. But having been exposed to it once, it's amazing how quickly the knowledge comes back when you need it. I did advent of code over Christmas and when the 3D transformations came up I thought about it for a bit, then remembered... something about matrices... linear algebra..? And then searched for the resource I needed to refresh myself on it. Just the fact I was exposed once a decade ago means I was able to refresh myself in a few minutes.
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