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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?

#11

Post by RealityVoid »

ohiovr wrote: post #4

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 bee…

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.

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

#12

Post by superfamicom »

ohiovr wrote: post #4

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 bee…

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.

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

#13

Post by dataflow »

ohiovr wrote: post #4

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 bee…

> 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.

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

#14

Post by jessenichols »

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.

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

#15

Post by graycat »

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.

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

#16

Post by aweofjwef »

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.

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

#17

Post by syntaxing »

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.

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

#18

Post by Shared404 »

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, especially in calculus.

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

#20

Post by netizen-936824 »

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…

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
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