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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?

#81

Post by dekhn »

technothrasher wrote: post #71
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 We need to do this for science education as well. The foundation of science that we need the population at large to be educated in is not the steps of the scientific method, how to dissect a pig, or the difference between a covalent and an ionic bond. It is instead logic, critical thinking, rationalism and empiricism, and why science is superior…

it's funny when you mention the difference between covalent and ionic bonds.

my teacher in high school chemistry or physics told us cutting a piece of paper was a physical, not a chemical change (the textbook spent a lot of time differentiating those). It wasn't until many years later that I learned that cutting paper breaks hydrogen bonds. H-bonds are neither covalent nor ionic, but more like in-between (partial sharing of electron density by two different nuclei) but can be modelling (approximately) using ionic models (partial charges separated by a distance).

Is breaking an h-bond physical, not chemical? I want to talk to my teacher.

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

#83

Post by Jtsummers »

zozbot234 wrote: post #61
imglorp wrote: post #7

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.

We should teach calculus first, because one cannot understand the foundations of stats and probability without calculus.

Using probability and statistics and understanding their foundations are two distinct things. Prob/stat can be taught (to the point of utility) without calculus and often is. More advanced applications are inaccessible or only learned by rote without calculus, but that doesn't mean that you need calculus first.

Of course, this is what commonly comes up in topics like this, a confusion over the two notions: Understanding the basis of something and understanding it well enough to utilize. You don't need a graduate level physics course in electromagnetism to be a competent electrician.

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

#84

Post by indigodaddy »

alexashka wrote: post #37
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…

> Math is incredibly useful For what? It isn't useful for teenagers who are trying to get laid and be cool, at all . It also isn't useful for what 99% of humans end up doing, unless by math you mean basic arithmetic, enough to add and subtract on your 'smart' phone. Math isn't useful. People who are amazing at math and are interested in it - they can be useful, but mostly not. What they don't teach in school is how t…

This isn’t a reason to not learn it or take it out of curriculums.

We use these skills a lot more than we may realize automatically and without really realizing we are utilize the skills.

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

#85

Post by cknakal »

hnmm23 wrote: post #27
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"?

This website has helped me out a lot with understanding the ideas that math represents: https://betterexplained.com/

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

#87

Post by dekhn »

mulmen wrote: post #70
bjarneh wrote: post #28

Earlier quoted context omitted.

> 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?

I recently saw a great photo [1] by Ben Cooper of a Falcon 9 on ascent crossing the Moon from the photographer’s perspective. I wonder how much math went into finding that vantage point. [1]: http://www.launchphotography.com/Starlink_4-6.html

It's not really that hard. I set up several systems to do this for the previous total solar eclipse. The ephemerides for the moon are easy to download and calculate the position in the sky (IE, altitude and azimuth at time t) with a python script.

I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time.

A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).

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

#88

Post by alisonatwork »

alexashka wrote: post #37
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…

> Math is incredibly useful For what? It isn't useful for teenagers who are trying to get laid and be cool, at all . It also isn't useful for what 99% of humans end up doing, unless by math you mean basic arithmetic, enough to add and subtract on your 'smart' phone. Math isn't useful. People who are amazing at math and are interested in it - they can be useful, but mostly not. What they don't teach in school is how t…

I agree with you that math is pretty much useless in most people's lives. However I disagree that teaching it to everyone is useless. The whole point of making kids learn a whole bunch of different things is that it gives them a chance to figure out if they are, in fact, interested. If you don't provide lots of different topics of learning to children in school, where are they going to find out that one of those topics might be just the thing that fascinates them? Most parents aren't going to expose their kids to every topic under the sun. I think it's great that schools expose kids to math, physics, chemistry, biology, languages, music, physical education, social studies, history, geography, cooking, sewing, painting, carpentry, religion, you name it. I hated doing at least half of those things when I was in school, but I still appreciate in retrospect that I did it, because now I know much better what I like and don't like.

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

#89

Post by munk-a »

hnmm23 wrote: post #27
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"?

I'd suggest the youtube channel 3Blue1Brown - the teacher that runs the channel likes to pull problems into physical space and applications often.

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

#90

Post by motohagiography »

It's recently clicked for me that our economies and civilization may in fact rely on a vast majority of people without basic quantitative reasoning skills.

If I were teaching a middle school kids math today, I'd start by teaching them poker and blackjack with card counting to practice doing fast calculations and then learn risk and probabilities. Then maybe create a stock picking group so they can learn to read charts and calculate simple functions with concepts like averages and moving averages, medians, and then some bayesian statistics, time value of money, interest and compounding on debt with logarithms. An example of a person with two maxed credit cards with different interest rates and a fixed income shows equilibria and how predatory those products are. I might also use a eurorack synthesizer rig with an oscilloscope to demonstrate functions and wave forms, integration, modular arithmetic and combinatorics in musical scales, harmonics, musical transposition as an example of conservation laws, ohms laws and electronics, and pulsed information (binary). Catapults vs. trebuchets and siting a rifle scope for simple ballistics and physics. Bicycle or engine repair to show differential gearing. Another unit would be some variation of cryptopals, because that's an intro to new currencies, economics, number theory, proofs as "shapes," information theory, and computer science.

The way I learned algebra in high school was like learning to read music without ever hearing it, let alone playing it. Glimpsing the things I don't understand now as an adult, I can't help but think it was by design.

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