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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?

#141

Post by the_only_law »

mlyle wrote: post #22

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 tha…

There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting.

… which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.

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

#142

Post by the_only_law »

kleer001 wrote: post #97
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.

> When people are free, they learn the math they need for the problems they are trying to solve. Citation needed.

Yeah really, when I finally found a reason to get interested in higher level math, I then realized it built on much knowledge from my 12 years of school that I neglected to care about to learn, all further down the chain of abstraction and further away from my problem to the point where it’s no longer interesting again.

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

#143

Post by pfranz »

I feel like I have a different perspective than this article. I don't see any problem with how the cottage cheese problem was solved.

I feel like most learning is part building a mental model, part rote memorization, and part practicing their interaction. I understand how multiplication works, but memorized my times tables to make harder problems much easier. I practiced multiplying 3 or 4 digit numbers to see them interact.

The way people solved the cottage cheese problem shows they understand how fractions work. They just don't use them enough to warrant multiplying fractions and reducing the result. If they were dealing with that problem every day, they would use more efficient solutions. People that work in construction are very good at certain types of math. People working on 3d software are usually good with different types of math like trig or linear algebra. Having a general knowledge helps us muddle through rare problems or have a base to learn more specific types of math.

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

#144

Post by Ekaros »

temp8964 wrote: post #49

There’s a sickness in today’s American/western culture related to learning / education: against practice. Teachers design all sorts of activities to facilitate student learning, but they are disgusted to do the most important thing for early learners: repetitive practice. When students start to learn algebra, many of them can’t even do two digits addition/subtraction by hand. Not to mention to do calculations in the…

Basic math and algebra are the fields where I actually see that repetition is needed and useful. Huge part of being proficient is pattern recognition and repetition is only way to get to this. And I actually often wish that I had bee teached more than 10x10 tables... Maybe up to 20x20.

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

#145

Post by TheMightyLlama »

GPerson wrote: post #132
technothrasher wrote: post #71

Earlier quoted context omitted.

> 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…

I’m just curious, but what do you think is the difference between “critical thinking” and “common sense”? Ostensibly, they both seem to mean something like effective thinking done outside the boundaries of predefined dogmas. On the other hand, “critical thinking” often appears to be Orwellian-Newspeak for “accept the dogma I am telling you”. Granted, maybe “common sense” plays the same role, but for a different audie…

I struggle to see how “critical thinking” can mean anything other than the application of tools to ascertain the true state of things. Certainly far from “accept the dogma I am telling you”

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

#146

Post by pfranz »

voldacar wrote: post #31

> Many students are only taught math as symbol manipulation. Less instruction is focused on identifying situations where it might be useful. We need to give students more training in noticing and converting everyday situations into the math problems they know how to solve. No, please don't do this. When I was learning math as a kid I found word problems incredibly irritating and stupid. It's just a way to waste a few…

I think the reason most word problems suck is that they're manufactured abstractions on the same problems elsewhere on the worksheet--which seems to be your critique.

In real life, a lot of those situations are hidden, but there are often multiple correct ways to approach the problem and hopefully some intuition will help you if you're too far off track. 2/3rds of 3/4ths of a cup of cottage cheese shouldn't be more than one cup and shouldn't be a tiny amount, either. (I also don't see a problem with people who scooped it onto the table). Similarly to the woodworker (elsewhere in this thread) trying to evenly measure out where 3 legs on a stool would go.

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

#147

Post by huetius »

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…

I love this post, I would only add that “useful” is not the inspiring criteria it is made out to be, as demonstrated by the example of Farmer Bob’s fence. What needs to be resuscitated is the transcendent, aesthetic dimension.

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

#148

Post by mlyle »

the_only_law wrote: post #141
mlyle wrote: post #22

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 tha…

There was another “I’m bad at math” thread a while back I stumbled across and drilling was considered basically the way to get good at math by most people posting. … which is all the more reason I’ll never become good at math. I’d rather drill a hole in my head than subject myself to drilling back to back, contextless, boring problems I don’t care about.

I think there's a few points where drill makes sense. In each case, after you have a good understanding, and you're seeking to become fluid and avoid dumb mistakes. (Even if you have a good understanding, if you're consciously thinking about each step you'll error a fair bit, and on a 20 step problem you can't afford this error rate and slowness)

Arithmetic facts, basic algebraic manipulation, big polynomials, derivatives and integrals.

But we do much more drill than that. And, worse, it's often as homework, where you can be guaranteed a decent slice of the class is practicing it wrong.

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

#149

Post by huetius »

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…

This rings true to me. I was only able to get an intuition for calculus when I was able to conceive of it in geometric terms. I later learned that this was how Newton originally derived it.

This helped me to “trust” it in more advanced contexts where geometric intuition becomes exceedingly difficult.

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

#150

Post by jacobr1 »

Shared404 wrote: post #105
netizen-936824 wrote: post #20

Earlier quoted context omitted.

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

Same here - that experience is why I aded that exception. Until Calculus/Physics though, I don't think there's much added benefit - except maybe an occasional "here's how algebra helps while grocery shopping".

When I tutored elementary kids, physical examples really helped with fractions.
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