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Math education: It’s not about numbers, it’s about learning how to think

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Re: Math education: It’s not about numbers, it’s about learning how to think

#91

Post by dahart »

Jtsummers wrote: post #76
dahart wrote: post #66

Earlier quoted context omitted.

I'm not sure what that means. Are you saying the use of Greek letters is a good thing, and that we need more of them, not less? Or do you mean that all symbols are equally easy to learn for beginners, whether they're English or Greek or Chinese or abstract? Or do you mean that we should do away with symbols that don't mean anything and use real language to describe math instead? The symbols we use in math aren't to b…

> The symbols we use in math aren't to be confused with the ideas, they are shorthand. Ideas and symbols are independent, and we still have to explain what Greek letters do using English anyway. We use Greek letters for convenience, not for expressive power. Writing "∫ x ∂x" is only faster and more compact than writing "The integral of the equation x over x", it is not an improvement of the concept, right? It is not,…

Very true, good point, it's much easier and more convenient to do algebra on the symbolic expression. There is a reason math has evolved the way it has. Not using any symbols would suck, no question.

But, nothing about writing math in text prevents manipulating the text, right? You can do it, it would just be laborious and exhausting for people who are familiar with the use of symbols.

Re: Math education: It’s not about numbers, it’s about learning how to think

#92

Post by alimw »

J_Sherz wrote: post #77
MengerSponge wrote: post #73

Earlier quoted context omitted.

You couldn't finish your tests in high school, but you're good at math? Have you ever been evaluated for test anxiety? https://www.adaa.org/living-with-anxiety/children/test-anxie... There's no shame in it (although high schoolers can be assholes), and it can help your school accommodate your needs eg extra time to take your exams.

I've never been evaluated but I don't think test anxiety fits in my case - the speed issue was only ever in math / physics. My accuracy on the questions I got to was very high, I just couldn't go fast enough to complete enough questions. Same deal on SAT type math papers too.

Where I did my undergraduate degree they squared the marks scored for each question before adding them up! Slow but accurate was an advantage.

Re: Math education: It’s not about numbers, it’s about learning how to think

#93

Post by joe_the_user »

d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

I don't really think the situation in the article is directly about people not being skilled in math. It's about math-phobia with it's after-affect of people not having skills in math.

It seems like an especially American thing - being good at math makes someone a freak and so it's something kids actively avoid at the ages in which being a freak is not tolerable.

That kind of attitude would need to be actively confronted because what happens is that kids who previously were developing skills tend to drop out given the peer-pressure.

Edit: best documenting link I could find but Google book won't let me copy a quote:

https://books.google.com/books?id=CzmpDAAAQBAJ&lpg=PA74&ots=...

Re: Math education: It’s not about numbers, it’s about learning how to think

#94

Post by eeZah7Ux »

dahart wrote: post #66
redial wrote: post #40

Earlier quoted context omitted.

Symbols are symbols, are symbols. Instead of trying to compress everything into a very limited set of "daily language" symbols we should be trying to expand our ideas, including our language(s).

I'm not sure what that means. Are you saying the use of Greek letters is a good thing, and that we need more of them, not less? Or do you mean that all symbols are equally easy to learn for beginners, whether they're English or Greek or Chinese or abstract? Or do you mean that we should do away with symbols that don't mean anything and use real language to describe math instead? The symbols we use in math aren't to b…

> unfamiliar and foreign looking

The whole point of education is to approach and embrace unfamiliar concepts.

By the way, arabic numbers are... arabic.

Re: Math education: It’s not about numbers, it’s about learning how to think

#96

Post by Jtsummers »

d8421l01vv4r wrote: post #65
adamnemecek wrote: post #57

Earlier quoted context omitted.

Let's add Chinese, Amharic and Arabic characters. Why not, expanding is expanding.

In some branches of engineering (traditional engineering, not software), there are sometimes too few symbols in the Latin and Greek alphabets, so they have to rely heavily on subscripts. Expanding the set of symbols would be useful here, but I guess it's hard to get people to accept change unless they absolutely have to.

A part of the problem is character entry. If it were easy to enter in all these symbols APL may have taken off and we wouldn't have gotten ASCII variants of it like J. So it's somewhat easier to just take our latin alphabet and turn a single symbol into a pair of letters or a letter with a subscript.

The symbols in math are great for writing by hand, but can become cumbersome when typing.

Re: Math education: It’s not about numbers, it’s about learning how to think

#97

Post by jeffdavis »

My theory is that math anxiety is really anxiety about a cold assessment.

In other subjects you can rationalize to yourself in various ways: the teacher doesn't like me, or I got unlucky and they only asked the history questions I didn't know.

But with math, no rationalization is possible. There's no hope the teacher will go easy on you, or be happy that you got the gist of the solution.

Failure in math is often (but not always) a sign that education has failed in general. Teachers can be lazy or too nice and give good grades in art or history or reading to any student. But when the standardized math test comes around, there's no hiding from it (teacher or student).

Re: Math education: It’s not about numbers, it’s about learning how to think

#98

Post by bitwize »

taco_emoji wrote: post #86
d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi wit…

> I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables.

This was tried. It was called "New Math". Spectacular failure. Do you want to know what worked? Memorizing times tables.

There's just no way around the fact that drilling is key to early mathematical learning.

Re: Math education: It’s not about numbers, it’s about learning how to think

#99

Post by jack_h »

taneq wrote: post #2

As my old boss once said, "never confuse mathematics with mere arithmetic ."

As someone who went to university for mathematics (and computer science) I can tell you this is the most common misconception. People think that I spent years studying how to become a calculator.

I love talking about both subjects I went to university for actually and both can be difficult to get people interested in. There are massive misconceptions about both.

Re: Math education: It’s not about numbers, it’s about learning how to think

#100

Post by yequalsx »

eeZah7Ux wrote: post #88
yequalsx wrote: post #82

Earlier quoted context omitted.

In theory it shouldn't matter but it does. We brainwash students to think in terms of y being a function of x. y = f(x) If you give a problem with x = f(y) it really confuses people. If I label the horizontal axis y and the vertical axis x in the cartesian plane then confusion ensues. t = b(a) where t is the velocity and a is time That's confusing. I suppose it's analogous to me saying "The male, fluffy, white, large…

If this is enough to "really confuse" someone than there's a serious problem with understanding VS rota learning.

I'm certain you would be confused by non-standard usage of notation. It's not just symbols and that any symbol can be used. Try reading or speaking English with the adjectives in an order that is not expected. It's confusing as hell but grammatically correct. Our brains get trained to see things in a certain way and when the symbols get jumbled up so do we.

(x1(x2+x3) - x1(x2))/x3

is simply not as understandable to a first year calculus student as

(f(x+h) - f(x))/h

I've been teaching university level mathematics for 25 years and I know mixing up symbols confuses people. Try reading Newton's Principia. It's really hard to know what he's talking about.

EDIT: Try this equation. What famous one does it represent?

(sex(sxe) - sex(xes))/(sxe - xes) = xse sex/xse sxe

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