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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

#121

Post by justicezyx »

acjohnson55 wrote: post #104
bitwize wrote: post #98

Earlier quoted context omitted.

> 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 lea…

It's way too early to judge "New Math" to be a failure. I think the idea of focusing on concepts over computation 100% in the right spot. The biggest problem to its acceptance is cultural. Parents don't feel comfortable with math concepts, and in my opinion, most of the negativity is coming from that insecurity. So they demand for things to be taught the "old way", even though that's produced a generation or two of m…

> I think the idea of focusing on concepts over computation 100% in the right spot

Concepts of what? Without intuitive understanding of basic computation procedures, what concepts can anyone build out of nothing?

Math is concrete. It's from observation of actual quantitative phenomenon.

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

#123

Post by ythn »

gusmd wrote: post #75

I studied Mechanical Engineering, and it was my experience that several professors are only interested in having the students learn how to solve problems (which in the end boil down to math and applying equations), instead of actually learning the interesting and important concepts behind them. My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot…

Reminds me of an anecdote in Richard Feynman's book in which the Brazilian education system revolved around memorizing definitions without understanding the underlying concepts: http://v.cx/2010/04/feynman-brazil-education

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

#124

Post by hackinthebochs »

acjohnson55 wrote: post #104
bitwize wrote: post #98

Earlier quoted context omitted.

> 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 lea…

It's way too early to judge "New Math" to be a failure. I think the idea of focusing on concepts over computation 100% in the right spot. The biggest problem to its acceptance is cultural. Parents don't feel comfortable with math concepts, and in my opinion, most of the negativity is coming from that insecurity. So they demand for things to be taught the "old way", even though that's produced a generation or two of m…

>I think the idea of focusing on concepts over computation 100% in the right spot.

Concepts over computation (or well, before computation) is probably right. But New math was about learning the abstract before the concrete. This was predictably an abject failure.

I think the best way to teach math is to follow the trajectory that humanity took when discovering it. The key that's missing is that math doesn't just come out of thin air, its just a systematization of precise quantitative thinking. If we motivate the concepts using real world examples, then explain how to abstract away the particulars into a general procedure, then these connections will get made that make math "real" and relevant.

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

#126

Post by jdmichal »

hasenj wrote: post #84
jdmichal wrote: post #54

Earlier quoted context omitted.

Are you thinking of derivatives? I agree that those are relatively easy -- it's the rate of change for a function. Or, in geometric terms, it's the slope of the tangent line of the function's curve. Like I said, limits are used when a function "breaks", so they're naturally hard to visualize. I'll use my typical example for when I discuss teaching math by solving problems: Approximating the area under a curve using r…

Will, speed breaks when you consider a specific instant in thing because there is no time span nor a distance the be traveled.

Ah, good point. I forgot about that problem with instantaneous speed.

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

#127

Post by cosinetau »

As a someone with a degree in applied mathematics, I feel the problem with learning mathematics is more often than not a problem or a fault of the instructor of mathematics.

Many instructors approach the subject with a very broad understanding of the subject, and it's very difficult (more difficult than math) to shake that understanding and abstract it to understandable chunks of knowledge or reasoning.

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

#128

Post by SubiculumCode »

joe_the_user wrote: post #93
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 confro…

I blame TV in the 80's and 90's..and to today. The smart kid is the dorky, beat up kid. The dad is usually a guy who thinks he can figure stuff out and repair stuff, but hes wrong and just breaks everything.. better just buy it at the depot.

Our media praises stupidity

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

#129

Post by dyarosla »

inanutshellus wrote: post #85
throwawayjava wrote: post #69

Earlier quoted context omitted.

Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated. Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.

But it works at-scale, which is where the focus is. Bang-for-the-taxpayer-buck. Further, socially-speaking, being with your actual peers is extremely valuable, obviously. But yes, the ideal would be a tailored-to-each-child education. Personally, having seen the power of a good Montessori education, I think it's frickin' genius and should be the template for all education (specifically the grouping of 3 yrs together…

Cheaper? I also don't know if that's necessarily true. If it's ineffective for many, is it a cheaper solution or just simply cheaper?

Personally, I think Khan Academy is one of the few forward-thinking organizations doing something right in education. It tries to skew learning towards a 'mastery-based' model which keeps kids from falling behind by not advancing them too early. Of course, teachers and parents still need to implement the usage of Khan Academy in this way for it to be effective.

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

#130

Post by d3ckard »

swiley wrote: post #109
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 never had any problems with math until I went to university, so I was merely a passive observer of everyday struggle for some people. This is the opposite of my experience, I did horribly in math and hated it until I took calculus (which, I guess I should have taken in highschool but I tried to avoid it since the rest of math sucked.) EDIT: just want to clarify: I did have a reasonably intuitive understanding the…

I couldn't develop internal understanding of calculus, so while solving the equations wasn't that hard, I never felt really comfortable with it. Discrete mathematics - total opposite. Proofs were very intuitive to me.
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