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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

#131

Post by ghettoCoder »

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 disagree. I am not uncomfortable with math in general or the "new math". What I am uncomfortable with is the fact that my kids, and everyone else's kids, are essentially lab rats in a massive experiment. The result of which is 1+ generation of kids who can't calculate tax in their head or split a restaurant bill . They can't manage more than a few number without a calculator and are missing many of the basic blocks of math that are learned through rote.

I find it disheartening that I have to teach my kids basic fractions, ratios, and transformation cause the teachers don't or barely touch on it. Kids are supposed to "discover" and "explore" math, whatever that means. In my opinion it's all bullshit.

Math, in many ways, is like an engine, either it works meaning the answer is correct, or it doesn't.

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

#132

Post by [deleted] »

yequalsx wrote: post #100
eeZah7Ux wrote: post #88

Earlier quoted context omitted.

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…

[deleted]

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

#133

Post by kenjackson »

bitwize wrote: post #98
taco_emoji wrote: post #86

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. 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 lea…

I was a proponent of "New Math" types of philosophies before I had a kid. It was only when I tried to teach concepts did I realize how important it was to be able to be able to arithmetic quickly off the top of your head. Its hard to explain, or even to grasp, how fundamental basic arithmetic is to almost everything in math. For us arithmetic is as simple as thinking a thought -- but only when I tried to actually explain concepts to a young kid did I realize how difficult it is for them to understand these concepts when arithmetic isn't ingrained in their brain.

I hate to admit it, but I am now a believer that strong arithmetic skills are important, and drills get you there. I don't like to call it memorization, since I'm not sure it necessarily is simply memorization. But you do need the answers at a moments thought. It should be as natural as saying a word.

And its not to say that you don't teach concepts concurrently... but that the arithmetic is fundamental.

That said, I still believe that the long division algorithm taught isn't so useful. :-)

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

#134

Post by nategri »

bitwize wrote: post #98
taco_emoji wrote: post #86

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. 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 lea…

PhD physicist here. Struggled through the 'normal' public education math program, and didn't get good traction on stuff until college when my instructors starting focusing on more 'evidence based' math and physics.

Also I never completely learned my multiplication tables to the point where they were reflexive, such was my loathing for rote memorization. To this day I sometimes need to pause to mentally crunch something. This sucks for small numbers but it means I have the mental tools to grind out bigger ones that other people would need calculators for.

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

#135

Post by Jtsummers »

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…

∆ - delta - d as in difference

∑ - sigma - s as in sum

∫ - long s - s as in sum

It's not totally arbitrary.

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

#136

Post by taco_emoji »

bitwize wrote: post #98
taco_emoji wrote: post #86

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. 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 lea…

1) Did New Math actually try to do those things, or did you just bring it up to poison the well against any alternative pedagogies?

2) Did New Math fail because of poor results or because of popular revolt? (Would New Coke have failed if there was never any such thing as the original Coke?)

2a) If New Math did actually have poor results, was it because it hewed too closely to the goals I brought up, or because of other issues?

3) Memorizing times tables clearly didn't work, or we wouldn't be having this discussion

4) I never said that drilling times tables isn't important, so I'm not sure what your last sentence is in response to

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

#139

Post by coldtea »

throwawayjava wrote: post #69
ashark wrote: post #63

Earlier quoted context omitted.

Schools (at least around here) do not hold kids back anymore. No matter what. Some of them get behind in one or more subjects (math, say) as early as 1st or 2nd grade and all their later teachers are stuck trying to give them the remedial math help the desperately need, while teaching their other students on-grade-level material, and also trying to teach the remedial kids enough of the new stuff that their scores on…

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.

>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.

Sounds quite logical to me. If we assume a gaussian distribution (which tests seem to verify), most kids of the same age will have the same skills/level.

So at worse you mismatch what's taught to some kids towards the edges, whose level there are ways to accommodate anyway in most school systems (skipping a class or two for extra smart kids, or staying behind/supplementary teaching for less than average smarts).

And it's not just about learning and who can cram more into one's head (akin to e.g. preparation for the Olympics), but also about sharing the same teenager and adult-making experiences as other kids of your age, which is probably even more important that what's actually taught (the majority of which most people will forget anyway).

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

#140

Post by randallsquared »

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…

Is it way too early, or has it produced a generation or two (or three!) of mathphobic Americans? How many generations of avoiding rote memorization would it take to judge an alternative, in your view?

Many problems that people have with math seem to stem from not having internalized the most basic facts about addition and multiplication. If you don't know at least to 10 by 10, each tiny step of working through a problem will tend to be interrupted by counting. Fluency requires memorization.

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