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« After the Ryan pick - I need a vacation! | Main | Still Watching the Political Circus »

August 28, 2012


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Aboc Zed

I have been curious for as long as I remember myself and I am thankful to my parents who always said yes to educational toys.

I always loved math. And I still do. I think math is fundamental for system thinking and early exposure to math in a right way is crucial for retaining curiosity and developing skills of systematic learning.

I think it is futile to expect educational system to remedy a failure of the parents.

I think the basics of math and system thinking develop together with language skills from age 2 to age 6. Language is a representational system and as such mathematical in nature.

By the time people enter school system at age 6 it is already too late. And school system kills curiosity and initiative in learning. Our school system is not designed to promote critical thinking. It is designed to churn out robots that know the minimum necessary to be able to punch picture buttons in cash register at McDonald's. It is the reflection of general dire situation with system thinking in the society as a whole.

Only those who have parents determined to invest in their kids by keeping them engaged in stimulating educational activities like math and language games from very early age have the chance to withstand the dumbing down effect of educational system.

As overpopulation continues and the educational gap between elites and everybody else widens we can expect the situation to get worse.

Don Sanderson

I'm a Ph.D. mathematics and for 20 years was a mathematics professor and later a Silicon Valley engineer. My wife is a wine chemist. The most mathematics we've needed in many years are ratios. Stop wasting kids' time!

George Mobus

This morning Diane Rehm's second hour was devoted to Prof. Hacker's article.

She had several people with contrary views, of course, and the discussion was pretty interesting. Most seemed to think that the issue is black or white. You either have math courses, like algebra, or you give up teaching people math.

As I stated above, it isn't that we want to abandon math (in this case algebra), dumb down the curriculum, but to teach it in a way that it will be meaningful to students.

Since posting this I've been pleasantly surprised by a number of supportive e-mails, personal calls, and Don's comment above, all recognizing the same problem. Yesterday I had conversations with two colleagues who immediately saw the potential benefit of teaching math embedded in the curriculum of other courses (there are experiments with what is called "math across the curriculum"). Maybe it isn't so far out to think this is a reasonable proposal after all!

But it remains problematic to implement this kind of thinking unless the education of educators is drastically changed. All educators (even visual art teachers) will need to embrace the notion that they have to provide problem-oriented projects that are highly motivational and contain interesting mathematical issues (e.g. calculating perspectives in drawing!) That in itself represents a major hurdle I think. Given the nature of the general curriculum for schools of education this is most likely a deal buster. On the other hand, if enough people started calling for this kind of reform...

Anyone interested in starting a grassroots movement?


Jim Williams

I've always said that we should be teaching Topology in grade School, followed by Set, Group, and then Lattice Theory, and finally some Geometry. Arithmetic can be taught in college after some exposure to Field theory.

Basically, we should be providing a framework for them to parse the world themselves rather than providing a parse of the world upon which they must build a framework.

It comes down to this simple fact. The only thing worth learning is how to learn. The rest is excess baggage.

Robin Datta

The problem, of course, is the packaging. Where I learnt algebra, I never heard of "quadratic" equations, but I know now that some of what I learned goes by that name here. The cut-and-dried way it is presented here takes all the life out of mathematics. The Arabs called algebra Hisaab al Jabr, meaning the powerful computation, but it is endowed with its power only by the motivation of the person using it.


From personal experience, I wholeheartedly agree that the teaching of maths, especially algebra, needs to be done better.

I have memories of my high school maths teacher bellowing that Y equalled MX plus C, as if it was my hearing that was at fault rather than his ability to teach.

It's interesting: I recently watched The Pleasure Of Finding Things Out
in which Feynman suggests a "chaotic" teaching method, to catch differently motivated students on different "hooks" as you go along.

I was "saved" by the self-paced PLATO system on a training course for the unemployed: let the dog see the rabbit and there's no holding it back.

Paul Chefurka

I really wish I could remember what it was that triggered the "Aha!" moment I had when I grokked logarithms in early high school. My teacher was good, but not that good. I had a home life that revolved around the sciences, but as I've recently discovered, I'm not the scientistic sort. Whatever the reason, that moment was part of a lifelong love of discovering the hidden, abstract underpinnings of reality. I had no intrinsic love of mathematics - my university math marks were a monotonically decreasing function over time, and extrapolated to intersect the y axis at 0 right about when I graduated...

In any event, perhaps this is a moot point. Given what's about to happen to civilization, mathematical skills may shortly rank somewhere below cooperage and cobbling in social and survival importance.


On Sixty Minutes yesterday there was a segment on the 10-minute Khan Academy videos on every kind of math from elementary school to advanced calc and stat, as well as many other scientific subjects and engineering. Khan, a PhD from MIT with multiple degrees in other fields quit his hedge fund job to devote all his time toward a "FREE world-class education for all." His site is viewed over a million times a day all over the world and he's looking to "flip the classroom" at some CA schools who have students watch his videos at home and then do what would be described as "homework" at school - modules to check learning and concept mastery. Every problem that every child works on is timed and the feedback is analysed and provided on a "dashboard" computer program to each teacher. He/she can immediately ascertain which of the students needs some one-one-one or small group "workshops" in class to help them along. Everyone learns at their own rate. It's brilliant.

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