Most people don't use anything but the most basic forms of math, so if you're going to teach beyond that, there has to be a purpose. And I think that purpose is how to solve problems in different ways, like by calculator or some weird system. It's a good idea to stretch the mind by learning new approaches. That being said, yes, the education system is totally broken and textbooks publishers are a cancer in that system. I think in order to effect real change, it's going to have to be at both the local level and the national level, and the former is going to be totally hindered by the latter's insistence on state exams.
Jeanne: You didn't have number lines? That's just And, by the way, the neutral tables are for teaching -basic- math, because negative numbers are basic math. That's ridiculous. A neutral table--bah, humbug! Love, Janie. I've never gotten along with math. We've agreed to remain distant acquaintances. You sound a lot like me talking about everything. I'm kind of with you, a bit? First my complaint: I don't like homework. I've come to realize how dumb it is.
When you give homework, you take a kid who doesn't know this stuff, and say "Go work it out and teach yourself. I have a poli sci and law degree.
And also, what do I know about teaching? So homework delegates an important function -- teaching -- to thousands of unqualified, untested, possibly unmotivated people. Homework should end. Anyway: About all this different math. I agree with you that they shouldn't just invent new things to sell textbooks. But as I have been working with Mr Bunches this year on his math because I am apparently an adjunct teacher to our school district thanks to homework I've noticed the many many different ways the present information, some of which are new to me.
Number Triangles or something like that baffled me. But Mr Bunches in particular has a really hard time with abstract concepts like math, and seeing things several different ways seems to really help him. So if number lines work for me and you but neutral tables help teach the concepts to someone else and Mr Bunches needs Number Triangles, I don't think that's such a bad thing.
I struggled with math all my life, until one day I thought "Math is just a different language. It's like Spanish or computer programming. What we learn in school is merely the end product. And it seems impossible that one could teach sculpture without revealing that there is an art to it. Yet that is what we do with math all the time. If school curriculums fundamentally misrepresent math, where does that misrepresentation come from? Lockhart views it as a self-perpetuating cultural deficiency.
Nor have they become all that integrated into our collective consciousness. In schools, mathematics is treated as something absolute that needs no context, a fixed body of knowledge that ascends a defined ladder of complexity. There can be no criticism, experimentation, or further developments because everything is already known. Its ideas are presented without any indication that they might even be connected to a particular person or particular time.
Lockhart writes:. What other subject shuns its primary sources—beautiful works of art by some of the most creative minds in history—in favor of third-rate textbook bastardizations?
Efforts to engage students with mathematics often take the form of trying to make it relevant to their everyday lives or presenting problems as saccharine narratives. It has relevance in the same way that any art does: that of being a meaningful human experience. Children would have as much fun playing with symbols as they have playing with paints. If the existing form of mathematics education is all backward, what can we do to improve it? How can we teach and learn it as an art?
For almost everyone, believing that you were born dumb—and are doomed to stay that way —is believing a lie. IQ itself can improve with hard work. Because the truth may be hard to believe, here is a set of links about some excellent books to convince you that most people can become smart in many ways, if they work hard enough:.
So why do we focus on math? Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough. Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth and eighth graders score quite well in international math comparisons—beating countries like Germany, the UK and Sweden—our high-schoolers underperform those countries by a wide margin.
In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math— for example, Andrew Hacker has called for algebra to no longer be a requirement.
The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x. We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hard-working foreigners. But even more importantly, it may contribute to inequality. Too many Americans go through life terrified of equations and mathematical symbols. We believe that this has to stop.
Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz here and here , that echo many of our views.
One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans. In Intelligence and How to Get It , Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:. Confucius set that matter straight twenty-five hundred years ago.
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