What’s with math education?

Lockhart Laments (PDF) about the sorry social view of the field of mathematics. He sees it as an art form and, hence, an integral human endeavor towards making sense of how our minds think in patterns creating emotional satisfaction. In this vein, he wails about the motivations foisted on students – to learn ‘practical’ math – to create “cutesyness” to entice memorization of rules and algorithms and what schools (and society) do to the children.

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide— a relief from daily life, an anodyne to the practical workaday world.

The main problem with school mathematics is that there are no problems. Oh, I know what passes for problems in math classes, these insipid “exercises.” “Here is a type of problem. Here is how to solve it. Yes it will be on the test. Do exercises 1-35 odd for homework.” What a sad way to learn mathematics: to be a trained chimpanzee.

But a problem, a genuine honest-to-goodness natural human question— that’s another thing. How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

So put away your lesson plans and your overhead projectors, your full-color textbook abominations, your CD-ROMs and the whole rest of the traveling circus freak show of contemporary education, and simply do mathematics with your students! Art teachers don’t waste their time with textbooks and rote training in specific techniques. They do what is natural to their subject— they get the kids painting. They go around from easel to easel, making suggestions and offering guidance:

The key points are that the teachers need to be mathematicians to the point of sympathy with its own qualities as an intrinsic human endeavor. The mathematics teacher needs to be a mentor willing to risk an intellectual relationship with the student. Teaching is the process of selecting the right problem for the right student at the right time so as to lead the learning towards an efficient progress of growth and development.

Too often, math teaching in high school is an easy job. Use the text. Do the chapter on the wall. Assign busy work to keep parents happy that their children are doing homework. Rote, mechanical, step through the defined process. Let the chips (and students) fail where they may.

The Lament perhaps goes overboard bashing current pedagogy but the ideas and the complaints and the criticism provide good insight into how to move from wherever it currently is to something better.

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