Dismantling Mathematical Privilege

It’s great to be in this room – I am among my people – but also uncomfortable to be here because you all make me really aware of how many people are not in this room. link

One of my earliest mathematical epiphanies was the realization that if you let the number of sides on a regular polygon increase without bound, you get a circle.

circle with a regular polygon inscribed, animated with increasing number of sides in the polygon

And that all the relationships you find in a regular polygon have analogous relationships in a circle. For me, that realization was literally a religious experience. I finished that limit on the back of a church bulletin while a churchlady glared at me.

line divided into two segments. a square below the line, adjacent to the left segment with perimeter equal to the length of the left segment. a circle on the right and mostly above the line, with circumference equal to the length of the right segment. Animated to adjust the point separating the two segments and show how the square and circle change size accordingly.

_[Here we explored together [Circle-Square](http://www.101qs.com/2859-circlesquare), a task that involves questioning, estimation, intentionally declaring wrong answers, recalling what you know about circles and squares, computing an answer, and verifying it. You can watch it.]_

YOUTUBE KLW7PZoh4hs Exploration of Circle-Square from about 8m until 15m from the talk at #MAAthfest

Compare that exploration with the more traditional expression of that problem:

Mark an arbitrary point P on a line segment AB. Let AP form the perimeter of a square and BP form the circumference of a circle. Find P such that the area of the square and circle are maximized.

That experience offers people only a certain kind of mathematical work. You recall what you know about perimeter, circumference, and area, compute it, and verify it in the back of the book.

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I have often complained that we live in a culture in which it is socially acceptable to proclaim one's mathematical ignorance. But you almost never hear someone publicly admit illiteracy.

That said, I also find our traditional approach to teaching mathematics to be mostly abusive. I performed well in my own math education, but I think only because of natural inclination and interest in puzzles.

Reminds me of Mathematician's Lament.

Reminds me of Bret Victor too, reaching for ways to apply our new digital media to better ways of thinking mathematically or otherwise.

There are similar appeals in Alan Kay's Inspiration to remake our culture to ensure everyone can learn these essential skills.