In this context the parabola may be first encountered by a child creating a videogame as the trajectory of an animal's leap or a missile's flight; here, the natural first formalism for the parabola is an expression in a child-appropriate computational language of something like "the path followed when horizontal speed and vertical acceleration are both constant."
Think of children creating AngryBirds instead of only playing it..
why the quadratic equation of the parabola is included in the mathematical knowledge every educated citizen is expected to know. Saying that it is "good math" is not enough reason: The curriculum includes only a minute sliver of the total body of good mathematics. The real reason is that it matches the technology of pencil and paper: It is easy for a student to draw the curve on squared paper and for a teacher to verify that the assignment has been done correctly.
Technology of pen and paper drives the content, form and assessment.
Whewell was prominent not only in scientific research and philosophy but also in university and college administration. His first work, An Elementary Treatise on Mechanics (1819), cooperated with those of George Peacock and John Herschel in reforming the Cambridge method of mathematical teaching.
What was the specific change in mathematical teaching instituted by Whewell, Peacock, and Herschel in An Elementary Treatise on Mechanics (1819)?
The recipe details, moreover, assume that these “unmarry’d Women” had the kind of knowledge of arithmetic that the book’s earlier instructional sections had taught. The recipe insists on careful attention to measurement and counting. And it asks the preparer to work with repeated multiples of three. Franklin had a track record of promoting female education, and of arithmetic for them in particular. He advocates for it in his early, anonymous “Silence Dogood” articles, and in his Autobiography singles out a Dutch printer’s widow who saved the family business thanks to her education. There, Franklin makes an explicit call “recommending that branch of education for our young females.”
Evidence for Benjamin Franklin encouraging the education of women in mathematics.
A mathematics lecturer at UC Berkeley went against the grain and got fired for it. I'm curious what his teaching secrets were.
<small><cite class='h-cite via'>ᔥ <span class='p-author h-card'>Yusufa</span> in Improving how universities teach science (<time class='dt-published'>11/04/2021 13:26:34</time>)</cite></small>
https://www.maa.org/external_archive/devlin/devlin_03_08.html
<small><cite class='h-cite via'>ᔥ <span class='p-author h-card'>FARNAM STREET </span> in Why Math Class Is Boring—and What to Do About It (<time class='dt-published'>09/01/2021 09:22:50</time>)</cite></small>
Research tells us that for skills like the ones students need for mathematics short practices that recur frequently are far more effective than the same amount of time packed into one session.
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As Uri Treisman said, “The most common use of algebra in the adult world is helping their kids with algebra.”
CUNY found that more students went on to graduate when they were allowed to take statistics instead of remedial algebra. And the results were the same regardless of race or ethnicity.
Sunil Singh asks us to stop promoting mathematics based on its current applications in business and science. Math is an art that should be enjoyed for its own sake.
This reminded me of A Mathematician's Lament by Paul Lockhart. This is a 25-page essay which was later worked into a 140-page book. (And Sunil Singh has read at least one of them. He credits Lockhart in one of the replies.)
It also reminds me of this article on the history of Gaussian elimination and the birth of matrix algebra. Newton's algebra text included instructions for solving systems of equations -- but it didn't have much practical use until later. (Silly word problems are as old as mathematics.)
We should let people learn at their own pace. We should neither rush them, nor hold them back. If they show a talent, then encouraging them to push themselves is fine.
Math isn't for everyone, and that's fine. The same is true of any other subject. We should help people learn what they are interested in learning.