An Open Letter to Sal Khan

Unjust.

The Khan video fails to clearly distinguish definitions and derived results, so his formulae are effectively God-given from a student's perspective.

However, the writer's attack on this video is wrong as well. Presenting slope from the "rate of change" definition before _defining_ the slope of a straight line is nonsensical. Questions of axis rescaling are important but inessential to the basic definition. Trying to discuss these points in order to connect to the "real world" (the theme of the site?) before the basic definition is given can only confuse and give a false sense of understanding.

This isn't to advocate a purely formal exposition, either: there are various points of view (Euclidean, Cartesian ...) and reconciling them is probably above the level of this lecture, but one should not define a straight line as "a graph of a function with constant derivative".

Ultimately this seems like a rather forced argument presumably designed to distinguish the poster's "real-world-focused" materials.

</pedantic>

I really enjoyed reading that letter. His point boils down to "You can teach how in a clear way, but you're not teaching the 'why'". I had never thought about that before, but it seems obvious now.

Charlie Munger speaks of taking the big ideas from various disciplines and building a latticework of mental models so that you can use all your knowledge to solve problems. A Khan Academy devotee will learn lots of math and science, and other things, but will he or she understand how it relates to real life, and how to apply those ideas to other disciplines?

Are these videos helping to develop "mathematical thinking" ?