[nileshtrivedi]

> when most mathematicians look at a set of abstract symbols they don't "see" the symbols per se, they see what those symbols are meant to represent.

Might we benefit from a different set of symbols that actually convey the geometrical meaning behind them? If instead of π, we used a glyph that shows a circle over a diameter, instead of x for a variable, we show an empty rectangle that shows that it's a placeholder for a value?

> Students who said the answer was 44, how did the students who said 26 arrive at their answer?

I came across a great example of this approach in Chess: The Complete Self-Tutor by Edward Lasker. Instead of just showing the right answer for a chess puzzle, he tells you what you did right in your answer and what you missed in getting an even better answer. This was a printed book that was completely interactive.