
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.
https://www.amazon.co.uk/CHESS-COMPLETE-SELF-TUTOR-Self-Tuto...
and i can see several of the others on secondhand sites (eg ABE books) for varying prices, but often not too expensive, if you don't need to deliver outside of the US.
If the chess one is any guide, they may have lost the explicit TutorText branding (and changed title slightly) if and when they moved to other publishers so best to search by author.
I wrote it up in /r/chess: Problem 66 from Chess for Fun, Chess for Blood by Lasker: white to mate in 3 [1]
[1] https://www.reddit.com/r/chess/comments/73h23o/problem_66_fr...
5B2/6P1/1p6/8/1N6/kP6/2K5/8 w - - 1 1
The version from Lasker's book is much more interesting. It happens that the version from HAKMEM is also a mate-in-3, but kind of a mundane one, relative to Lasker's anyway.
[1] Lasker's book is on Google Books, and you can see the relevant page (page 145) https://books.google.ca/books?id=y90UTQeLeeIC&pg=PA145 (spoiler: the solution is described on that page).
[1] You can see it on Google Books https://books.google.ca/books?id=y90UTQeLeeIC&pg=PA145
[2] FEN for Lasker's version: 5B2/6P1/1p6/8/1N6/kP6/2K5/8 w - - 1 1
[3] FEN for HAKMEM's version: 8/5BP1/1p6/8/1N6/kP6/2K5/8 w - - 1 1