In recent discussion about Bret Victor’s Kill Math project Ben Blum-Smith brought up the books Visual Complex Analysis and Visual Group Theory which as he puts it “all arguments are geometric and illustrated by diagrams”. (I’m not familiar with the latter, but Visual Complex Analysis is fantastic and I highly recommend it.)
I feel like these sorts of books will eventually create a revolution in upper-level mathematics — I’m eagerly awaiting someone to write Visual Linear Algebra — but could we re-conceive lower level mathematics in the same way?
By Visual Algebra I’m not meaning graphs, I’m meaning the more mundane symbolic “solve for x” manipulation.
Solve for x: 2x + 3 = 5.
In the same vein as my puzzle equivalent to solving a quadratic, solid lines mean multiply, dotted lines mean add.
Solving for the highlighted circle is equivalent to solving for x in 2x + 3 = 5.
(I swear I have seen something closely resembling this elsewhere for equations, and I think it even has a buzzword attached — anyone know?)
I originally thought of these sorts of puzzles as a gentle introduction to the topic, but would it be possible to integrate this kind of visual-symbolic thinking in every part of an algebra course?
ADD: Here’s an image where the puzzle is closer in look to the equation:
This sort of thing is risky because rather than applying inverses and so forth students may make it a general method to draw circles and arrows everywhere.