Some prototype pages of Visual Algebra

While I theorized a book called Visual Algebra it was non-obvious what such a beast would look like; perhaps this prototype from my work in progress gives an idea. The original is a single page (intended for web or iPad or Kindle Fire or whatever gizmo happens to be around when I finish this thing) which I have split up to be blog-margin friendly:

Instead of applying the Rule of Four…

…or the less common five representations (“pictoral” is like my example above with the boxes)…

…I am trying to apply a sort of Rule of Six, adding my tree structure matching the mathematical symbolism. I am attempting to show representations simultaneously as much as possible. This is a very image-intensive approach and would not be remotely practical in dead-tree book form, but given the book is meant to be electronic I can use as many images as I want.

However, I’ve got terrible angst in that it’s very difficult to write in a relaxed and friendly matter while still being exact enough for mathematics. Here is a page that pains me (click for full size):

Would I ever really say “the numerical value on one side of the equal sign must be balanced with change on the other side”? I can’t just say “you have to keep them balanced”; that would be unclear and vague enough to cause potential misconceptions. Such a statement also shuffles under the rug manipulating an expression without changing it.

Also, when I turn the tree diagram from a puzzle into a pedagogical tool, it starts to get clunky and confusing. I’m unclear the best way of patching it up or if I should just pitch it.

(For those worried about the fate of the long-awaited video Giant Space Whales vs. Logarithms, it won’t be too much longer, I promise.)

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