Don’t get too excited yet — the big one (Why Algebra Works, you’re best off reading this post for an idea of how it is being written) isn’t done.
However, in the midst of work I realized I was assuming the readers would remember how integer operations went, and it was quite possible they forgot, so I worked on a appendix. The appendix ballooned into a full fledged … short story? novella? … and got to the point that I even separated addition/subtraction from multiplication/division.
So the first part (addition/subtraction of integers) is close to ready, and it does follow my percepts, namely–
1.) that it should have a smooth writing style modeled after popular math articles (like Steven Strogatz or Martin Gardner) rather than textbooks
2.) that there are no “problems” but rather “puzzles”, roughly defined as anything that wouldn’t be out of place alongside a Sudoku book or in the middle of a Professor Layton game
3.) that there is a strong emphasis on meta-thinking; that is, having readers examine whatever mental model they are using in a particular part of mathematics and diagnosing where misconceptions may come about at the internal level.
As an example of #3, I start by asking the reader to add 2 + 2 (really), examining the possible ways of visualizing it and which ways might be more or less helpful.
In any case, everything is so unlike the textbook approach that I need some beta testers. In particular, while I would like some people who are adept in mathematics, I would also like some people who think that are not good at math or even actively dislike it. I’m guessing the latter don’t read this blog I’m going to need some help — if you know someone who might be a good candidate, could you send the word along? I’ll get back to everyone in a few weeks.
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