On Fri, 2007-06-15 at 11:11 -0400, Steve Litt wrote: > Hi all, > > I'm writing an introductory algebra book, meant to teach without a teacher, > meant to be easy to learn for kids 12-16. It's been my impression that > traditional textbooks try to make the material seem complex so as to require > a teacher, so that the school will order it (what school would order > something that would put them out of business).
First let me commend your aspirations! I was a very good mathematics pupil at school, then later was a teacher at secondary school level for 19 years. My main subjects were Latin and French, but as I had qualifications in maths at University level, I was dragooned into teaching maths as well to pupils up to the age of 17 years. I found maths very easy to teach (compared with Latin and French) and I was successful as a maths teacher. But in all that time, whether as a pupil, a student, or a teacher I NEVER once found a maths text book which I understood. I would read the book in vain, then a few words and an example from the teacher, and comprehension was instant. So my comments are: 1. Your book will have to be different from any I have read. 2. The teaching style which works for me is: a. Some background on why this topic is good, fun, interesting, a challenge, or possibly even useful. The book Mathematics for the Millions is good at this (you know: Egyptians needing to mark off their fields after the Nile floods has erased their boundary markers etc.) b. A worked example. (In the classroom, they copy this down.) c. Some explanation of how or why the example worked. (This seems back to front to most people, giving the example then the explanation. But it always worked for me.) Keep it short and punchy. d. Similar problems for them to do, progressively getting more difficult. My training college days taught me that 6 drills of anything was enough to consolidate learning, any more produced boredom. e. Some sort of quick quiz which allows you or them to gauge whether the concepts have been picked up. 3. On reflection, most maths books are impenetrable because they go from the general to the particular. My belief is that paedagogically the reverse works better: Use a concrete example as an introduction to an abstract concept. Incidentally I share your enthusiasm for LyX. I regard it as the best piece of software ever written (along with the Unix kernel, C language, Korn shell, and Prolog). regards John O'Gorman > > So in a way, my book is diametrically opposed to math textbooks, yet I also > want to benefit from literally generations of math teaching and writing, > which is why I use the AMS Book document class.
