There is also a three volume series that covers three grade bands, all together comprising K-8 again. I have two of those, for the lower and middle grade bands. Not a lot to choose from based on my limited experience with the latter series, other than the notion of working one’s way up over time, if you’re starting with really little kids. It’s safe to say that van de Walle was well aware of the notion of mathematical maturity, though this is a complex notion that partially involves notions of developmental psychology, and later perhaps involves ideas that are specific to mathematics itself (like notions of proof, for example).

Stepping out of the above, I recommend checking some free materials that I believe most kids (and many adults) will find engaging: COMPUTER SCIENCE UNPLUGGED is a series of lessons now downloadable as pdf files that look at some of mathematics underlying computer science as well as important applications (e.g., searching algorithms, minimal spanning trees, etc.) from discrete mathematics. Check http://csunplugged.org/ Also worth looking at by one of the same authors, Michael Fellows: THIS IS MEGA-MATHEMATICS: http://www.c3.lanl.gov/mega-math/papers/main.ps

Professor Homunculus sez:

Thanks for the suggestions. I haven’t checked them all out, but I have checked out the last one, and it is excellent. If you introduce a child (or adult) to the material in that book, you will probably help him/her learn more than a year of public school curriculum.

Which seems to reinforce the point that a good book, or books, can whup some canned public school curriculum any day.

I use a program that helps me keep track of what I have taught my boys, what they are reviewing for long term retention, and what I need to cover over time in order for them to get ready for Algebra at some point. And it encourages math in real life as much as possible, and waiting for math maturity. I use Math on the Level, available at http://www.mathonthelevel.com . This is NOT your traditional “curriculum” and in fact has NO worksheets! But it does have instructions for the teacher (you) so that you know HOW to teach or introduce a new concept to your child, and most parents are finding it very easy to learn and teach with. You might want to take a look at it!

Professor Homunculus sez:

Cindy, that is brilliant advice. I had never heard of the mathonthelevel stuff and just checked it out. It looks like a very well-thought-out program that doesn’t have any of the “pap” stuff of other programs.

Thank you as well, for mentioning “math maturity.” This is an Idea that needs to be talked about more. One of the worst educational crimes of our school systems is to tell kids what they’d “better know or else you fail or get left back.” That is the dumbest way to teach that I can imagine. Much more about this later, but I just wanted to say how right on target I feel you are.

Folks, it’s comments like Cindy’s that make this site worthwhile.

Keep it comming!