LMom,

You say you and your spouse are math geeks. Can you define �math geeks�?

Okay, putting it that way probably proves that I am a math geek! But, seriously, are you both folks who really like math, are you both in technical fields, were you both math majors or what?

I�m curious because I�m always trying to figure out how to teach math better to our kids, who are middle-grade school by age, upper-grade school by math grade level (tests show them as five years beyond grade level, though from my own experience I think they are not quite that far ahead � I�d peg them as three years beyond grade level).

I learned a lot of math, not thoroughly but at a beginning level, years before I was �supposed� to, largely by random sampling. For example, I learned the basic ideas of Galois field theory (not all the theorems, but enough to do some calculations) from some book (I�ve forgotten which) in high school just for fun. This turned out to be a good thing, because, after I finished my Ph.D. and was out in the real world, I serendipitously was talking with a co-worker and found that he was working on a project using Galois field theory for satellite communication systems. I ended up being co-patentholder on several patents using GFT for satellite and computer hard-disk applications.

So, I�m trying to replicate my experience with our kids. As I�ve said above, while mastering the standard algorithms is of course an absolute must, I�m really keen on trying to convey the idea that math is more than that � it�s basically a set of beautiful concepts and a way of thinking about the world.

That�s hard to convey.

The nice thing about the Fred books, of course, is that they have a �young� feel to them but that they do real math, so that a child whose math ability is well beyond his chronological age but who is not quite ready for the formality of higher-level books can learn a lot from them.

I assume your son is very accelerated in reading if he can read the Fred books. As you know, the beginning one starts with fractions. Is your son accelerated enough in math that he can handle that mathematically? My kids are several years older than yours and are finding some of the problems somewhat challenging.

On the issue of supplementing �Fred� with additional problems, I�m philosophically opposed in general to relying on one book to teach a subject and then just relaxing. I think the parent always needs to ask himself or herself if the kid really �gets� it or if using other books would help for different perspectives, additional problems, etc. Usually, I think, the answer is �Yes � other books would help.� We�re doing that even for Chinese � instead of just going through one introductory curriculum until we have it memorized, we�re jumping from one to another (this turns out to be a good thing, among other reasons, because all of the introductory series have some real lacunae in their vocabulary).

Anyway, I�m curious to know where you and your spouse are coming from math-wise and if you have any thoughts on how to replicate my own personal experience with learning some �advanced� math before one is �supposed to.� I�m hoping to do it in a little less random way than happened to me personally, but without simply trying to push kids to plow through college-level math books. Math can be so beautiful, but it is usually taught in such an ugly way!

All the best,

Dave