Lorel,

You wrote of the �Life of Fred� math books:
>the stories are so enticing that my kids tend to read ahead and do not always do the math along with them.

Yeah, that certainly happens! I don�t really think it is a problem unless the kids simply refuse to ever do the problems when they reach the level at which they really can handle them.

Of course, it is not possible to really learn math without doing a lot of problems (or, at higher levels, proving a lot of theorems). But math is not fundamentally about doing problems � it is ultimately about understanding concepts. Simply reading through the silly stories in the �Fred� books will help the kids get the concepts, so that, when they are ready to do the problems, they will be better prepared.

Again, I am not offering any excuses for simply avoiding problems � you have to do problems, and, ultimately, you�ve got to learn how to get the right answer and be secure knowing that you can get the right answer and why it is the right answer. But reading serious books about math (and the �Fred� books are serious despite the silliness) can be as important as actually doing problems: the two things are not mutually exclusive.

There is a wonderful book long out of print but still available through abebooks.com etc.(and nowadays through public-library interlibrary loan services � though I recommend buying a copy) that illustrates my point, Irving Adler�s �Giant Golden Book of Mathematics.� It has no problems at all, but does a fantastic job of getting kids to think about math up through calculus, infinite series, etc. It�s at a middle-school reading level and only requires knowledge of grade-school arithmetic (i.e., no knowledge of algebra required at all). A friend of our family gave me a copy when I was nine or so and I devored it � it was quite easy for me to read. And yet, I only fully understood all the implications of the book after I got my Ph.D. � for example, Adler remarks on an interesting formula for pi, which you can easily check by hand or with a calculator, but I finally learned where that formula comes from only as an adult.

So, the Adler book has an �open-endedness� to it that allows a kid to get the basic ideas but keep coming back and thinking more about things, wondering if he has really seen the whole picture. That�s what real math (and real science and, for that matter, real history, literautre, music, etc.) is all about, but it is something that most textbooks simply ignore.

Let me emphasize again that I am not excusing the sort of �fuzzy math� that makes excuses for kids� never learning to get the right answer. The mantra should be �right answers through conceptual understanding�: neither right answers without understanding nor understanding without right answers is acceptable.

(Liping Ma has a wonderful book making just this point, �Knowing and Teaching Elementary Mathematics,� that every parent interested in their child�s education ought to read.)

Lorel also asked:
>the books have relatively few problems and I wonder if that is "enough" to cover a subject.

Probably not, though I think it depends on the child. I myself needed a lot of drill on the arithmetic tables and arithmetic algorithms (this is at a lower level than the Fred books of course), but, starting with upper-grade school math, I grasped the algorithms with a very small amount of pracitce.

Stan has a system with the regular problems versus his �bridges� (test problems) that I would generally advise following. We�re now in his �Fractions� book, and, since the kids have already done that level in �Singapore Math,� I�m letting them skimp a bit on the �Fred� problems. Once we get to the �Fred� algebra books, I expect to follow Stan�s recommended system.

The nice thing about homeschooling is that, since I interact closely with the kids, I�lll know if they are really getting the stuff. I expect that I may have to pick up some other algebra books for some extra problems, but we�ll see. Of course, they will be doing arithmetic and algebra anyway in physics, chemistry, etc. and that too will provide some additional practice.

Sorry for writing a treatise in response to your brief questions, but I�m rather passionate about kids� learning math the right way! Math is quite fascinating once you understand that solving problems is only the tip of the iceberg (a very important tip, to be sure), but most children (and adults) never have the opprotunity to learn what math is really about at all.

All the best,

Dave