<p>reasonable dad wrote, back on October 16, "I'm an engineer and so is my wife: both of our children showed early signs of being very interested in math and science. What a surprise! For this kind of kid, you are not too early in the planning stages, as you want to feed the appetite for science and math, and probably plan his future curriculum so that your oldest can take calculus early, since calculus is quite helpful with other scientific subject matter." </p>
<p>Yes. Learning enough math early enough is something rarely achieved in the standard United States curriculum. ALL of the math tested on the GRE math section is junior-high math in most east Asian countries, and it's certainly possible for most kids in the United States to learn math at a faster pace than they are taught. </p>
<p>My son's subject matter interest has focused pretty strongly on pure mathematics until recently, and I note with relief that State U. has a strong program in math. My son is in State U.'s accelerated mathematics program for secondary students, so if he stays on track he will taking calculus I next year (eighth-grade age). Even if his subject matter interests veer over to computer programming or engineering, all the math he is learning now will come in handy. </p>
<p>You mention learning math in your household, and I was wondering if you make any use of the EXCELLENT calculus textbook (titled Calculus) by Michael Spivak? That book is a joy and delight to read, full of thought-provoking ideas. Alas, my son will surely NOT be assigned that book for his calculus class--he will probably end up using one of the James Stewart textbooks--but we will use the Spivak book at home as a reference tool and source of supplemental exercises. I think we will also have the Apostol two-volume calculus textbook at home by next school year. </p>
<p>Another math resource that I just can't say enough good things about is the Art of Problem Solving (AoPS) online forum and its associated reference pages. </p>
<p><a href="http://www.artofproblemsolving.com/Forum/index.php%5B/url%5D">http://www.artofproblemsolving.com/Forum/index.php</a> </p>
<p>On AoPS we have learned how much HARD math there is to learn before calculus, and have "met" some International Mathematics Olympiad gold medalists, MATHCOUNTS national champions, and other interesting people. That is a great online community for math-eager young people. </p>
<p>Interestingly, my son's predominant leisure activity this school year has been reading English novels, both Newberry Award children's literature and classic English literature. He seems to be evening himself up on the verbal side without any pushing by me. </p>
<p>It's fun to see your perspective on parenting issues. Good luck to your children.</p>