I recommend including some enrichment like Ed Zaccarro books along with ALEKS or regular elementary classroom math. Once you get to algebra AoPS and math contests are good forms of enrichment. Elementary and secondary math education is lacking in this country. I went through Calculus in high school and made all A's. When I got to college I realized that I learned a great deal of "how to do math" in K-12 but not much about "the whys behind the math." I figured much of that out in my college level engineering classes. It was not that the concepts were difficult; it had more to do with the way the concepts were presented.

Oh, sing it, sister! That's how I felt about my math education, too, and it's one of the things I'm really trying to avoid with DS7. I want him to be a thinker in math, not just a doer, like I was/am.

Kriston, et al, you might find this interesting; right now in our elementary school system there is a struggle between folks who have instituted a new system of math based on the whys and what fors behind math (pattern recognition, estimation, etc.), and parents who feel their kids are not getting enough ROTE math work to reinforce concepts. Really, I think we are lucky they are at least trying to go broad, and when Dh and I feel ds8 needs more rote work on an area, we cover that at home. - The repetitive work is the easiest part to work on at home, imo.
I mean literally I see ds8 coming home with work dealing with concepts applicable to computer science, science in general, pure math, (math for funs sake!) etc. In 1st grade he was inspired to make up a game involving tallying up various truck types as we drive. We still enjoy playing this one on the road together, and the accompanying discussion of why in this area or city there might be more of one type... Maybe the whole system will be a bust, but I see my son still enjoying math, so I think that is ok.

Ah, yes, these are the Math Wars.

FWIW (not much!), I do think that there's a need for practice of arithmetic skills. I just don't think that arithmetic = math, and I don't think drill-and-kill is the way to teach math.

Rote Drill has its place. Its a great tool. I highly recommend it.

By rote drill, I mean being able to solve a problem or recite a theorem on demand with no hesitation and at the fastest speed possible.

To survive Very Hard tests in college, I had to have some things down cold. I took advanced thermo and stats classes that required us to derive methods to solve general classes of problems then solve specific cases. All the math had to be second-nature. And we ended up using ALL our math skills - from calculus, diff-eq, Linear Algebra, theorems from RA, Stats, etc. Those kids who did could not slam out the math or reach for a theorem, were left behind.

The first week, the instructor told us we had to take this "easy" week to get up to speed. He told us how to do it.

I had already been doing rote drill for calculus and Linear Algebra prior to the semester to get warmed up. But he upped our game. Every night I spent 12 hours outlining all my other texts, categorizing problems, setting up flash cards, then just started going through it. I had over 200 flash cards with theorems and problems - both pure and applied - on them. Once I had all the subjects down, I shuffled the cards, then took 50 with me on the bus each morning. As the class progressed, I added cards from that class.

After I started this method, I usually finished the finals in one hour vs four most of the other students needed. It all came down to that rote drill. A friend of mine started using it when he was in the math program and from then on he got A+ in classes.

To this day, I can look at most applied math problems and do them in my head. And I can usually look at something that is not right and be able to grasp the theorem being used and which of its givens are being violated.

When you look at other human pursuits - such as sports or marksmanship or cqb - rote drill is a key part of the training method. Sure, there are unstructured problems - but the solution to them often involves pieces taken from actions which are down cold. Academics - and problem solving - are no different.

A mathy kid should start his or her set of flash cards by putting the hardest problems from the week on them. Its like baseball cards for math! On the front should be the problem statement. On the back should be the elements for the solution.

Another set of cards should have definitions and theorems on them. Name of the item on the front, the explication on the back.

This method can be explanded to other subjects as well.

Sorry, Austin, but rote drill would destroy my 7yo's interest in math. Like with a sledgehammer.

I'm not saying practice and even memorization don't have their place. I just don't think the place for the sort of drill you're describing is necessarily elementary school math...which is where most of it is currently located! Flash cards are about the worst way to teach my son. I know--we tried them!

Different kids have different needs, so different approaches suit them better. A lot of GT kids are concept kids, and drill-and-kill simply isn't the right approach for them. Especially for visual-spatial kids, they need to see the big picture first and then the details come more naturally to them.

One-size-fits-all just doesn't work.

I understand Kriston. Good point. I am a spatial learner, too. There were times I would take the whole deck and organize it in one big jigsaw puzzle just for fun.

The way I used the cards was to organize the information and then ensure the retainment of information once the knowledge was obtained. Once I had the stuff down, it got a few cards, then they went into the deck.

I did not use it to learn new stuff.

Yes, that makes sense. As a review tool or to build speed where speed is desirable, I think strategies like that can work wonders.

DS7 is not fast at anything except learning! And he probably never will be. I always say that there are (at least) 2 kinds of GT kids: the fast and the deep. DS7 is deep. He prefers time to mull things over.

I think that style difference affects learning strategies, too. Things like flash cards or even educational video games that require quick retrieval of info stress him out. We're working on it, but I'm pretty well convinced that we have to come at things that are typically memorized--like his times tables--from another direction or it will not be good for his love of math. He needs lots of concept, very little drill at this point.

Maybe that will evolve as he gets older. I guess we'll see...

Kriston - your post rang a bell for me. In "Re-forming Gifted Education" the author wrote about two different types of gifted kids. Those that need to learn fast and furious, more, more, more and those that need time to ponder, need to go deep, deep, deep.... those two types should not be in the same gifted program as they will frustrate each other.