Kriston,
My intention was not to imply that we should hold kids back. That is why we are using ALEKS. I am just suggesting spending more time on problem solving rather than rushing into algebra (although many algebraic concepts are taught prior to formally teaching algebra).
Oh, of course! I didn't mean to insinuate that you want to hold the kids back! I think this is a common debate in GT ed, and I know it's one I'm having with myself. I don't think either of us is talking about holding them back. It's a philopsophical debate about approach, that's all.
There are two components to mathematics. The first is learning the language of math, things like arithmetic and the mechanics of higher level math. I call these things "tools." The second is problem solving. I don't think I truly understood problem solving until I got to college and began working on a degree in engineering.
Historically in America our math curriculum has focused on learning the "tools" of math. There was not enough focus on the application of the tools and understanding the system behind the operations. For example a lot of emphasis is put on having kids learn their math facts while less is put on having them understand the foundations of the operations. Many students know that 3x4 = 12 but do not understand that concept of multiplication. As a result we have fallen behind other countries like China.
Hmmm. Maybe this is the root of my problem: I think my DS6 has a pretty good grasp of the problem solving skills even though he doesn't yet have all the "tools." If he's backwards from a typical American schoolchild, then my perception of this discussion may be skewed. This is helpful...
I highly recommend getting one of Ed Zaccaro's books. He really helped me see the value in higher level problem solving for elementary students. Our district uses his materials for 3rd-5th grade advanced math students.
We've mostly been pretty happy with Singapore Math and "Murderous Maths," a new addition to our curriculum from British Scholastic books. Since problem-solving is DS6's strength, I'm not sure we need more of this. But I'll certainly look at it. It never hurts to look.
Thanks for your response. It helped me.
