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).

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.

Good applications of problem solving involve having a student decide what tools to use. Often times there are several different tools that can be used to solve a problem. For instance when my dd was in 1st grade she often used multiplication to solve the problems that her classmates solved using addition. Both solutions were correct, my dd just had more tools available from which to choose.

Also many hands-on activities used in the elementary school can be applied at a higher level. I observed my dd's math class last week. The class was working on basic fraction concepts (which my dd had already mastered). My dd decided to use her manipulatives to work on improper fractions and mixed numbers.

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.

I am just beginning my research into the math competitions. I am working with my dd's GT specialist on starting an afterschool math club next year. I think we are going to use Math Olympiad but I still need to do some research.

I also like to see an interdisciplinary approach applied to teaching math. Showing math in the context of the world. If your child likes science there is so much math application available. I teach a Zome geometry class at our local PG co-op. I try to bring science, engineering, history, art, etc. into the lessons.

Summer