Dear Heather,
Wow! Thanks for sharing so much of your journey mathematically with you son. It does sound like it has been quite an adventure. Your son does sound brilliant and I am sure it must be hard to know how to challenge him without boring him. However, I do feel that starting with Level E would be beneficial for him. One reason is that it pulls together all the basic concepts of math in a very hands-on way, which sounds like his preferred style. Also, it is a pre-algebra course in many ways as it really challenges children, especially through the daily warm up exercises, to see the interconnectedness in math. I fell that it is essential to lay a strong foundation for algebraic thinking.

Starting with the Geometric Approach first may cause him to have some gaps that won't show up until later and will cause great frustration when he is trying to think mathematically at higher levels. When he finishes Level E, he will be ready to advance to the Geometric Approach and will really be challenged with thinking through the work more independently.

Plus one more factor, he is only ten. He has plenty of time to move through two levels and still be in Algebra early. The advantage is that you will be confident that he has a firm foundation and the gaps will be filled in before they cause more frustration.
Nancy

Thanks! That's the way I was leaning, I've received the same advice from a few different sources now, and even my son agrees! I totally agree that it's most important to understand everything properly before pushing on. I'm very 'rigid' with that in my 'other life' as a piano teacher... I spend MUCH more time with the 'beginner' stuff than most teachers do, (sometimes years if needed), I don't just automatically zip them through the grade levels like many parents expect, sometimes to their great consternation! But the result of this is that my students are always MUCH stronger than most by the time they reach the intermediate levels, because there are no holes or big weaknesses in their early training.

Before typing that up right now, I hadn't actually made this connection between my STRONG insistence on this philosophy for my piano students, and my struggles with how to approach things with my son. If I step back and ask myself "if this were piano instead of math, and he were a student instead of my son, what would I do?"

And the answer is a big DUH. Level E it is!!

Great!