Your question: Which comes first: Geometry or Advanced Algebra?

The government schools have the courses usually laid out as . . .

9th grade: beginning algebra,

10th grade: geometry,

11th grade: advanced algebra.

But they do a poor job of educating.

There are several reasons why I suggest that advanced algebra follow the beginning algebra.

First, advanced algebra is much more "mechanical" than geometry. Like beginning algebra, much of it consists of learning procedures—such as how to factor trinomials. Those who have had success in beginning algebra will continue on that same road. Some of the items in advanced algebra ask that the students remember what they learned in the first course in algebra. So taking advanced algebra right after beginning algebra will promote more success in advanced algebra than putting geometry in between them.

Secondly, the proofs and the reasoning that are a real part of geometry require a more mature mind that the mechanical stuff of algebra. There is not just a single way to do some of the proofs—more creativity is involved. And older brains seems to do that kind of reasoning more easily than younger brains. Jean Piaget said that we pass through different stages of reasoning as we go from childhood to adulthood. The last step—formal reasoning about abstract material—is attained in our late teens.

That's why I'm suggesting Life of Fred: Advanced Algebra come next.

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