I believe the world is made up of two kinds of people, math is good people, and math is not for me people, or quite simply, Algebra People and Geometry People.
I barely passed Algebra in high school. The next year I aced Geometry with the same teacher.
Geometry is obvious. You can see it. Algebra is abstract. Algebra is a mysterious mix of letters, numbers, and functions growing into strings of symbols that defy logic.
Geometry is sequential and logical with proof building upon proof, reaching the obvious conclusion.
Algebra is a tricky balancing act with two sides of an equal sign battling it out for a possible answer.
My sister, on the other had, majored in math in college. She loved Algebra and found Geometry abstract and confusing. The words I would use to describe Algebra are the exact words she would use to describe Geometry: abstract, not visible, floating around in the mist.
Ask most adults and they will tell you which which of these two subjects they prefer and you will find the same dichotomy. If you understand Algebra you struggle with Geometry. If you understand Geometry you struggle with Algebra.
What does this tell us about how people perceive and eventually comprehend these two aspects of mathematics? I found this in a math forum on the internet:
Algebra focuses on developing in students convergent thinking patterns (simplifying and solving) and the ability to manipulate abstractions (variables).
Geometry encourages the development of divergent thinking patterns (specific example to generalization) and the visualization of abstractions (geometric modeling).
So let's acknowledge that some people will do better at some things than other things and stop trying to make all our children proficient in everything.
