Making math divergent

On Edspresso, “John Dewey,” who’s studying to become a math teacher, observes that education professors value “divergence” (more than one answer exists for a question) and regard “convergence” (only one answer exists) with disdain.

I think ed school teachers take an oath to uphold these beliefs as part of an attempt to turn math into a “divergent thinking” type of subject like social studies or English. Such thinking reflects a significant and depressing lack of understanding of what math is about.

More emphasis on teaching students to solve proofs might help, but geometry has become proof-light.

The proofs that exist in today’s high school geometry courses are trivial; many textbooks have turned most theorems into postulates so that geometry has become a collection of “taken on faith” propositions with no proofs offered. Geometry classes have become nothing more than memorization of formulae (areas, volumes, surface areas of volumes) and very few proofs.

I remember asking my geometry teacher why the “given” was given. He couldn’t explain the underlying thinking. He just knew how to march us through the process.

1. Of course, math problems tend to have onlly one solution, though there are many different ways to get to that solution. Interestingly, when I taught college students, they wanted to know the “one way” to do a problem, and were annoyed to find out that you could do it lots of different ways (and that I didn’t much care which one they used, though it helped to know them all so you could do it two ways to confirm your answers.)

2. trotsky says:

As a kid who was pretty good at math, I recall 9th-grade geometery being pure torture precisely because of the seemingly endless repetition of proofs. Frankly, a lot of the theorems just seemed intuitive, and constantly “proving” the obvious didn’t seem like a great use of time.

That said, the logical rigor that math instills is one of the best things about it.

3. Indigo Warrior says:

On Edspresso, “John Dewey,” who’s studying to become a math teacher, observes that education professors value “divergence” (more than one answer exists for a question) and regard “convergence” (only one answer exists) with disdain.

I’d like the Politically Correct Thought and Behavior Police to value a little divergence (freedom).

4. Indigo Warrior says:

I remember asking my geometry teacher why the “given” was given. He couldn’t explain the underlying thinking. He just knew how to march us through the process.

“It’s because I said so!”