Monday, June 23, 2008

Geometry of Today is Not Geometry of Yesterday

I'm pulling up old stuff, I know, but you can't get better than Barry Garelick.

Barry posted this comment on the first Kitchen Table Math back on June 5, 2005.

"From NCTM's PSSM, here's what NCTM has to say about their geometry standard: 'Geometry: Geometry has long been regarded as the place in high school where students learn to prove geometric theorems. The Geometry Standard takes a broader view of the power of geometry by calling on students to analyze characteristics of geometric shapes and make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry is a natural area of mathematics for the development of stusdents' reasoning and justification skills.'"

Translation: High school geometry used to emphasize proofs. Now it just emphasizes shapes and formulae, with an occasional proof and in general is not much more advanced than the geometry presented in 7th grade, except for the fact that not much geometry is presented in 7th grade."

My observations and thoughts:

NCTM is the National Council of Teachers of Mathematics. They are a body of educationists (my word) who are responsible for writing the national math Standards which are supposed to define the expectations for students in each subject area at each grade level. I say "are supposed" because the expectations are so watered down and are so vague that no one can actually identify a specific expectation.

You have to hunt far and wide to find geometry in textbooks today. This "broader view" is part of that "1/8 inch deep and a mile wide" approach to teaching Math. The subject of Geometry is spread all through other textbooks and is no longer taught in a coherent fashion semester by semester.

A high school teacher commented to me 2-3 years ago how much he wished he could teach geometry as an isolated subject so he could concentrate the students' focus on geometry.

Your student is probably being robbed of the opportunity to learn to prove geometric theorems. It's no wonder our high schools students score so much lower than Asian students.


Barry Garelick said...

Congratulations on your blog. (I tried to leave a comment yesterday, but it didn't take for some reason).

Geometry is still watered down since I wrote what you quoted. Ironic that those who cry out that students need to learn critical thinking, seem to find learning how to do proofs to be unnecessary.

Concerned Teacher said...

". . .Ironic that those who cry out that students need to learn critical thinking, seem to find learning how to do proofs to be unnecessary.?


I also find it ironic that those who want students to explain math by "writing the steps" do not see that "proofs" in geometry are really the very same thing.

The precision with which we were expected to explain our proofs forced us all to quickly analyze the theorems to use, and the shorthand ("S.A.S." etc) enabled us to proceed quickly in explaining it, so that our minds weren't bogged down with laborious, wordy proofs (sentences).

Each problem required deep focus, (critical thinking), and rigorous effort. The repetitive "doing" of the work enabled us to see how the concepts hung together.

I contend that our proofs were a form of writing, but just more efficient and certainly more appropriate for math.

And it amazed me that students who were quite good with the proofs, were often the very same ones who always struggled with essays.

Thanks for your input. Your expertise and defense of traditional math is appreciated in homes and communities throughout the country, and perhaps around the world.