To Read:

Polya, George. “Mathematical discovery: On understanding, learning, and teaching problem solving.” (1981).

Krulik, Stephen, and Jesse A. Rudnick. Problem solving: A handbook for teachers. Allyn and Bacon, Inc., 7 Wells Avenue, Newton, Massachusetts 02159, 1987.

Schoenfeld, Alan H. “Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics.” Handbook of research on mathematics teaching and learning (1992): 334-370.

To Solve:

Work on more problems, write about the experience (what I learned, what I tried, how I failed, what I figured out, etc.)

Work on problems from Polya, write about the experience.

To Make:

Make a list of specific heuristics for a portion of a high school geometry class?

To Write:

Write a series of posts trying to make sense of Polya, Rudnick/Krulik and Schoenfeld’s ideas.

To Decide:

Whether to continue with this project.

I spent a week working on this.

What ended up helping?

• Checking Geogebra and finding the exact values of x and all the other angles, and realizing that this meant that the diagram was made of an equilateral triangle and an isosceles triangle. I spent a lot of time trying to prove that the triangles were either isosceles or equiliateral, to no avail.
• In a previous problem from GoGeometry I had been asked to show that an angle was 30 degrees. I was stumped, but when I looked at some solutions I saw that people used the side lengths to show that a right triangle was 30/60/90 and that (therefore) the given angle was 30 degrees. I realized that this was a possible strategy.
• I know that sometimes it helps to draw an altitude.
• I was on the look out for similar triangles, since triangle relationships (especially similarity ones) often open a problem up.

Then, essentially, it was a week of randomly trying to make each of these individual things work. I had (and I have) no understanding of why I should have known that these three strategies should be used at once. It took me a week to solve this, I think, until my continued attempts happened to let me combine these four tools at once.

I find it helpful (and fun!) to try to understand aspects of problem solving from trying to solve problems on my own. This is a problem that I got stuck on. I had a few ideas to start and then I got stuck.

At the urging of some folks on twitter I used Geogebra to figure out what the value of x is, and now I know and am trying to find a proof. Then, I’ll try to figure out what I would have needed to try to discover the answer on my own, in the first place.

I’ll check back here when I’m ready for spoilers. In the meantime, feel free to use the comments to discuss any aspect of the problem. Here are some prompts:

• What solutions did you find?
• What possible hints could you offer me (or anyone) who gets stuck on this problem?
• What math could one/I learn after working on this problem?
• What strategies/heuristics could come in to play while working on this problem?

Looking forward to reading more when I give up or figure this out!

(Also, this is my first post in this space. Maybe I’ll keep on going, maybe I won’t. Subscribe at your own risk.)

(PS Oy, wordpress sticks ads at the end of posts these days? Sheesh. Maybe I’ll jump ship back to blogger. Or get my own domain. Or something.)