[kator]

Funny when I read the image I thought the student was optimizing to less work. His way was faster "I can use multiplication strategies to help me multiply." Seems the student's strategy was to do less work by adding 5+5+5.

When I took geometry I often was burned by my teacher when she'd ask me to come to the board and solve a problem. She'd say "You can't do that we haven't gotten to that part of the book yet, sit down already!" It all just seemed to logical to me. Maybe I didn't know what "it" was called but it was logical and easy to work out.

Most of my math teachers treated me this way, they'd be upset with me because I didn't write 100 copies of the problem on my homework but I'd pass all my tests. I was constantly in trouble with my teachers often being reported to the administration as a cheater. One teacher made me take my shirt off he was so convinced I must have written the answers on a sleeve or something. All because I didn't miss a single problem on his test but never turned in a single page of homework to his class.

[ryandrake]

Yep, the "erase your brain of that technique because we haven't gotten to that part of the book yet" reasoning was the most frustrating part of math (and science) classes in high school. It's a miracle I got through my teen years still interested in STEM. Contrast with how they treat these situations at the university level:

University: "Ahh, you seem to be pretty far ahead for MATH 140! You might as well go test out of the class and enroll in 141 instead! Save some time."

High School: "Conform to the curriculum. Repeat this technique. Obey the rules or fail."

[ecspike]

Yep. My dad taught me a bunch of math on his own and I would also get in trouble for "not showing my work" on tests.