To make students show how they solved math problems, give them the answer and tell them to explain why it’s right, advises Coach G’s Teaching Tips.

. . . I never saw students more resourceful than they were on assignments where I provided the answers. But that’s not all. The process of working backward from the answer also improves students’ grasp and retention of the material.

When I was in fifth grade, I finished the math work early, as did my classmates who’d been in Mr. Parker’s advanced math group the year before. Since we’d covered sixth-grade math with Mr. Parker — we also had time to learn different number systems and build different kinds of clocks — the fifth-grade teacher gave us a teacher’s edition of a seventh-grade geometry book. Meeting in an unused classroom, the Mr. Parkerites would look up the answers in the back and try to figure out why those answers were right. It was fun.

Update: On Classroom Chuckles:

I had a 4th grader turn in a math test with the following answer:

Q: Explain how you got your answer (to the problem above).

A: “I work my head off.”

Good answer.

Back when I was in college, several of my engineering teachers would email out the answers to the week’s problem set a day or two in advance. It actually was pretty great because all you had was a number and some units. You solved the problem and checked the answer sheet. If you got the same answer you went on. If you got something very close, you checked if it was a rounding error somewhere. If you got something completely different you knew you blew it and started over. If you still couldn’t get it you asked a friend or TA.

There are, of course, limits to how well this can work in certain situations. You cannot, for instance, give the answers to history exam questions, multiple choice questions (!), or even simple math like 4+5=9…. explain.

But it’s no doubt a technique that teachers should be aware of and able to draw upon at appropriate times.

Interesting idea. I am fond of posting a problem that is entirely solved with an error somewhere, so the answer is wrong; then I ask the group to find the error

Cheers

I appreciate the reference to my idea, Joanne, as well as your related anecdote. I also appreciate everyone’s comments. If more teachers did what you do, Sofia, test scores would go up–and not because of teachers merely teaching the test but because of students thinking more critically. I know this because I did it too, and my students’ proficiency rates were twice the school average.