Did You Solve the Problem You Meant To?

A few posts back, I shared that I would be teaching problem solving to my daughter’s fourth grade class. I ended up having a slightly different emphasis than I planned when I wrote my post. I also ended up using the very relatable problem of “how do you share cookies” which seemed to resonate. Especially when one of our activities was eating cookies.

Instead of focusing on the “mistake” I decided it would be great if my key message was to re-frame mistakes as “you solved a different problem.” The class was great at answering my questions. Since we’re in Colorado, I started with the analogy that problem solving is a bit like hiking to the top of a mountain. You look for clues you are going the right direction. Sometimes things are obviously going right, other times you are not so sure.

Most of my focus though was on the idea of “alternative problems.” For example, that when you set out to solve a math problem if you accidentally miss one piece of the problem, you solved a different version of the original problem. Or that when you are asked a question like “If your mom gives you 6 cookies to share with your friend, how many cookies do you each get?” you usually assume that the cookies have to be shared equally, but there are other possibilities. For example, you could be greedy and give your friend only one cookie (I think less than that would be suspicious, and giving them nothing wouldn’t count as “sharing.”). The kids felt pretty strongly about fairness, and their first suggestions were all about sharing some of the cookies with a third person.

I also shared that the way multiple choice problems are constructed is by the power of “alternative problems.” What happens if you accidentally multiply by 2 instead of dividing? What if you miss a piece of the problem entirely? These sorts of misses make for plausible distractors (wrong answers) to a multiple-choice question. As I mentioned to the class, if the right answer is 12, a wrong answer of 1,362,005 is not going to trick anyone.

My closing message, and also the lesson the class cited at the end, is that you can re-frame making a mistake as solving a different problem. That in fact you can think of it like a puzzle to figure out which problem you or someone else solved that was different than planned. Treating it like a puzzle is a much more positive framing and I find it makes it a lot easier to be patient when I am helping someone else too. Basic math might be easy, but figuring out what problem someone else solved is a more interesting, difficult, and even fun challenge.