I came across this puzzle the other day and found myself running through all of the strategies I use to figure out math puzzles. I am generally good at these types of puzzles and knew I could figure it out. I added, subtracted, multiplied, divided, squared numbers, etc. I knew the solution was obvious, but still I couldn’t find the answer. I ended up “cheating” and looking at the answer that was provided. The interesting part of this puzzle was not that it was challenging or that I couldn’t come up with the right answer. I love a challenge. It was that I applied tried and true strategies and they simply didn’t work. The answer* was simple…very simple.
How many times have you applied what you know to be true and not come up with the “right answer?” How many times have you been presented with a familiar situation and gone to the familiar rather than bringing a new approach to that problem? Did you become frustrated? Did you give up?
Each day we ask children to approach problems that we understand completely. We know the answer and want them to join us as “knowers.” We offer smiles, nods and perhaps an enthusiastic “Yes” when they reach the pinnacle of knowing. However, do we encourage diversity of thought? Do we join as thinkers and not simply knowers? Do we learn from their attempts to make meaning? It is only in doing these very things that we all learn. I have learned more from the students I’ve taught than I have ever learned from the books I’ve read and the courses I’ve taken. I’ve learned new approaches to “old” thinking. I’ve learned that there are multiple ways to approach any given situation and to still get a problem “right.” And what have those students learned? They’ve learned that it is important to try and that there are multiple ways to solve a problem. They’ve learned that others’ ideas and thoughts have an impact on their thinking. They’ve learned that it is OK to be wrong and that effort matters.
* Click here for the solution.