When I was young, we were told that there was a specific way that we had to show our answers/thinking in math class. We could only show the way that was taught, and we were often times deducted points if we didn’t show the correct algorithm or method. I think that did a great disservice to our generation of mathematicians. I think it limited us in our thinking, and taught us that we were either good or bad at math. There are times that I think math is more about finding creative solutions, than knowing the “right” way.
Take this classic example that happened in my class last week!
We are working on multiplication and division right now, but there is a group of 5 students who pre-tested right out of this topic. Their knowledge at the beginning stages of multiplication and division was so far beyond the rest of the class, that I have them working independently on my On Stage! Holiday Concert Performance Task. In this project they are charged with planning a whole entire holiday concert for their classroom. It is really fun to watch them work through each of the tasks in the problem. I schedule in a time to meet with them daily, and loved this moment I had last week.
Pictured below is one step of the project (there are 6 total). It is my sample invite that I pull out if they are struggling to understand that particular part of the task. In this part of the project they are asked to find half of an 8.5″ by 11″ piece of paper, draw the rectangle on the given paper and design an invitation for the concert.
I asked the students to describe the way they figured out the “half size” rectangle. I was, and always am, amazed at the many different ways they found it:
- Method 1: “I just folded a piece of paper, measured each side, and then drew those measurements on the paper.”
- Method 2: “I figured out that half of 8.5 is 4.25, and that half of 11 is 5.5, so I drew those lines on my paper.”
- Method 3: “I had no idea how to figure this out, so I folded a piece of paper in half and traced it right on my paper. It seemed like the easiest way.” (LOVE the HONESTY here!!!)
We talked about how each way was just fine for each type of learner. For someone who understand fractions/decimals, method 2 is great. Perhaps you don’t have a clue how to use a ruler, then method 3 can work. We discussed that there was always more than one way, even if your way isn’t “perfectly mathematical”, we can then think about how we can do it mathematically the next time. The student who used method 3 became a sponge as she listened to how the other two students described the way they figured it out.
Allowing students to share their ideas allows them to see that there is ALWAYS more than one way!