A Mathematical Conversation and Why Experiences Matter

The other day I was talking to a student that I tutor about measurement. He was having trouble visualizing a yard outside of the flat grassy area in front of his house…his words. I knew that the student was an athlete so I immediately started inquiring about yard lines on a football field. We then took out a ruler…a real one (not a formula chart with a printed one) and began talking about inches and feet. We drew one yard by moving the ruler 3 times.

The student then started talking about the number of rulers that would fit between two yard lines on a football field…specifically the 30 and 35 yard line. He drew a picture. As he drew, he looked at the ruler several times. He looked at the lines that we measured. He came up with a way to think about the problem.

Below is the problem that started this discussion. Below that is his picture.

To be clear…I have several problems with this problem. Technically, this is from a 5th grade unit on algebraic reasoning. Should he have been able to reason through this problem? He was stuck on the variable, f. He was stuck on the word furlong. When he originally completed the problem, he seemed to be stuck on the entire problem.

Our discussion and actions were about experience. What do you do when you don’t know what to do?

Added to his arsenal….

  • Draw Pictures
  • Connect it to something else
  • Rethink about the problem

Last night during our session, he excitedly told me how they worked on feet and yards in class. He understood it.

That was win…





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