Currently, I am in the midst of raising a 16-year-old who has been learning to drive. Recently, I was reminded of what it feels like to do something new while I was doing a math demo lesson in a classroom and how circumstances can bring us back to those early behaviors.
Here in the central valley of California, the fog can get really bad. It can make even seasoned drivers mimic the nervousness I saw in my daughter when she first began to get behind the wheel. All of a sudden instead of driving on autopilot, fog can make you slow to a crawl, hands tightly on the wheel, unsure of your surroundings, behaving like a beginner.
So how does math relate to driving in the fog?
I was reminded of a common phenomenon we have seen as we have been researching how children learn math. When we present a situation to a student that is just outside of what they have already learned, they will often resort to less sophisticated behaviors to tackle the unfamiliar problem.
Let me give you an example.
A particular student I was working with was demonstrating that her way to add two numbers was to count on from the first addend. All of the problems I presented to her so far had contained a second addend within 10 (therefore she could use one set of hands to track her second addend as she counted on). Next, I presented her with a problem where the second addend was 11. She immediately said she didn’t have enough fingers. I worked with her to count 11 fingers, and she began to pull her fingers back after she had counted 10 and then reuse them. So she worked out a finger pattern for 11 that could be useful as she tried to solve this unfamiliar problem. Her next move was to use her new finger pattern for 11 as she counted on, or so I thought. But what she did was start counting all (started counting from one until she reached the first addend and then began to use her fingers to track 11 more counts). Something about the newness of this situation may have put her in a fog so to speak. She needed to revert to counting all to achieve her goal. She demonstrated less sophisticated behavior, while she tried something new.
What is even more interesting is that after counting all for a few problems where the second addend was beyond ten, she began to count on even with the larger second addend. I wonder if she would have made this growth if I had interrupted her counting all method, and expected her to count on? I may have done that in the past, believing that she had the ability to count on, so why shouldn’t I expect it of her? But I think differently now. Now I think of how I revert to beginner behavior when it gets a little foggy, and that enables me to drive in the fog.
Maybe for students, it is similar as they approach new math territory. Do you ever see your students go back to less sophisticated behaviors as they work through a new and unfamiliar problem? Please share.