As I was working on my Bachelor’s degree in mathematics, I had a professor that drove us all crazy. He would be discussing a topic, new to all of us of course, and as he was going through his process on the board, he would skip all sorts of steps, casually stating “it’s obvious”. My peers and I would look at each other, hoping someone had a clue as to what just went on in that man’s head (which he didn’t feel was important to share, being that it was obvious and all). To this day, I know I could call any one of my old friends and just stating the phrase “it’s obvious” would make us both break into laughter.
What I’m finding as a Research Associate for AIMS, delving into the research on how children construct their understanding, is that we as math educators are guilty of the same assumption. We often forget to step back, out of our adult minds, to look at seemingly simple concepts such as counting, addition, and multiplication, from the perspective of a fresh mind with far fewer experiences. We rarely take the time to reflect upon what actually has to happen within a child’s mind for them to develop these ideas and become fully functional within what we consider elementary concepts. Are we assuming that just because we know something, that it’s obvious to the child?
Identifying what a child is thinking is not so obvious for us, though. It turns out that researchers have looked into children’s thinking for us, and this research continues today. Through this work researchers have identified stages which a child goes through in the process of developing the concept of number and operating with number – all from the child’s perspective. The research also gives us ways to present tasks to students that will initiate in them a need to modify their current ways of thinking. In doing these tasks, the students grow in complexity of the number sequence that they work with, as well as capacity for coordination of units, multiplying and such.
Let me give you an example of what this is like. Do you remember learning to drive? I’m sure you had to stay pretty focused on what you were doing at first, thinking about your destination, your blinker, the correct pedal, etc. Nowadays, how often do you find yourself so consumed with thought about everything except driving, that upon arrival you’re not quite sure how you got there? Driving has become automatic – second nature. There is room in your mind for other things. That’s what this way of “teaching” math can do for a child – help them to make working with numbers in more and more complex ways, sort of second nature. Then, as they progress into Algebra and Geometry, they can save their mental space for the new concepts.
So, I’ll keep reading and I’ll try out these new research-based ideas with the students I work with. Keep checking our blog and I’ll share what I learn!