Every once in a while, something will happen at work that makes me miss the classroom and the kids that I taught. It’s like a craving at times, but today I feel more like the athlete on the bench that wants a shot at winning the game. Here I am on the sidelines, wanting to yell “put me in, coach!”
The instigator for that feeling was reading the article Adaptive Mathematics Teaching by Dr. Leslie Steffe(1) (1990). I love what I am doing as a researcher and believe I will be able to affect more children through this work, but the content of this article made me want a do-over as a classroom teacher. It was an “aha” moment for me as to why this research is important and why teaching from a student adaptive pedagogy frame of reference is so much more powerful than even the conceptually-based teaching I was a proponent of when I was in the classroom.
It was the perfect time for me to read this article since we have just finished a semester working with 2nd and 3rd graders with tasks that, from an adult perspective, are multiplicative in structure. We presented students with varied situations that all had a basic multiplicative structure in common. I watched students develop understanding through their engagement with actual material and contexts that were within the students’ real life. At the end of the year we were told by the classroom teacher that there was evidence of student growth through testing when comparing their scores with the scores of students that were not within our study.
So when I read the article from Steffe, I was reminded of my path to learning about how students learn math. Just as he described his earlier years in teaching, I thought of myself as a good math teacher in my classroom years, connecting the strategies to concepts and foregoing rote memorization of procedures. Although I could see that this new way of teaching that I have been learning about since becoming a research associate at AIMS is far more effective than simply conceptually teaching material, I had never been able to put my finger on why it is so different and important. But here’s the difference: creating.
You see, my students could understand why something worked in situations, they could talk about the reasons for doing or not doing certain things in problems, but I did not help them become powerful enough to create their own mathematics. Some of them no doubt got there without my help, but I did not create an environment that prompted this development.
Today I want back in the game! Ideas are flowing like a fountain and I want to go use them, but have no classroom for my outlet. So, let me live vicariously through your experiences in your classrooms. Comment with other mathematical structures and think of different contexts in which you could present them to allow students to abstract out the structure for themselves.
Steffe, L. P. (1990). Adaptive mathematics teaching. In T. J. Cooney & C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990s (pp. 41–51). Reston, VA: National Council of Teachers of Mathematics.