I have had the privilege of being a part of the AIMS Center from its birth. Having been a teacher, coach, and staff developer for the last 15 years, the world of a teacher is something I have experience with. I am now called a Research Associate and my role is to be a bridge between the educational research world and the world of a teacher. To meet this challenge, I needed to learn and understand a entirely new world.
One of the first tasks I was given was to deeply understand a line of research which includes the work of Piaget, von Glasersfeld, Steffe, Norton, and Ulrich, among others. These are mostly all new names that I have come to greatly respect. What stands out about these researchers is their attention to the “students’ mathematics”. Throughout my career I have learned different ways to teach math concepts, but now I realize I was working out of an adult mathematical frame of mind. One of the new lenses I have acquired through my studies is the concept of the “mathematics of children”.
So what is “adult mathematics” versus “mathematics of children”? Is this important to a classroom teacher? How would having this new lens benefit a teacher? Much of what Dr. Les Steffe has published begins with a discussion around the importance of the “mathematics of children”. I wondered and reflected about this. It was through this reflection that I realized I had been working out of an adult mathematical frame of mind. I needed to learn more about the “mathematics of children”. This is critical to the work of these researchers.
I’ve come to realize that the “mathematics of children” is about inferring what might be going on in the mind of the child. It is different than adult mathematics because an adult may have already constructed the concept. What seems completely obvious to an adult, might not be obvious to a child.
This line of research is qualitative, which means they don’t look at statistics but instead focus on change in behavior. How does this work? In a nutshell, first the researchers observe student behaviors. Based on what they see, they infer what might be going on in the mind of the child. They watch for trends in multiple children and then sort the gathered behavioral evidence into a developmental progression. Hopefully this progression will then provide a teacher assistance in identifying where a child is in terms of constructing their understanding.
What is the journey to constructing math concepts? Research that articulates the “mathematics of children” can provide powerful tools that enable a teacher to identify where a child is in their math journey and what our next teacher step might look like. I am thrilled to be studying research that shows how children come to know certain math concepts and to discover tools that can empower teachers to be that catalyst for learning that all children deserve.