In previous blog posts we have, in various ways, talked about the commitment of the AIMS Center to a constructivist understanding of how children come to know. There are several reasons for this choice, but probably the most relevant is that the most significant and extensive research related to how children come to know whole number and the whole number sequence has as its theory base a strong Piagetian constructivist understanding. Therefore, along with coming to understand the research we are reading and reenacting with children, one of our challenges (and opportunities) as Senior Researchers and Research Associates at the Center is to deeply understand and know constructivism, its concepts, its constructs, and its language – of which there is an abundance.
Our challenge is to come to understand children’s knowledge of number and how children are constructing that knowledge. At the same time, we must be constructing our own knowledge of the constructivist theory base for that research, which will also be the theory base for our translation of that research into practice. As a Center we’ve not been given the luxury of first coming to deeply understand constructivism before beginning to read and reenact research. This has complicated our work.
As I watch our teams juggling these two aspects of our work, I realize that the desire to better understand children’s knowledge of mathematics drives us to go back into the literature to better understand the notions and language of constructivism. Consequently, that deeper knowledge of the theory has an immediate payoff in better understanding the research and a better understanding of the progression in children’s acquisition of the whole number sequence and counting.
I wonder… do you too find yourself doing a similar juggling act? On the one hand you are coming to know the students in your classroom and coming to know something of where each student is in their learning of the concepts you’re responsible to teach. On the other hand there are the Common Core Standards, and in particular the Standards for Mathematical Practice, which serve as a bit of a theory base for how to better facilitate children’s learning. You too may not have been given the luxury to first deeply understand those standards before being asked to attempt to implement them.
Theory and content – they are tightly intertwined.