Author Archives: Richard Thiessen
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.
One day several years ago while interacting with our two little grandchildren who were then 3 or 4 years of age and 4 or 5 years of age, respectively, I presented the younger one with a collection of eight blocks, and asked, “How many blocks are there on the table in front of you?” He… Continue Reading
The Research Division of the AIMS Center is organized into four teams, of which three teams are presently focused on research related to how children come to know number. Our ultimate goal is to translate that research into classroom practice. The theory base underlying the research we are following is what might be called a… Continue Reading
The members of the Early Math Team at the AIMS Center for Math and Science Education are Research Associates Jason Chamberlain, Liz Gamino, Wilma Hashimoto, and Aileen Rizo, along with myself, Senior Researcher, Richard Thiessen. We are really excited to be working with preschool children in partnership with Fresno EOC Head Start. This year we… Continue Reading
The last post in this series about AIMS—past, present, and future—ended with the statement that in the next post I would talk about a vision for AIMS that would involve translating research into practice. In a sense, that is what AIMS has been doing over the years–but in a very general way–by exploring ways to… Continue Reading
In my previous post I talked about where AIMS came from, what AIMS has been doing over these past more than 30 years, and what it continues to do. In this post I want to talk a bit about the underlying understanding about how children come to know concepts of mathematics that has guided AIMS… Continue Reading
This post is the first of several that will outline some new directions for AIMS. Here I would simply like to give you a bit history. Some of you will know that AIMS is an outgrowth of the Graduate Math/Science Program at Fresno Pacific University. The AIMS Education Foundation got its start as the result… Continue Reading
In my last post, Tangrams: A World of Geometry, Part Two, I talked about the thirteen convex polygon shapes that can be formed with the seven tangram pieces. In the video, I showed how to make five of them, and then I left a challenge for you to look for the remaining eight convex shapes.… Continue Reading
I just realized that in my post two weeks ago, Tangrams: A World of Geometry, I only included part one of the tangram video. The forming of the pieces is completed in part two of that video. I’m hoping that some of you noticed that what you saw was not complete and that you were… Continue Reading
The tangram puzzle has been a favorite of mine for many years. When I regularly taught a geometry course for teachers, I would use this puzzle as the opening activity for the course and would then come back to it periodically. Of all the things we did, this puzzle, and the ways it can be… Continue Reading