Author Archives: Richard Thiessen

Braided Strands of Knowledge Translation

The AIMS Center Research Associates who regularly post on this blog site are challenged to not only read, understand, and translate into practice research related to how children come to acquire knowledge of mathematics—specifically we are presently focused on how children acquire knowledge of number—but also to read and come to know the theoretical underpinnings for the research they are working on.

A book that each of the research associates has read at least once— those who have been at the Center a bit longer have read and reflected on it two or three times—is titled, Radical Constructivism: A Way of Knowing and Learning. The author is Ernst von Glasersfeld, a psychologist, philosopher, and linguist, who was involved with the multi-disciplinary research team at the University of Georgia that produced the primary focus of the work of the research associates.

In his book, Professor von Glasersfeld outlines and braids at least four strands or components that constitute the theory base that guides the research project at the University of Georgia with which he and Dr. Steffe were involved. These strands include an understanding of biology and neuroscience, which is important because we are each, as human beings, a biological organism with a nervous system. It also includes psychology, which might be thought of as the study of the human mind and its function.  In addition, it includes epistemology, which is concerned with the study of knowledge and justified belief, which provides a way to understand what it means to know, to have knowledge. The result of the way in which Glasersfeld develops and braids these strands is a braid that he calls radical constructivism, which is the underlying theory base for the research we are following and translating here at the AIMS Center for Math and Science Education.

We’ve developed the above graphic to highlight these strands and to suggest the braiding of them together. Over the next several blog posts I will pick up on each of these strands to show how and what they contribute to the theory base. The second graphic (below) is designed to show how the research related to how children come to know number is braided into the first braid that is already in progress. These strands are the domain of mathematics, children’s knowledge of mathematics, and finally a strand that represents what Steffe has called second order models of children’s mathematics.

This final braid represents the knowledge that we as a Center have as our goal to translate into classroom practice. I realize that there are additional strands that involve teacher strands, yet to be included in the braid. That is something we are just beginning to work on. This is simply a first attempt to think about a way to visualize the work we are doing. I look forward to critique and suggestions. I’m hoping in future blogs to elaborate various strands, I’m especially wanting to share about how a deep understanding of the first four strands informs the work of the research associates.

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Pi – Pe – Pa Principles

This past weekend I heard a powerful, inspirational presentation by a wise, older gentleman, Mr. Janzen, who has been a college president, a pastor, and a counselor. He talked about three principles that have guided him through the years. He calls them the pi – pe – pa principles, where pi stands for powerful insights,… Continue Reading

A Dream Coming True!

This blog post is being written from Tucson, Arizona, where Tiffany Friesen, Paul Reimer, and I are attending the annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. The approximately 600 men and women attending this conference are almost exclusively university professors along with their graduate students,… Continue Reading

A Juggling Act

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… Continue Reading

How Many Blocks?

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

Constructivism and More

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 Early Math Team at The AIMS Center

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