Author Archives: Richard Thiessen

The Way Piaget’s Mind Works

There are words that I come across in my reading that, while not unfamiliar, are words for which I have only a very cursory understanding. One such word which keeps coming up in relation to Piaget’s writing is the word, dialectic or dialectical or dialectical method. Recently, when once again it was front and center in something I was reading, I decided I should work at getting a better understanding of what exactly it means, especially as it relates to Piaget and his way of working. I guess that in the language of Piaget’s constructivism it could be said that I’ve been in long term disequilibrium where the meaning of this word is concerned. I was somewhat encouraged when I read on a philosophy web-site that “a number of history’s most illustrious thinkers have wrestled with the meaning of ‘dialectic,’” and that thus the meaning of the word has gone through some change, especially in Western philosophy. So, while I might be in good company, my reasons for being there are nothing like theirs might be.

As I googled ‘dialectic’ and began to read on sites that I deemed respectable and reliable, I found myself saying over and over, “oh, yeah, that makes sense,” or “of course, that’s what he’s doing.” The Stanford philosophy website defines ‘dialectics’ as “a term that describes a method of argument that involves some sort of almost contradictory process between opposing sides.” As I read those words I had to think about my frustration with Piaget as I recently read his 1947 book titled, The Psychology of Intelligence. Throughout the book he describes a variety of other theories that he compares and contrasts with his own developing theory. Sometimes he describes how he agrees with a part of a theory and how he has incorporated it into his own, and at other times he shows how he developed his theory in opposition to another with which he strongly disagreed. Within what is called the dialectical method this is called synthesizing. Often as I was reading that book I wished he would stop talking so much about how he arrived at this theory of intelligence and simply tell the reader the end-result of his synthesizing. I guess I wanted to hear about his theory, not so much about how he arrived at it. I must say that listening to him describe these other theories and how what he knew of them helped him arrive at his theory did help me better and more deeply understand him and his theory. This gives meaning to another author who stated that “dialectics is tightly bound up with synthesis” and that “every advance in Piaget’s work represents some sort of synthesis.”

In the book, Piaget or The Advance of Knowledge, the authors comment that “Piaget’s mind works in a fundamentally dialectic way.” They went on to say that whenever he was faced with a problem or a situation upon which he was reflecting, he tended to break it into a dichotomy of opposing points of view. As we come to know Piaget’s constructivism, we are again and again confronted with these opposing points of view: assimilation as opposed to accommodation, empirical abstraction as opposed to reflective abstraction, or operative as opposed to figurative.
Understanding “the way Piaget’s mind works,” that it works in a fundamentally dialectical way, has been a tremendous insight for me into his writing and theorizing. Why on earth did it take me so long to finally do the work necessary to begin to understand what writers meant when they talked about Piaget’s dialectical method?

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

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

Introducing the AIMS Center for Math and Science Education

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

Our AIMS for the Future

Our AIMS for the Future

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

Where did AIMS come from? What has AIMS been doing? Where is AIMS going?

Where did AIMS come from? What has AIMS been doing? Where is AIMS going?

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

Tangram Polygons: Composing and Decomposing

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