Constructivism and More

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

Show Your Thinking

Recently I was speaking with a parent who was expressing frustration with their child’s work habits in their math class. It was a conversation I have experienced many times throughout my 20 years of teaching. It’s about that child who says they can do the math in their head and they do not need to… 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 AIMS Center – Wow!

WOW!  I have been absolutely blessed to have been brought in to direct the transition of the AIMS Education Foundation into the newly envisioned AIMS Center for Math and Science Education!  What does that mean?  Well… Dr. Arthur Wiebe left a legacy through the work of the AIMS Education Foundation.  Since 1981, AIMS has worked… Continue Reading