Gleanings From the Tree of Life

August is the month when educators return to work. Many of you have spent days preparing for the start of school and are now in full swing in your classrooms. It’s almost like we never had a vacation right? While I work year round, I am still feeling the excitement of the start of school this year. Most of the Research Associates that I work with here at the AIMS Center are going back into classrooms and getting to work with students so we can continue to gain insight on how children come to know number.

We have asked two of our Research Associates, Beverly and Grace, the question: “How would you teach differently now that you have knowledge of research on how children come to know?” They, of course, won’t be able to answer this question without going back into the classroom. So we have asked them to become the daily math teachers into different classrooms. Grace is in a kindergarten classroom and Beverly is in a first grade classroom. I hope you follow their blogs to see their progress.

Some of the children that we are seeing this year are new to us and some of them are familiar because we’ve worked with them over the past year or two. In working with these children we have gotten to know some of them really well and are able to predict how they will likely responded to a given situation. While we may not be able to predict everything about their response, we do seem to know something about their approach and strategies. This is one of the big ideas found in the research of Dr. Leslie P. Steffe, which he calls building a second-order model.

What is interesting about re-enacting this research is that not only is the child changed because of the student and teacher interaction, but the teacher is changed as well. The child may change because they are able to reflect on questions that the teacher asked them or are prompted to try something new. The teacher changes because they now see the child a little bit differently and understand something more about the way they think. That means that the second-order model the teacher builds of the child’s thinking is adapted with each new interaction. In his book “The Tree of Knowledge,” Humberto R. Maturana describes this process as “structural coupling.” This means that both the teacher and student are interacting with a common experience as well as interacting with each other, and as one of the individuals changes so does the other.

Another example of structural coupling happens between a reader and written material. While it seems obvious that the reader would change because of what they read, itt may seem strange to think that the written material would change. The ink on the page does not change. The contents of the written material do not change. Yet the material seems to change because the reader understands it differently because of prior reading material, outside experiences, or new insights. Haven’t you ever had to read an article or a book more than once to truly grasp it? Or maybe something that you read years ago that was complicated and frustrating for you seems so much simpler now. You have been a part of structural coupling.

I expect to see many examples of this in the near future. As students work with my team, I expect that we will change together in some ways. We will drift in the same direction because of our common experiences and our common knowledge. Where do you see structural coupling in your world?

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