Peter Liljedahl on...Building Thinking Classrooms: Conditions for Problem-Solving
Peter Liljedahl is a professor of Mathematics in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University. The following is an excerpt from his 2016 article on building thinking classrooms in order to create conditions for problem-solving. This article was originally published here:
Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer. [ResearchGate, Academia]
In this chapter I first introduce the notion of a thinking classroom and then present the results of over ten years of research done on the development and maintenance of thinking classrooms. Using a narrative style I tell the story of how a series of failed experiences in promoting problem solving in the classroom led first to the notion of a thinking classroom and then to a research project designed to find ways to help teacher build such a classroom. Results indicate that there are a number of relatively easy to implement teaching practices that can bypass the normative behaviours of almost any classroom and begin the process of developing a thinking classroom.
MOTIVATION
My work on this paper began over 10 years ago with my research on the AHA! experience and the profound effects that these experiences have on students’ beliefs and self-efficacy about mathematics (Liljedahl, 2005 ). That research showed that even one AHA! experience, on the heels of extended efforts at solving a problem or trying to learn some mathematics, was able to transform the way a student felt about mathematics as well as his or her ability to do mathematics. These were descriptive results. My inclination, however, was to try to find a way to make them prescriptive. The most obvious way to do this was to find a collection of problems that provided enough of a challenge that students would get stuck, and then have a solution, or solution path, appear in a flash of illumination. In hindsight, this approach was overly simplistic. Nonetheless, I implemented a number of these problems in a grade 7 (12–13 year olds) class.
The teacher I was working with, Ms. Ahn, did the teaching and delivery of problems and I observed. Despite her best intentions the results were abysmal. The students did get stuck, but not, as I had hoped, after a prolonged effort. Instead, they gave up almost as soon as the problem was presented to them and they resisted any effort and encouragement to persist. After three days of constant struggle, Ms. Ahn and I both agreed that it was time to abandon these efforts. Wanting to better understand why our well-intentioned efforts had failed, I decided to observe Ms. Ahn teach her class using her regular style of instruction.
That the students were lacking in effort was immediately obvious, but what took time to manifest was the realization that what was missing in this classroom was that the students were not thinking. More alarming was that Ms. Ahn’s teaching was predicated on an assumption that the students either could not or would not think. The classroom norms (Yackel & Rasmussen, 2002 ) that had been established had resulted in, what I now refer to as, a non-thinking classroom. Once I realized this, I proceeded to visit other mathematics classes—first in the same school and then in other schools. In each class, I saw the same basic behaviour—an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions, it was unreasonable to expect that students were going to spontaneously engage in problem-solving enough to get stuck and then persist through being stuck enough to have an AHA! experience.
What was missing for these students, and their teachers, was a central focus in mathematics on thinking. The realization that this was absent in so many classrooms that I visited motivated me to find a way to build, within these same classrooms, a culture of thinking, both for the student and the teachers. I wanted to build, what I now call, a thinking classroom —a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together and constructing knowledge and understanding through activity and discussion.
EARLY EFFORTS
A thinking classroom must have something to think about. In mathematics, the obvious choice for this is a problem-solving task. Thus, my early efforts to build thinking classrooms were oriented around problem-solving. This is a subtle departure from my earlier efforts in Ms. Ahn’s classroom. Illumination-inducing tasks were, as I had learned, too ambitious a step. I needed to begin with students simply engaging in problem-solving. So, I designed and delivered a three session workshop for middle school teachers (ages 10–14) interested in bringing problem-solving into their classrooms. This was not a difficult thing to attract teachers to. At that time, there was increasing focus on problem-solving in both the curriculum and the textbooks. The research on the role of problem-solving as both an end unto itself and as a tool for learning was beginning to creep into the professional discourse of teachers in the region.
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