Wednesday / April 24

14 Questions to Build Thinking Math Classrooms

Sixteen years ago I had an opportunity to visit 40 classrooms in 40 different schools. I was in elementary classrooms and secondary classrooms, in English speaking classrooms and in French speaking classrooms, in public schools and private schools, and in low socio-economic settings and high socio-economic settings. And everywhere I went I saw the same things – students not thinking and, as a result, teachers having to plan their teaching on the assumption that students can’t or won’t think. This is a problem. If students are not thinking they are not learning.

Building Thinking Classrooms is a reaction to this realization and is the result of 16 years of research into student non-thinking behaviors and the role that teaching practice has on sustaining and changing these behaviors. Working with over 400 teachers in two week cycles we were able to run hundreds of micro-experiments where we compared students’ thinking across a wide variety of enacted teaching practices. Out of this research emerged 14 practices that any teacher can enact to optimize the number of students who are thinking and for how much of a lesson they think for – each of which is an answer to the central questions upon which a teacher’s practice is built upon.

  1. What are the types of tasks we use?
  2. How do we form collaborative groups?
  3. Where do students work?
  4. How do we arrange our furniture?
  5. How do we answer questions?
  6. When, where, and how we provide tasks?
  7. What does homework look like?
  8. How do we foster student autonomy?
  9. How do we use hints and extensions?
  10. How do we consolidate a lesson?
  11. How do we give notes?
  12. What do we choose to evaluate?
  13. How do we use formative assessment?
  14. How do we grade?

For example, we learned that if we grouped students for collaborative work (question #2) using a visibly random generator heightened thinking in the classroom. Likewise, we learned that the best worksurface for getting student to think (question #3) was a vertical and erasable surface like a whiteboard, blackboard, or window. We learned that if we give students a thinking task (question #6) in the first five minutes of class we get more thinking than if we ask at any other time in the lesson.

Once the 14 optimal practices were found the research shifted gears into trying to figure out a teacher new to these ideas could build their own thinking classroom based on these practices. This research resulted in the Building Thinking Classrooms developmental framework wherein the 14 practices organized themselves into a pseudo-sequence of four toolkits. What order the practices were implemented within a toolkit did not seem to matter. What mattered, however, was that the practices in the first toolkit are enacted before those in the second toolkit, and so on.

When the 14 optimal practices are enacted according to this framework we get 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. What we get are classrooms that look radically different from the 40 classrooms that I visited sixteen years ago. We get classrooms where 90% of students spend 90% of class time thinking. We get thinking classrooms.

Written by

Dr. Peter Liljedahl is a Professor of Mathematics Education in the Faculty of Education. He is the former president of the International Group for the Psychology of Mathematics Education (PME), and the current president of the Canadian Mathematics Education Study Group (CMESG), as well as a senior editor for the International Journal of Science and Mathematics Education (IJSME). Peter is a former high school mathematics teacher who has kept his research interest and activities close to the classroom. He consults regularly with teachers, schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy.

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