Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning by Peter Liljedahl.

5/5 rating. 299 pages.

Book #36 of 2022. Read September 19, 2022.

This book has absolutely restructured my approach to teaching and shaped my actions in my classroom.

My former mentor teacher recommended this book to me and told me “I’d be shocked if this doesn’t score a 5.” He was definitely right! Peter’s framework is backed by mounds of evidence in the classroom of its efficacy. As I am always looking for ways to improve my teaching, this was perfect for me.

This framework revolves around the difference between a more traditional math classroom where mimicry is the main point, and the idea of the “thinking classroom,” where we ask students to collaboratively problem solve. The entire class periods are basically composed of students working together on problems. Instead of telling students how to approach the problems, they rely on their teams, and the class as a whole to understand ways to move through the tasks. This idea of teaching students how to learn, and the importance of perseverance, trying wild ideas, and collaboration is what true math is about.

I have already experienced a lot of success in implementing this type of structure in my classroom, and can’t wait to see how it further evolves as I become better at my skills in it, and my students become more comfortable with the idea of math as solving problems, as opposed to memorizing or copying some process. If you are a math teacher, this might be the book that changes your professional life!

Quotes:

“In this class, they’ll be expected to think.”

“Could there be anything more important and pressing than teaching students how to think?”

“The first was the realization that at no point in the three days of observation had I seen Jane’s students do any thinking—at least not the kind of thinking that we know students need to do to continue to be successful in mathematics in future grades. This is not to say that there was no activity. There was lots of activity—the students were busy from the beginning of class to the end. They were taking notes, answering questions, filling in worksheets, and starting on their homework. They were busy. They just weren’t thinking.”

“In a typical one-hour lesson, 75%–85% of the students exhibited non-thinking behaviors for 100% of the time. The rest of the students exhibited non-thinking behaviors for all but 8–12 minutes of the time.”

“Much of how classrooms look and much of what happens in them today is guided by these institutional norms—norms that have not changed since the inception of an industrial-age model of public education. Yes, desks look different now, and we have gone from blackboards to greenboards to whiteboards to smartboards, but students are still sitting, and teachers are still standing. And although there have been a lot of innovations in assessment, technology, and pedagogy, much of the foundational structure of school remains the same.”

“It turns out that when students walk into a classroom that looks like every other classroom they walk into, they assume that the lesson is going to go like every other lesson they have been part of. And, therefore, they bring all of their habits and studenting norms into the room with them. If those studenting norms are non-thinking behaviors, then they are going to not think in this lesson as well. When the students walk into a room that looks very different, however, then they leave their habits and norms at the door and allow themselves to be different—at least to begin with.”

“Problem solving is a messy, non-linear, and idiosyncratic process. Students will get stuck. They will think. And they will get unstuck. And when they do, they will learn—they will learn about mathematics, they will learn about themselves, and they will learn how to think.”

“It turns out that almost any curriculum tasks can be turned from a mimicking task to a thinking task by following this same formulation – begin by asking a question that is review of prior knowledge; then ask a question that is an extension of that prior knowledge.”

“Irrespective of the grouping method being used, the vast majority of students do not enter their groups thinking they are going to make a significant, if any, contribution to their group.”

“Thinking is messy. It requires a significant amount of risk taking, trial and error, and non-linear thinking. It turns out that in super organized classrooms, students don’t feel safe to get messy in these ways. The message they are receiving is that learning needs to be orderly, structured, and precise. In these perfectly organized classrooms, the physical spaces in which they are being asked to think is incommensurate with the messiness of thinking.”

“What is important is that the message that is sent is commensurate with the activity that is intended. That is, a thinking classroom needs to be organized in such a way that says thinking, collaboration, and risk taking are expected.”

“That is, there was no context in which giving a task verbally led students to perform worse than giving it textually—whether on a board, on a worksheet, or in a textbook/workbook.”

“That is, in situations where homework was marked, approximately 50% didn’t do it or cheated. When homework was not marked, this percentage drops to approximately 40%—not marking homework had a positive effect on how many students did their homework.”

“The goal of building thinking classrooms is not to find engaging tasks for students to think about. The goal of thinking classrooms is to build engaged students that are willing to think about any task.”

“Student difficulty with mathematics has been a pervasive and systemic problem since the advent of public education – not because students can’t learn mathematics, but because, by and large, students can’t learn by being told how to do it.”

“I have never asked a question that is so predictive of student performance on a unit test. About 15% of the students told me that the unit they just finished was made up of a number of subtopics, and they were able to name or describe what those subtopics were. These students, for the most part, scored above 90% on the upcoming test. There was a group that could tell me that there were subtopics, but they were not able to completely delineate them or describe them. These students tended to score between 75% and 90%. The rest of the students all said that the unit was just one big topic. These students tended to score below 75%.”

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