Are Your Students Mimicking or Thinking?

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I first learned about Peter Liljedahl’s work from a session at the FCTM conference in 2019 that Laura Tomas presented on, and I was able to participate in a book study that Laura and Karina hosted this fall. Liljedahl is on a mission to transform math classrooms from classrooms where students are mimicking to classrooms where students are thinking and therefore LEARNING! I will highlight my top 3 strategies from his research and I encourage you to read the book if you can and if not check out the Executive Summary shared below.

Building Thinking Classrooms in Mathematics

by Peter Liljedahl

Building Thinking Classrooms in Mathematics Grades K –12 by Peter Liljedahl, highlights 14 teaching practices for enhancing learning. He spent 15 years researching in classrooms to write this book. Tracy Johnston Zager said it best in the foreword about his research.

“Peter Liljedahl’s work is that second kind of research, the research I can’t get enough of. In my reading of Liljedahl’s work, research means exploring important, testable questions with more than four hundred teachers and their thousands of students over 15 years.” 
Tracy Johnston Zager


Task Selection
Visibly Random Groups
Vertical Non- Permanent Surfaces

Task Selection

The first teaching practice he describes is to consider what types of tasks we use and when we use them. He researched 3 types of tasks: non-curricular tasks, scripted curricular tasks and as is curricular tasks. 

He promotes using highly engaging thinking tasks which are usually not directly related to the curriculum at the beginning of the lesson. Begin lessons, the first 5 minutes, with a thinking task. At first these tasks should not be directly related to the curriculum, he suggests 3-5 of these, then you can transition to using curriculum thinking tasks.

He found that students did much more thinking throughout the lesson if the lesson began with a highly engaging thinking task. These may include puzzles, card tricks, numeracy tasks and problems with novel solution paths.

Another great source for task Alicia Burdess’s site. Here is a second grade example.

Visibly Random Groups

We all know the power of using collaborative groups in math class. What I learned from his research was that visibly random groups were the most powerful. This means students must know and trust that the groups are random. Make the groups publicly or visible so they trust they are random. For example, use playing cards or random number generators and then send them to work on the thinking task, on a vertical non-permanent surface (see below). He also found for K-2 the groups should be two and grades 3 and up, trios work best. Benefits of visibly random groups are:

  • willingness to collaborate
  • elimination of social barriers
  • increased knowledge mobility
  • increased enthusiasm for mathmatics learning
  • reduced social stress

Vertical Non-Permanent Surfaces

Where to do the thinking? We start by kicking off the lesson with thinking tasks and putting students in visibly random groups. Another key detail is where they do the thinking. He compared 5 work surfaces: vertical whiteboards, horizontal whiteboards, vertical paper, horizontal paper, and notebooks. Overwhelming he found students should be standing at vertical non-permanent surfaces. He measured average time across 9 measures and vertical non-permanent surfaces outperformed the rest

  1. time to task (seconds)
  2. time to first notation (seconds)
  3. time on task (minutes)
  4. eagerness to start
  5. amount of discussion
  6. amount of participating
  7. amount of persistence
  8. amount of knowledge mobility
  9. non-linearity of work

Learn More!

Read the Executive Summary and visit the Building Thinking Classrooms website.

Learning Through Math Podcast: Episode 63

This episode describes how Building Thinking Classrooms complements the classic book from Margaret Smith and Mary Kay Stein – 5 Practices for Orchestrating Productive Mathematics Discussions. 

Making Math Moments that Matter Podcast:

Episodes 21 and 98 – Interviews with Peter Liljedahl

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