Building Thinking Classrooms for K-5 Math Educators

building thinking classrooms in mathematics
Learn how to start building a thinking classroom that considers Peter Lijedahl's research and movement-based learning strategies.

Table of Contents

You may have heard of other educators building “thinking classrooms” or finding new strategies to promote student thinking. Furthermore, you may have even heard of the research on US classrooms by Peter Liljedahl. If you haven’t, there are great benefits to building thinking classrooms in mathematics, even in elementary schools. We’re sharing the highlights from Peter Liljedahl’s work and our take on the thinking classroom, including movement-based tasks elementary educators can assign their students.

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What is a "Thinking Classroom"?

Dr. Peter Liljedahl, a professor of mathematics at Simon Fraser University in Canada, turned 15 years of educational research into a 14-step practical guide to help teachers create the ideal workspace and teaching practice to promote student thinking. He called the framework a “thinking classroom.” 

Peter Liljedahl's Research

Liljedahl thought that math was too commonly taught by telling students how to do it. He saw students mimicking their teachers in traditional classrooms. Over a span of 15 years, Liljedahl worked with over 400 K-12 teachers in their classrooms, trying to come up with the best strategies to get students thinking on their own, rather than just mimicking their teachers.

Additionally, during this time, Peter Liljedahl noticed that classrooms across the country and grade levels looked more alike than different. The desks faced forward toward the teacher’s vertical writing surface (commonly a whiteboard, chalkboard, or smartboard). The teacher also always stood, and the students sat and wrote on horizontal surfaces. Liljedahl believed that these normal classroom spaces were perpetuating the non-thinking behaviors he observed in students.

Peter Liljedahl
"Thinking is a necessary precursor to learning, and if students are not thinking, they are not learning." - Dr. Peter Liljedahl

Using the data, teacher testimonials, and classroom photos he collected, Liljedahl came up with a comprehensive list of 14 factors that make up the core of every teacher’s practice. How a teacher enacts each factor creates each educator’s unique teaching practice. He experimented with these factors, or variables, in order to find the optimal practices to increase student thinking in classrooms. 

Finally, Dr. Peter Liljedahl published his book Building Thinking Classrooms in Mathematics, which explores the optimal practice for each of his 14 teaching variables and the research behind each one.

Liljedahl's 14 Factors of a Teaching Practice

  1. The types of tasks educators assign
  2. How teachers form collaborative groups
  3. Where students work
  4. How educators arrange furniture in the classroom
  5. How educators answer students’ questions
  6. When, where, and how tasks are assigned
  7. What homework looks like
  8. How educators foster student autonomy
  9. How educators use hints
  10. How educators consolidate a lesson
  11. How students take notes
  12. How educators evaluate students
  13. How educators use formative assessment
  14. How educators grade students

A thinking classroom is a space that keeps students engaged, enthusiastic about learning, and thinking deeply and independently. 

Building Your Thinking Classroom with Math & Movement

Did you know that kinesthetic learning strategies can also help keep students engaged, enthusiastic about learning, and thinking deeply? It’s true! The Math & Movement program is all about taking a child’s natural inclination for movement and turning it into excitement for learning.

Young elementary students never like to sit still for long periods of time. Math class can be particularly frustrating, especially when students are simply mimicking their teacher. Math & Movement is a multi-sensory approach to learning that uses physical activity to teach students. Physical activity increases blood flow and oxygen levels in the brain. As a result, the brain can function at optimal levels for learning. Additionally, proteins that the brain releases during exercise support the function and growth of neurons. Movement really works to boost learning and student thinking!

Implementing the Math & Movement program can help educators turn their traditional, sedentary classroom into an active, thinking classroom. We’re sharing how our program aligns with Liljedahl’s ideal practices for building a thinking classroom.

The Types of Tasks Educators Assign

When building a thinking classroom in mathematics, Peter Liljedahl says that educators must give their students “highly-engaging thinking tasks.” These classroom tasks should require and encourage thinking.

First of all, kinesthetic activities are proven to increase student engagement. Secondly, brain scans show that exercise makes the brain more active. Take a look at the image below!

student thinking after exercise

Movement-based tasks are highly-engaging thinking tasks! Students will be interested in what they are doing, and their brains will be active and ready to process information.

Liledahl says that students can start off with non-curricular thinking tasks in order to get the thoughts flowing. This could be any question not related to the curriculum, for example, “what did you do this past weekend?” It gets students thinking and warmed up for higher order thinking math.

Moreover, teachers can consider the Depth of Knowledge framework when creating assignments and aiming to promote higher order thinking skills in math.

The Importance of Randomized Groups

Assigning students to randomized groups can ease social tensions, break down social barriers, and promote student thinking.

Liljedahl found that when the teacher assigned groups or when students chose their own groups to work in, 80% of students entered these groups with the mindset that they wouldn’t have to think. Other students could do the hard thinking. 

After working with students for several weeks using randomized groups, 100% of students entered groups with the mindset that they would have to think and contribute. This eventually led to much more successful collaborative thinking!

Adding movement into the mix can further help students overcome social anxieties. Exercise reduces stress, meaning that kinesthetic learning activities can help shy students feel more comfortable around their peers!

Math & Movement is designed to work with both small groups of students and full classrooms. Our activities encourage students to work together and use movement to solve math problems.

Where Students Work

As mentioned, students sit and work at their desks in the traditional classroom. Liljedahl’s research revealed that student thinking increases the most when students are 1) standing and 2) working on non-permanent vertical surfaces.

When building your thinking classroom, adding Math & Movement materials will not only have your students standing but also stepping, hopping, and skipping! We create kinesthetic educational products, including floor mats and stickers, that students interact with by getting on their feet and moving around.

Place your Math & Movement materials by a vertical whiteboard and you’ll have Liljedahl’s ideal workspace for students! 

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Answering Students' Questions

Peter Liljedahl found that there are three types of questions students ask:

  • Proximity questions – the questions that students ask simply because the teacher is close by
  • Stop-thinking questions – the questions that students ask to reduce their thinking effort, such as “Is this correct?”
  • Keep-thinking questions – the questions students ask so that they can keep working, trying, and thinking about the material in front of them

In a thinking classroom, teachers should only answer keep-thinking questions. Educators should build students’ self-confidence so that they can solve math problems independently. By creating workspaces that allow students to work individually with materials and manipulatives, they can learn to solve problems on their own.

Math and Movement’s Skip Counting Mats are a great way to do this. For example, to solve the problems 3×6, students can hop six times on the Skip Counting by 3s Mat or 6 times on the Skip Counting by 6s Mat. Teachers can set up the mats when giving their students a multiplication assignment. On their own, students can jump to solve the problem.

thinking classrooms tasks
Skip Counting by 3s
student thinking
Skip Counting by 6s
When, Where, and How Tasks Are Assigned

The thinking classroom framework states that more student thinking occurs when a task is assigned within the first five minutes of a lesson rather than any later. Additionally, more student thinking took place when the task was assigned while students were standing in a loose formation around the teacher rather than sitting at a desk.

With Math & Movement, educators can explain an activity to their students while they stand around the floor mat they are using during the lesson. What a simple trick to building thinking classrooms!

thinking classroom
Foster Student Autonomy

In a thinking classroom, students work together in groups, they stand more than sit, and teachers answer fewer questions. This requires greater independence on the students’ part. 

With Math & Movement, students have more opportunities to interact with each other. Furthermore, they are able to use the materials accessible to them independently to solve problems.

Give Hints Asynchronously

Peter Liljedahl encourages educators who are building a thinking classroom to give hints asynchronously. Each student processes the same information differently and at a different pace. When students get in a flow of thinking, it’s crucial not to interrupt that. That’s why hints should only be given to students who need it to keep their thinking flow going.

Movement-based learning helps students get into a thinking flow more easily and quickly. Students usually have so much fun moving around on our materials that they forget they are doing math! That’s why Math & Movement is great for intervention, after school, and summer school programs.

Consolidate Lessons

In a thinking classroom, Liljedahl suggests that teachers should have students work upwards from the basic foundation of a concept. Then, students can make conclusions based on their thinking that occured during similar tasks.

The great thing about Math & Movement materials is that one mat can be used to teach multiple concepts. Plus, our materials are heavy-duty and made to last, meaning that several classes over multiple school years can use the same material!

Final Thoughts on Student Thinking

Building a thinking classroom can help foster hard working math students. Consider adding kinesthetic learning strategies when brainstorming mathematics tasks for the thinking classroom. Math & Movement is here to help educators tackle building a thinking classroom with a focus on mathematics and active learning.

FAQs

How do you create a thinking classroom?

Educators can create a thinking classroom by following Peter Liljedahl’s 14 optimal teaching practices. Liljedahl’s suggested optimal practices for each of his 14 teaching variables and the research behind them are discussed in his book, Building Thinking Classrooms in Mathematics.

What is the thinking classroom model?

The thinking classroom model is a teaching framework by Dr. Peter Liljedahl that focuses on promoting student thinking in mathematics. It emphasizes using randomized groups, vertical non-permanent surfaces (like whiteboards), and meaningful problem-solving tasks.

What is the goal of building thinking classrooms?

The goal of building thinking classrooms is to create an environment that promotes student thinking. This approach aims to move students beyond imitation of the teacher, as well as foster independence, collaboration, and deeper comprehension.

What is the difference between a traditional classroom and a thinking classroom?

A traditional classroom often centers on teacher-led instruction, passive note-taking, and rote memorization. In contrast, a thinking classroom focuses on student-led exploration, active problem-solving, and collaboration. The thinking classroom is arranged to emphasize and support critical student thinking, with teachers acting as facilitators rather than information providers.

What are the characteristics of thinking classrooms?

Thinking classrooms are characterized by:

  • a different setup where students sit facing every direction
  • collaborative work in randomized groups
  • use of vertical non-permanent surfaces like whiteboards
  • more tasks in which students are standing and on their feet learning
  • open-ended tasks that promote student autonomy

References and More Reading

Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning, Grades K-12 by Peter Liljedahl. Copyright © 2021 by Corwin Press, Inc.

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Movement isn't just for recess

Want to get started with movement-based learning right now? Enter your email to get our training manual with over 250 active math movements. No materials necessary!