Wednesday / July 24

How to Engage Students in Learning Mathematics

Engagement is a fundamental goal for educators. We want our students to be engaged because we know, at an innate level, that if students are not engaged they are not learning – they can’t be learning. But what is engagement exactly, and how do we achieve it in our mathematics classrooms?

Schools were originally modelled on the institutions of church, factories, and prisons (Egan, 2002) and were designed to create conformity and compliance—not thinking and engagement. Much has changed in public education since its inception over a century ago, but many of the initial norms are still with us. Teachers are still standing while students are still sitting. Teachers are still writing on boards while students are still writing on paper. And students are still not thinking (Liljedahl, 2020)—at least not in ways that we know they need to in order to be successful in future mathematics classes. Instead, they are conforming and complying with what they have been shown. Students are mimicking—not thinking (Liljedahl, 2020).

So, to get our students to engage we are going to have to get them to think. Over 15 years of research into how to build thinking classrooms (Liljedahl, 2020) has proven that, if we break some of these norms in intentional and deliberate ways, we can get more students thinking and thinking for longer. And to begin, all you need to do is get your students (1) working in visibly random groups on (2) vertical non-permanent surfaces to (3) solve a thinking task in math. These three changes alone will not only radically transform what teaching looks like in your classroom, but also radically transform what learning looks like. Your students will be thinking rather than mimicking and engaged rather than disengaged.

1. Visibly Random Groups

Having students work in visibly random groups has been shown to increase student engagement, intra- and inter-group reliance, and remove social barriers (Liljedahl, 2020). This same research has also shown that the optimal group size is three and that each group should only have one marker.

2. Vertical non-permanent surface

A vertical non-permanent surface can be a whiteboard, a blackboard, a window, or even a vinyl picnic table cover stapled to your bulletin board. It doesn’t matter what it is as long as it is erasable and vertical. The fact that it is erasable removes the barriers of risk that often prevent students from starting. Research has shown that when working on vertical non-permanent surfaces, students risk more, risk sooner, and risk for longer as compared to vertical permanent surfaces (like flip chart paper, horizontal permanent or non-permanent surfaces, or even their notebooks (Liljedahl, 2020).

3. Thinking Tasks

Finally, to get students to think we need to give them something to think about—something that cannot be mimicked. What fits better, a square peg in a round hole or a round peg in a square hole?  And then, we need to make sure that we, as teachers, do not suck the thinking out of the task by reminding them that they should be focusing on surface area and by defining a best fit as a ratio. Thinking is what we do when we do not know what to do. If we show them how to do it then we are robbing them of opportunities to think, to engage, to learn.

But this is just the beginning—the first three changes to our practices that allow us to build thinking classrooms. It turns out that there are twelve more such practices ranging from how we answer question to how we operationalize homework to how we use formative assessment. Each of these is a radical departure from the industrial era institutional norms that still permeate our schools and classrooms today and prevent us from achieving the kind of engagement we all want to see in our students. All twelve practices are listed in my book, Building Thinking Classrooms in Mathematics, Grades K-12.


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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