Wednesday / July 24

3 Ways to Keep Students Thinking in COVID-Restricted Math Classrooms 

If you are among the many educators who have recently read Building Thinking Classrooms in Mathematics (Grades K-12): 14 Teaching Practices for Enhancing Learning, you may have been feeling excited, energized, and ready to start getting your students to think more in math when school started in the fall. And then it became sadly clear that COVID-19 is still with us and your school will likely look more like it did last year than three years ago. Worried and disappointed, you are likely wondering: Is it even possible to implement the thinking practices when restrictions are in place? Shouldn’t we just focus on getting through the content and not worry about trying something new in our teaching?  

First, let me say, I hear you. I don’t think there has ever been a time where so much has been asked of teachers. Teaching is challenging enough under normal circumstances; but doing it under the strain of COVID-19 health restrictions is beyond challenging. Trying to also shift our foundational thinking about teaching seems out of reach. But when we look at the bigger picture, we realize that if we can do anything to get our kids thinking (and learning) more, we have to try. There are two primary reasons this is doable and necessary.  

  1. Thinking in mathematics is not a value-added enrichment activity. It is not a soft skill or something we do on Fridays or the week before Christmas, after we have “covered the content.” Thinking is a necessary precursor to learning and, as such, if students are not thinking they are not learning. It is not really a question of whether this is the right time to get students to think more. It’s a question of what happens if we don’t? 
  2. Throughout the last two years creative teachers have found ways to keep the sprit of thinking classrooms alive, despite teaching in difficult circumstances where students were required to social distance, stay in their seats, work online, or work in hybrid settings—or some combination of the above. They made it work. They realized that not only is it possible, it is worthwhile. If we can keep students thinking, we can keep them learning, and we don’t have to torture ourselves (or them) with another year-worth of debates and worries about “learning loss.” 

The question remains how do we do this? How do we modify our practices in ways that encourage students to think more—and thus learn more—in math, even with environmental restrictions.  

Students are naturally curious people. Just because they are physically stuck in a seat—or in another location altogether—doesn’t mean that they will or should stop thinking. The basic tenets of the thinking classroom don’t change, though some of the details might. If we want students to think we have to give them: 

  1. Something to think about: In mathematics this comes in the form of a task. And not just any task, but a task that they do not yet know how to do—thinking is what we do when we don’t know what to do. We still avoid “now-you-try-one” tasks and instead focus on tasks with engaging contexts, easy entry points, evolving complexity, that drive students to want to talk and collaborate. You can still start with non-curricular tasks and move toward curricular tasks. 
  2. Someone to think with:  Visibly random groups can still work even in socially-distanced fixed seating or virtual instruction. One of the reasons collaboration is so effective in helping students think is that it gives them someone to talk with and talking requires the externalization of thought, which is a form of metacognition. And not just any form of metacognition, but the most accessible form of metacognition. In essence, collaboration is effective because it makes students more metacognitive. 
  3. Somewhere to do this workVertical non-permanent surfaces (VNPSs) can come in many forms. Having students work on non-permanent surfaces, with their ease of erasability, helps students to risk sooner, to risk more, and risk for longer. Having them standing up and working on vertical erasable surfaces removes their anonymity and makes it less likely they disengage.  

If you have read the book, you have already seen the research that underpins these results. These results remain true irrespective of the restrictions you are working under. What changes is how we enact each of these depending on context. Here are some tips: 

If students have to stay 3 feet apart:  

You’re in luck! Tasks and groups stay the same. To ensure students can still work at the VNPSs, you can use masking tape to mark out an equilateral triangle on the floor at each workstation. The length of each side of the triangle should be 3 feet, and only one vertex of the triangle should be at the VNPS. While working on the VNPS, students stand at the three vertices of the triangle and rotate around the triangle as they switch who is writing (each with their own marker).  

If students have to stay in their seats:  

There are two modifications that are needed with this restriction. First, groups will, by necessity, be made up of the students who sit close to each other (see figure 1).  

Figure 1: A seating chart denoting groups.

Second, you will need to find an alternative to VNPSs. The best choice, in this regard, is to have everyone working on a Google Jamboard (see figure 2). This is a digital whiteboard that allows students to draw with a stylus or a mouse, add textboxes or sticky notes, add images, and erase. It also allows for students to use text boxes, sticky notes, and images as manipulatives. Every member of a group would work on the same Jamboard so that they can see what each other are writing while still being able to discuss what they are doing.  

Figure 2: An example of a Google Jamboard.

If students are starting the school year online: 

If this is the case, the task stays the same. The groups and collaboration space are what change. To form random groups, most collaborative platforms (ZOOM, Google Meets, Microsoft Teams, etc.) have this feature built in. However, we have found that when building a thinking classroom in an online environment, the groups need to be larger—5 students per group to begin with. As the students become more comfortable working in groups and more adept with the technology the group size can be reduced to 4 students per group and eventually 3 students per group. Like with fixed seating, once these groups are formed, they will need to use a digital whiteboard like Jamboard to take the place of the VNPSs as a shared representational space for their work.  

My hope is that we continually inch our way back toward “normal” but the truth is, Covid and its related shifts may well be with us for some time. And if we know how to get and keep our students thinking in “the new normal,” why would we wait? 

Written by

Dr. Peter Liljedahl is a professor of mathematics education at Simon Fraser University in Vancouver, Canada and author of the best-selling Building Thinking Classrooms in Mathematics (Grades K-12): 14 

Teaching Practices for Enhancing Learning (Corwin, 2020) and Modifying Your Thinking Classroom for Different Settings: A Supplement to Building Thinking Classrooms in Mathematics (Corwin, 2021). 

Peter is a sought-after presenter and professional development facilitator who has worked all over the world on the topic of Building Thinking Classrooms, for which he has won the Cmolik Prize for the Enhancement of Public Education and the Fields Institute’s Margaret Sinclair Memorial Award for Innovation and Excellence in Mathematics Education. Peter is a former high school mathematics teacher who has kept his research close to the classroom and consults regularly with teachers, schools, school districts, ministries of education, and universities on issues of teaching and learning, assessment, and numeracy. 

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