Visibly Random Groups in Math Class

By Dylan Kane, Math Teacher

When I first started teaching, I assigned seats. Every so often I would write new seating charts, laboring over the perfect combinations of students that would help them collaborate and engage in class each day. I had no indication anything was wrong with this system. It was what I had been used to as a student, and it was what most other teachers did.

Then I learned about visibly random groups. The premise was simple: instead of engineering groups or letting students choose themselves, randomize them, and repeat this process every day. And do this visibly, by passing out cards, projecting a randomizer, or other means, so students know that they are being put in random groups that are not socially engineered.

I learned about visibly random groups from a paper called “Building Thinking Classrooms: Conditions for Problem Solving” by Peter Liljedahl. He offered a vision of what classes looked like using random groups:

  • Students became agreeable to work in any group they were placed in.
  • There was an elimination of social barriers within the classroom.
  • Mobility of knowledge between students increased.
  • Reliance on the teacher for answers decreased.
  • Reliance on co-constructed intra- and inter-group answers increased.
  • Engagement in classroom tasks increased
  • Students became more enthusiastic about mathematics class (Liljedahl 2016).

Those all sound like ideas that would improve the teaching and learning in my classroom. I had never even thought about mobility of knowledge between students as a variable I could influence in my classroom. But over time, I saw much of what Liljedahl described happening. Group work became a routine part of class, I saw fewer issues within groups and a greater willingness to take risks and engage with challenging tasks.

The impact of visibly random groups was also connected with the idea of status, which I learned about from Ilana Horn’s blog. She writes:

Status is the perception of students’ academic capability and social desirability… Students with high status have their ideas heard, have their questions answered, and are endowed with the social latitude to dominate a discussion. On the other side, students with low status often have their ideas ignored, have their questions disregarded, and often fall into patterns of nonparticipation or, worse, marginalization (Horn 2014).

Visibly random groups created the opportunity to break the cycle of status, where some students play out a role of the “smart” student, and others play out a role of the “dumb” student. Students worked with all other students, and they knew that they are assigned to a random group, rather than thinking, “I must be with these smart people so they can do the work for me”. They were willing to contribute more quickly and freely, and created a more collaborative and learning-oriented environment in group work. These were humble changes. They didn’t happen overnight. But they are one example of the changes that have made me, in small ways, over time, a far better teacher than before.

Works Cited

Horn, I. S. (2014, March 5). Status: The Social Organization of “Smartness” [Blog post]. Retrieved from

Dylan is a high school math teacher in Leadville, Colorado, and previously taught middle school math in Boston. He earned his master’s degree from the Sposato Graduate School of Education. He writes regularly on math education and the intersection of research and practice in teaching on his blog, Five Twelve Thirteen.

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