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Online Math Discourse: Can The Five Practices Work?

Six years ago, I was faced with a situation where I needed to transfer my face-to-face geometry class to a virtual classroom. I began with a list of pedagogical practices I wasn’t willing to compromise for the convenience of an online setting. These non-negotiable practices included all of the elements of Smith and Stein’s 5 practices for orchestrating productive mathematics discussions: anticipating, monitoring, selecting, sequencing, and connecting (Smith & Stein, 2018). My goal was to engage students to engage in a rich, open-ended math task. I wanted them to collaborate together to discover different strategies and various possible solutions, with multiple representations such as concrete, drawing pictures, and using symbolic notation. I wanted the ability to walk around the classroom and monitor student work, purposefully select and sequence student strategies and representations for the whole group discussion, and have students connect these various pieces in order to make connections to the bigger mathematical idea. After years of studying and implementing the 5 practices, there was no way that I would consider moving online unless I could implement these practices with fidelity.

In keeping aligned with the 5 practices, I have developed and implemented an online routine over the past six years for a successful synchronous online classroom.

Much like a face-to-face class, I begin with an open-ended and rich mathematical task and anticipate various student strategies and potential correct answers, as well as misconceptions.

I use breakout rooms and Google slides. Breakout rooms (a feature of Blackboard Collaborate Ultra and Zoom) allow for a small group of students to use audio to collaborate amongst themselves. Google slides enables me to give students access to edit the slides. This is essential for them to work together and to make their thinking visible (Hattie, 2012) because every student is responsible for contributing their thinking on a blank slide. This is where online learning excels. I am able to monitor the students’ work in real time. I can observe six groups of students on six different slides. On each slide, four students are writing, uploading photos of their work and pasting screenshots of virtual manipulatives. As the student slides become inundated with new ideas, different perspectives, and misconceptions, I am observing 24 students thinking through the problem simultaneously. As the students continue to collaborate, develop new strategies, and find additional representations to model their thinking, I monitor students in breakout rooms, ask questions, listen to conversation, and view each group’s slide.

When preparing for the whole group discussion, I select at least two different representations of the same strategy and a new perspective or misconception. I mark these with an arrow so that students know what, specifically, they should share.

As students wrap up their slides, I finalize the whole group discussion. I organize the sequence of the student work and develop a strategy map (Wills, 2015) which is a graphic organizer to identify (a) specific order of student work and (b) open ended questions to support their discovery of connections between student work and the overarching mathematical idea.

It is through these purposeful steps that I am able to implement the 5 practices with fidelity. In fact, over the years, I have found that my online class gives more student voice and a greater variety of pictorial and virtual manipulative representations. I do not compromise any part of my pedagogy when teaching online.


Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge/Taylor & Francis Group.

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

Wills, T.E. (2015). Use of strategy maps and virtual coaching: A case study of a teacher’s

development of connections in middle grades mathematics. Doctoral Dissertation, George

Mason University. Dissertation chair: Dr. Jennifer Suh.

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Theresa Wills is an Assistant Professor of Mathematics Education Leadership at George Mason University. Theresa has taught synchronous online classes and webinars for ten years and researches teaching practices that are adaptable to the online environment. Prior to online teaching, they worked as a secondary math teacher, technology coach, and mathematics coach in grades K-8. Theresa uses this background in mathematics, coaching, and technology to teach rigorous, interactive, and engaging courses. Students who complete these courses meet all requirements of face-to-face coursework, while learning additional technology coaching competencies.

Latest comments

  • Would you mind sharing the strategy map? Thank you!

  • Can you share with us the graphic organizer you use to sequence student work?

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