“Social interaction provides us with the opportunity to use others as resources, to share our ideas with others, and to participate in the joint construction of knowledge.”(Smith & Stein, 2011, p. 1)

The rapid transition to online instruction in the spring forced many instructors to develop remote learning strategies that sacrificed high-quality instructional practices out of necessity or institutional policy. Without proper support or training, many instructors are grappling with the same challenges this fall; in particular, creating opportunities for students to engage in collaborative problem-based learning requires that instructors have a combination of technological fluency and knowledge of effective online teaching moves. Although the resources below are not comprehensive, they provide a starting place for considering the challenges and opportunities associated with online mathematics instruction.

Teaching mathematics online requires us to rethink the way classrooms and interactions are organized. I see three main considerations: (1) the organization of materials (e.g., tasks, manipulatives, agenda/goals), (2) the organization of people (e.g., flexible groupings, individual work, whole-class), and (3) the organization of ideas (e.g., shared written mathematical thinking, formative assessments). 

Organization of Materials

An essential component of problem-based learning is the mathematical task that students engage with, so the success of a lesson can hinge on how well an instructor launches the task. Doing this well requires that students know what they are supposed to be doing, how they are supposed to be doing it, and who they should be working with. Online learning environments make it much more likely that students will miss some part of the launch discussion or forget part of the directions. In a classroom, they can just lean over to a groupmate and ask for help, but now they are physically and technologically isolated from their peers.
To address this challenge, use a consistent format for sharing your agenda, lesson objective, manipulatives, and expectations for class. See slides 3-11 of the additional resources.

Organization of People

To facilitate engaging and productive collaborative learning, we need to be able to group students in multiple ways. You can assign students to breakout rooms for small-group collaborative work in Zoom, BigBlueButton, or BlueJeans. If you want students to be able to choose their own groups, try Congregate or use multiple video calls and allow students to choose which room they go into. See slides 12-13 of the additional resources.

Organization of Ideas

To close a collaborative problem-based mathematics lesson, I try to use a variety of questioning strategies to make visible the relevant mathematics in a way that moves all students toward accomplishing the learning goals. When transitioning to the online environment, it’s important to have specific strategies for facilitating those discussions or you’re likely to get blank stares and silence as responses to what would normally be an engaging question. It’s important to recognize that online discussions are not just regular whole-class discussions through a new medium. Video conferencing software allows students to engage in fundamentally different ways that can be leveraged to increase participation by all students. The list below has strategies that enable all students to participate. See slides 14-17 of the additional resources.

• Virtual whiparound (slide 15).
• Use a Desmos Classroom Activity and utilize the Snapshots feature to put multiple pieces of student work in conversation with each other.
• Pose a question and ask students to write their response in the chat, but wait to press enter until you give the cue. When you’re ready, prompt them to submit their responses and then have everyone take a minute to read through them.
• Pose a question and then do a virtual Turn and Talk. Assign partners and have them initiate a private chat with each other to discuss the question. Have each pair use the “raise hand” reaction when they are done discussing. Alternatively, randomly assign pairs to breakout rooms for a few minutes.
• Ask students to respond to questions with other online resources, like Google Forms, Poll Everywhere, or Mentimeter (I like the data displays on this one).
• Have one student from each group annotate the screen to show their work for a problem, report out on a jigsaw, or write down a lingering question.
• Have all students respond to a question with nonverbal feedback on Zoom.