Interactive Teaching ​IS​ Possible with Virtual Learning Technologies

By Enes Akbuga, Drake University (Twitter: @enesakbuga; Email: and Zachariah Hurdle, Utah Valley University (Email:

Many academics and teachers have been struggling with facilitating classes virtually. The 2020 global pandemic has brought many challenges and disruptions to teaching, but opportunities to explore and learn as well. This blog post discusses what we have learned so far, with the hope that these reflections are useful to other higher education instructors.

We teach in two very different university settings. Enes teaches at Drake University, which is a small liberal arts college in Iowa. Zach teaches at Utah Valley University, a public school that is the largest in the state (and open-access, as well). Since the spring of 2020, we have been collaborating on opportunities to use and explore some technological tools. Via frequent discussions over the past year on the new teaching and learning space, we shared some of the successes and frustrations throughout the experience. Specifically in this post, we share some of the highlights of facilitating synchronous​ class sessions using video conferencing tools. From what we have learned so far, most students enjoy real-time, synchronous, virtual interactions and perhaps prefer that over non-synchronous interactions. Like most instructors, we found Zoom (or likewise) to be a useful tool in facilitating online mathematics courses that is an experience shared across other institutions. The main motivation for this post is to share some of our ​experiences​ teaching mathematics online as well as talk about our thoughts on the ​possibilities​ of interactive teaching pedagogies.

First and foremost, providing breakout sessions during synchronous class sessions is a must. Our students have been enjoying breakout sessions. Students provided insights that these sessions are great opportunities for them to interact with their peers and learn from them. We design these sessions to resemble the small-group work of our face-to-face class formats. Students generally work on a specific class handout or activity and collaborate with each other during that time. But how to best lead this process? We often discussed the possibility of using online tools such as Google documents or Desmos so that we could facilitate class discussions better and get instant feedback from students.

Enes experimented with this strategy in his precalculus courses at Drake University. He created a Google document (see examples in Figure 1) that has a class activity on it (similar to class handouts including instructions), and this is linked to a Google Form where students access the activity. This is given at the beginning of each online class session (but also provided on a learning management system for those who miss the class).

Figure 1: An example of a class activity on a Google doc to be shared with students.

After a quick check-in with students, and any other business that needs discussing, students are put into the breakout sessions of 3 or 4 students to work on the day’s activity. Students are encouraged to collaborate while working on the given activity with their group members, but are asked to submit individual answers to Google forms (see Figure 2).

Figure 2: Example of how students submit their work on a Google form.

We found using Google forms to collect student work to be the simplest when it comes to facilitating class discussions, easily collecting work, and getting instant feedback from the students. Whenever Enes pulled the class back from breakout sessions, he utilized the responses to these documents to shape the whole-class discussions (see Figure 3; the responses are instantly listed on a spreadsheet automatically created by Google). This was useful for bringing up issues about particular mathematical concepts. For instance, while looking at Column H in Figure 3, one can see that some students do not use ordered pairs for representing x and y intercepts. This issue can then be brought to the attention of the whole class.

Figure 3: Example of a spreadsheet created by Google with student responses to a Google form.

Overall, we found this strategy to be helpful when facilitating not only small-group but also whole-class discussions in online environments. We are aware that there are some other tools that can be utilized for this purpose (e.g., Desmos Classroom Activities) but we found Google to be easier to navigate and manage data (student submissions).

Next, we would like to provide some insights into specific pedagogies that we have implemented during our online class sessions to improve student engagement and peer interaction. One such pedagogy is assigning roles to students during breakout sessions. This semester, Enes has assigned his students into groups of 4 or 5, and each group has a group captain and a timer. He has asked group captains to be in charge of groups when the instructor (or TA) was absent from the group, and to make sure that students remained on track. This responsibility is more of a motivational and informal role assigned to the participants, and doesn’t really have a formal assessment mechanism. The group captains ask questions to their group members and keep track of their progress through the group work. They also make sure that everyone’s voice is heard during these times. Timers make sure that there is enough time left on each task, and that the group has allocated enough time to each part of the assignment.

Another pedagogy we think is important is considering how to assign students into groups. Enes has been experimenting with Zoom’s pre-assigned group feature. With this, it is possible to automatically assign students to pre-arranged groups during each Zoom session. This reduces the time spent on assigning people into rooms during live sessions. Another advantage of this is that the instructor can decide to keep the same students in the same groups for a certain period of time or throughout the semester. This way, the same assigned roles can take effect each time students are put into breakout sessions. Enes has observed that when students get to know each other and work together, they prefer to continue to be in the same groups for the rest of the semester. One can simply upload a list of names to Zoom in advance and this way, once breakout sessions are activated, students are always assigned to the indicated rooms in the list (to learn more about this:​).

We believe that breakout sessions provide more equitable and inclusive learning opportunities for all students. Math educators have long been advocating for including small-group portions for instructions to provide learning opportunities that do not typically occur in traditional classrooms (see Yackel, Cobb, & Wood, 1991 for just one example). We think that breakout sessions during online environments are a way to provide that opportunity.

While we previously were discussing some tools and pedagogies for breakout sessions including small-group work, we now want to shift our attention to large-scale classroom teaching practices, and we have experimented with a few pedagogies.

First of all, we like to ask students to turn on their cameras and click the gallery view. In order to encourage camera use (but not mandate it, as most universities prohibit) we have made remarks such as: “It feels weird to talk to a blank screen,” “I can’t tell if you are talking to me or sleeping,” or “Is there anybody out there?” We noticed that students appreciated honest and natural comments like these, through their own responses. In terms of encouraging students to put the gallery mode on, Enes would even ask random students to comment and describe other students’ camera views to make sure they can easily see others. So far, we think we had great success in students turning their cameras on in his class, as around 80% of students participated (although this has declined towards the end of semester). However, we recently found out about a report of the environmental impact of people turning their cameras on during virtual meetings and the results were somewhat concerning (​ This made us question whether to always require students to turn on their cameras or just ask on certain occasions (e.g., when speaking). This issue is definitely up for consideration.

Enes has been facilitating online class sessions in such a way as to reduce direct instruction (or lecturing) and increase student engagement and interaction. He is almost completely avoiding lecturing or directly talking. He provides pre-recorded videos and slides to provide detailed information before class sessions. He then mostly spends time on discussing key information and the bigger picture of concepts while letting participants discuss and contemplate important matters during live classes. This provides students the time and opportunity to think and reason about mathematical concepts.

One interesting practice Enes saw the mathematician Dave Kung (; Twitter: @dtkung) use in a talk provided by Project NExT ( was asking the participants to move their heads on the camera in certain directions to get visual feedback. We have tried that technique in our classes when posing questions or asking them if they are ready for a certain class activity. Most of the students found that super fun, although camera mirroring caused a great deal of confusion among the class!

Another interesting pedagogical technique that Enes recently found out about was during Maria Anderson’s (​; Twitter: @busynessgirl) talk at the Project NExT meeting in 2020. She would pose a question and ask the participants to come up with an answer to be typed in Zoom’s chat box. However, she wouldn’t ask people to submit answers right away. The facilitator asked students to not answer for a couple of minutes in order to provide opportunities for the participants to compose an answer. Then, she would count down from three for everyone to submit their answers at exactly the same time. The participants were excited about this and the chatbox would become a constant stream of answers! (We have even heard of this being unofficially called the Waterfall Method, at times.) Enes experimented with this in his precalculus course recently and noticed that students would get super engaged about trying to come up with some answers. He has observed that even the students who wouldn’t previously have attempted to answer questions are now willing to at least try and come up with something to contribute, which increases the student participation overall.

In conclusion, we have found that online teaching is less than ideal and is something we are still learning along the way. However, we believe that there are pedagogies that exist in facilitating ​active​ learning environments. The key is that technology does provide opportunities for getting connected with students and having them interact with one another.


Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for research in mathematics education, 22(5), 390-408.

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2 Responses to Interactive Teaching ​IS​ Possible with Virtual Learning Technologies

  1. Cindy says:

    I love this topic!

  2. Bill P. says:

    Thank you so much for this very useful post! Some techniques are applicable to high school teaching also.

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