360 Degree Whiteboards: An Equity Strategy to Improve Outcomes in Precalculus




When I envision my typical math class years ago, I see myself at the front of the room giving a long lecture as I filled a chalkboard with mathematics. Students are frantically copying from the board. If I ask questions, the same few students answer, but what does everyone else understand? Of course, I don’t know what they understood because in a lecture learning is not visible and it is easy for students to hide.

Later, in version 2.0 of my pedagogy, I tried to incorporate some active learning. A typical class day started with a quiz or review, followed by a lecture, and ended with students working alone or in pairs on worksheets.

Research shows that active learning strategies and low stakes collaborative practice produce the greatest educational gains for women, minorities, low-income students, and first-generation college students. But in this phase of my teaching career, I was still the “sage on the stage” lecturer at the front of the room and students were practicing the procedures that I had demonstrated. I knew that I needed to do more and become a “guide on the side” to promote meaningful active learning that fosters students’ thinking and values their contributions.

Now in version 3.0, my math classes look very different. Students are not only working in groups, but at multiple points in the lesson, all students stand and work simultaneously on vertical whiteboards that cover the classroom walls (or the online equivalent). A typical class day starts with a whiteboard adaption of the Think-Pair-Share strategy in which students complete a review, followed by a 360 degree whiteboard session with a series of challenging problems, and ends with students working in groups to complete their guided class notes summarizing key concepts and procedures from the day’s lesson. By the time they complete the lesson, students have worked on a topic four times (360 degree whiteboard work introducing the topic, development of guided notes, homework, and Think-Pair-Share review using whiteboards at the start of the next class).

This blog will focus on 360 degree whiteboards as a tool to enhance equitable learning, the research behind this strategy and how I use whiteboards in my typical lesson cycle.

360 Degree Whiteboards (Or Vertical, Nonpermanent Surfaces)

In an extensive study on work surfaces and their impact on math learning, Liljedahl found whiteboards (or any vertical, nonpermanent surface) promoted better engagement and mathematical thinking than the traditional use of paper and pencil with students seated at desks. His research documented the following about student behaviors during problem-solving activities using vertical whiteboards:

  • Students were more eager to start the task and began discussing and writing sooner
  • All students in the group were more likely to participate, discuss, and interact to transfer knowledge
  • Students were more likely to persist through challenges
  • Written work showed a non-linearity that reflects the thinking process

In my own classes, I observe similar promising behaviors using the 360 degree whiteboards. Because it is easy to erase the whiteboard (non-permanent surface), students are willing to take risks and try things. Since everyone’s work is visible (vertical surface), students are more likely to engage with each other to deepen their own understanding.

Contrast this to my experience with students working in groups at their desks. They were often hesitant to write anything down that was “not right.” They wanted their paper to show an organized solution, and this hampered the thinking required in more complex and challenging problem-solving tasks. It was hard for them to collaborate because they could not easily see each other’s work. If someone was explaining something, others could not easily see the graph or the mathematical notation that accompanied the explanation.

Liljedahl claims, “Unlike many other changes that can be made in a teacher’s practice, the vertical non-permanent surface is well received by students, easy to manage at a whole class level, and has an immediate positive effect on classroom thinking behavior. It is also infectious with other teachers quickly latching on to it and administrators quickly seeing the affordances it offers.”

vertical non permanent surfaces in math class

Activity: Think-Pair-Share Using 360 Degree Whiteboards

Think-Pair-Share is a familiar activity to most faculty. In the traditional Think-Pair-Share students have private think time, a low-stakes opportunity to pair off with a peer to discuss their ideas, which prepares them to participate in a class discussion, the share. Think-Pair-Share can be an effective strategy for bolstering student confidence and increasing participation; however, the “share” can also be dominated by a few vocal students, which results in an inequitable sharing of ideas.

My Precalculus class with corequisite support often begins with a review where I use a version of Think-Pair-Share, more aptly named Think-Square-Share for groupwork purposes. When this activity is used in conjunction with 360 degree whiteboards, the experience can amplify learning and be more intentionally equitable.

Here is how it works.

  • THINK: Randomly assign students to small groups of 4. Assign a problem from the previous class and give students time to think and work on the problem alone for 1-2 minutes. Every student is working on the same problem.
  • SQUARE (on 360 degree whiteboards): Give each group a marker. The student with the marker teaches the problem to the rest of the group using the whiteboard. If the student holding the marker gets stuck, groupmates naturally jump in, providing the real-time help and support needed. The discussion of the problem is low-stakes and prepares students to participate in the class discussion.
  • SHARE (on 360 degree whiteboards): As groups put their solutions on their whiteboard, students proactively look around the room, explore alternative solutions from other groups, and confirm their answer or identify their mistakes. After things have settled down, I facilitate a class-wide discussion where we explore different solutions, examine the logic behind common mistakes and summarize.

During the Square part of the activity, I often find that some groups finish early while other groups may be struggling. In my class I train my students to proactively help others after they have completed a problem by walking around the room and giving hints or asking guiding questions. I call this Uber-driving. This gives everyone in the “quick” group another chance to teach. Of course, some students in the “quick” group may not otherwise view themselves as experts, and this gives them a chance to shine and builds their confidence. It also provides immediate support to struggling students who may be too embarrassed to ask for help, and support from a peer can be much less threatening than support from a teacher.

Here is a tweak to make the experience more equitable: Do several rounds with new problems. Have students pass the marker so that everyone in the group has a chance to teach. We have all heard the adage, if you really want to learn a topic, teach it. By requiring all students to teach in this low-stakes manner, learning is amplified and more equitable.

Activity: All-Inclusive 360 Degree Whiteboard Session

My favorite activity in my lesson cycle is the 360 degree Whiteboard Session, where all students work individually and simultaneously on a challenging problem on the whiteboards. This is often how I introduce a new topic or problem type.

Here is a short silent movie showing a 360 degree whiteboard session in my Precalculus with Support course.

Because this happens almost every class period, students become accustomed to the intellectual discomfort of working on a hard problem without a blueprint. At the beginning of the semester, we discuss the benefits of productive struggle, and they understand that by trying to figure stuff out, they grow their brains and become better thinkers and problem-solvers. Of course, the instructor also contributes to creating this comfortable environment with positive encouragement.

As they work on the whiteboards, students will naturally look around the room to get ideas, to compare their approaches, and to debate answers. I walk around, too. I make positive and encouraging comments. I might spotlight and appreciate an aspect of someone’s work in order to nudge others in a similar direction. I look for learning opportunities. For example, I might ask two students to compare their work and discuss a particular issue, “One of you flipped the inequality in your solution and the other did not. I want the two of you to talk about that.”

When students finish, they know to Uber-drive around the room looking for someone to help. Since everyone’s work is visible, no one can hide, so there is an equitable opportunity for feedback and support. Since the whiteboard is easy to erase, errors and missteps are not a big deal. Of course, in some cases, I encourage students to leave interesting errors on their board next to their revision so that they can share what they learned with the class.

Because I can see everyone’s work, I can gauge when it is time for the class to discuss solutions. My favorite scenario is when the class is split, with one half getting one answer and the other half getting another. This provides a great opportunity for students to debate which solution is correct and give reasons why. When answers vary, we can also discuss the logic behind common errors and celebrate the learning that has come from making a common mistake. This is also an opportunity for making connections between solution methods to emphasize concepts.

After the whiteboard session, students work in groups to complete guided class notes to summarize key concepts and procedures from the day’s lesson. The class notes also include a small set of representative problems similar to those we discussed in the whiteboard session. I often use the guided notes provided by the publisher of our textbook. This is the only part of the lesson that does not use the whiteboards.

Activity: All-Inclusive 360 Degree Digital Whiteboards Online Using Google Slides

online sample using google slides

The benefits of Think-Pair-Share and 360 degree Whiteboard Sessions can be fully experienced and replicated in an online math class using Google Slides as a synchronous student workspace.

Similar to the 360 degree whiteboards in the physical classroom, each student has their own digital whiteboard workspace that is easily visible to the entire class. If students are stuck, they are able to scroll through the slides to see other students’ work.

In this setting, the instructor can zoom out to get an aerial view of all students’ work similar to the in-person, 360 degree Whiteboard Session to ensure each student is participating and actively on-task.

We can use Google Slides in much of the same ways that we use the 360 degree whiteboards:

  • Have students customize their 360 degree digital whiteboard by writing their name at the top of their whiteboard space.
  • Students can participate in Think-Square-Share activities online by first taking a few minutes to work on a problem alone (having all mics muted); then having a small group discussion (in breakout rooms), all while populating their answers onto their individual digital whiteboard space; and last having a class-wide discussion in the main Zoom room by highlighting students’ work.
  • Groups can be color-coded on their digital whiteboard so that it is easier for students to find their group after scrolling through the slides. Groups are automatically changed each class session.
  • The instructor can type positive feedback into students’ digital whiteboards to create a supportive and positive online learning environment.
    The many positive benefits of whiteboards found by Liljedahl apply to Google Slides. For example, student mistakes can still be easily erased (just backspace to delete), and students are more likely to persevere knowing they are able to get hints by scrolling through their classmates’ digital whiteboards.


I am aware that some instructors reading this blog may be skeptical. They may think that their students will not actively engage in the activities that I have described here or that weaker students will be too embarrassed to show their work on the whiteboard. But this has not been my experience in my open access Precalculus with Support classes at Citrus College. In fact, the opposite is true.

The use of whiteboards is an important component of creating a shared sense of community in my classroom and it promotes equitable learning. Studies show that women and students of color report feelings of isolation and a sense of not belonging as the main reasons for leaving STEM . Classrooms that are interactive may be the key to increasing their success rates, and in a 360 degree whiteboard classroom no one is invisible; everyone is engaged and supported.

Another concern I often hear from those who lecture is about content coverage. With all of this interaction and discussion, how can you cover everything? Almost all instructors who teach Precalculus with Support at Citrus College use the interactive whiteboard pedagogy and we have worked to focus class time on core concepts and procedures that we identified by designing backwards from the Calculus sequence and using real-life applications. Our data suggests that we are on the right track. Students in our open access Precalculus with Support course are considered “underprepared,” but they had a higher success rate than “prepared” students in Precalculus without support, which is taught with a traditional lecture style (59% vs. 47%). Furthermore, in a progression study, both groups completed Calculus I at nearly identical rates.

I understand that adopting a new style of teaching can be nerve-wracking for instructors. I have been through it myself. But once I saw the learning gains, particularly for my non-traditional students, I can never go back to the traditional lecture. I have found a new purpose and passion in my teaching as I watch the growth in my students that is fostered through this method of collaborative learning.

If you would like to learn more about 360 Degree Whiteboards, here are some resources:

  • Website: 360 degreemath.com
  • Article: “Get Up, Stand Up: 360 Degree Math Revolutionizes Classrooms”
  • Website: Peterliljedahl.com
  • Blog: “The Student- Centered Math Class: Transform your math instruction with three strategies you can start using today” by Laura Wheeler
  • Article: “In this school, the classroom revolution is now a reality – all 360 degrees of it”
  • For an inexpensive alternative to whiteboards, try whiteboard sticker paper.

The idea of using Google slides was first introduced in Edutopia and adapted from Kathleen Beachboard where each student has their own ‘Digital Desk’ similar to a whiteboard.

Sophia Lee

Sophia Lee is a Professor of Mathematics at Citrus College who teaches in an active learning classroom to fully transform the mathematics experience. She believes in building a strong sense of belonging for her students, based on teamwork, support, and growth mindset. She earned her doctorate degree in educational leadership with a specialization in community colleges from CSUF. She has presented at USC’s Racial Equity in Mathematics Leadership Institute (REMLI), UC Berkeley’s STEM Equity Conference, and the Strengthening Student Success Conference. Outside of the classroom, she enjoys spending quality time with her family and their two young sons.

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