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Inclusivity and Active Learning in the Mathematics Classroom

By Lina Sorg

Active learning—a unique approach to instruction during which students engage directly in the learning process via discussion, groupwork, case studies, problem solving, and other hands-on activities—can play a valuable role in the mathematics classroom (see Figure 1). “Why active learning?” Victor Piercey of Ferris State University asked. “The short answer is, it works. Active learning can improve outcomes for women and minorities, so there’s some hope that it can help and be related to issues of diversity, equity, inclusion, and justice.” During a minisymposium at the 2022 SIAM Annual Meeting, which took place last week in Pittsburgh, Pa., Piercey overviewed best practices for inclusivity and active learning in the mathematics classroom.

Figure 1. Active learning is a unique approach to instruction during which students engage directly in the learning process via discussion, groupwork, case studies, problem solving, and other hands-on activities. Victor Percey of Ferris State University employs this technique in his mathematics classrooms.
Piercey, who teaches courses in actuarial science and quantitative reasoning, praised active learning but cautioned that its effectiveness—especially in the context of equity, diversity, and inclusion (EDI)—depends on implementation. “We want to be able to engage the entire student—everything about who they are—when they walk into that class,” he said. “We want to be mindful of that because it plays a role in their learning process.” 

Piercey views inclusion as a foundation on which one can build equity and justice to ultimately foster a robust, well-sustained community. He outlined two separate dimensions that contribute to inclusion: belonging and value. “An individual has to belong, and everybody has to be ‘in’,” he said. “As part of their belonging, they have to be valued for what they uniquely contribute to the group.” Failure of either component results in pseudo-inclusion, which can lead to assimilation and/or tokenism; failure of both components results in exclusion.

Piercey noted that education is all about relationships, and he focused on three specific relationships during his talk:  teachers’ relationships to themselves, students’ relationship to each other, and the relationship between teachers and students (see Figure 2). He began by encouraging other instructors to create a positionality statement: a statement about one’s identity as it relates to the implicit power dynamics of the student-teacher rapport. Instructors can then use their positionality statements to recognize their own blind spots. “The students in my classes have such different life experiences,” Piercey said, adding that these experiences go beyond race, gender, and sexuality. “Many of them are working full time and some of them are nontraditional students with families to take care of.”

Figure 2. Belonging and value both contribute to a sense of inclusion. A lack of either component results in pseudo-inclusion; a lack of both components results in exclusion.
Next, Piercey shared a link to an online implicit bias test  and suggested that people who are aware of their own implicit biases can more easily interrupt them. Over the course of one’s life, the brain makes connections based on personal experiences and subconsciously processes information based on certain evolutionary predispositions. Therefore, instructors must actively work to disrupt these connections—which may represent stereotypes or biases—at the subconscious level.

Piercey then turned to the relationships between students. “To manage some of these student relationships, it’s helpful to build classroom norms and unpack them,” he said. “Invite your students to help create the norms, but they really do need to be unpacked.” Such norms should extend beyond simply “be respectful” and explore concrete examples of what respect looks like. Piercey also urged instructors to listen for and interrupt biases and microaggressions in class discussions.

When incorporating groupwork in the active learning structure, one should think carefully about group makeup. Piercey organizes his students into groups once he gets to know their personalities. Sometimes he maintains those original groups for the entire semester and other times he rearranges them periodically. “It kind of depends on my feeling, how the class feels, and my sense of who they are,” he said, especially because each class is different. He encouraged attendees to remain aware of student positionalities and refrain from putting them in positions that might trigger a stereotype — i.e., one woman in a group of all men.

Figure 3. Victor Piercey focused on three specific relationships during his talk: teachers’ relationships to themselves, students’ relationships to each other, and the relationship between teachers and students.
It is equally important for teachers to ensure that diverse groups speak and are heard. Piercey does so with a tool called “revoicing.” He asks three to four students to repeat something that their peer has just said in their own words, which encourages everyone to listen to and comprehend one another. “After a couple of times, they get used to this and start paying attention to each other better,” Piercey said.

Finally, Piercey addressed the relationship between teacher and student. “The most fundamental thing here is to build trust,” he said. “That takes a lot of hard work because of our position of power over them as an instructor who is going to be assigning a grade.” Piercey referenced grading practices as a great place to establish trust, especially because many students view their relationships with instructors as transactional: they complete the required assignments and receive a grade. He has used various types of grading over the years, ranging from a form of standards-based grading to ungrading. “No matter how traditional my grading system is, I always make sure that students have a chance to revise their work and learn from their mistakes,” Piercey said. “To me, every part—even if an assessment is supposed to be summative—is part of the learning experience.”

Other valuable techniques include humanizing the syllabus, displaying welcoming body language, and avoiding homophily: the tendency to seek out and cluster around people who are similar to oneself.   Teachers should also exercise compassion whenever possible. For instance, if one of his students has a death in the family, Piercey does not ask for a note or another form of documentation. Instead, he responds with either “I’m sorry for your loss, do you want to share a favorite memory?” or “Don’t worry about this class, we’re going to be there when you get back and we’ll get you caught up.” Students have been very responsive to these replies. 

Piercey closed his talk with a brief discussion about the dangers of microaggressions and deficit thinking. He suggested that instructors reframe deficit thinking into “ready to learn” thinking. For example, instead of focusing on concepts that students do not yet know, they should reframe their thinking as “concepts that students are ready to learn next.” Teachers should also regularly encourage their students to reflect on and acknowledge their own assets and strengths, especially when they are struggling with coursework. “It’s about compassionately recognizing our students as entire human beings,” Piercey said.


Lina Sorg is the managing editor of SIAM News.
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