Moving Mathematics Education Toward Greater Equity

The Marvelous Mathematician is kicking off the new year with a fantastic book by Pamela Seda and Kyndall Brown, Choosing to See: A Framework for Equity in the Math Classroom (2021). The authors lay out an equity framework (ICUCARE) to provide educators a lens and structure on which to build more equitable instruction to meet the needs of all students. What we most appreciate overall about the book is how the authors first define the need, such as “combating negative stereotypes,” explaining why this is important and linking it to research. Then, they provide practical ideas for addressing this need in the classroom. Ideas from other educators and researchers form the basis for the remedies shared throughout the book. To provide you the opportunity to experience a part of this excellent book, we are reprinting the section titled “Overcoming Students’ Lack of Confidence.”

We are excited that Kyndall Brown will be hosting our March 22 webinar, 7 Practices to Make Your Math Class More Equitable. Register to attend live or to receive the on-demand recording.

Overcoming Students’ Lack of Confidence

Excerpted from Seda, P., & Brown, K. (2021). Choosing to see: A framework for equity in the math classroom (pp. 38–44). Dave Burgess Consulting, Incorporated. Kindle Edition.

It is extremely important that students experience mathematics in ways that help them see the mathematical expertise that resides in themselves, their classmates, their families, and their communities. Critically conscious teachers recognize that students generally only seek help from those they perceive as competent. They know that their job is to help students identify the mathematical expertise that lies within themselves and all around them and to teach them how to leverage this expertise to build their own confidence and competence in mathematics.

Researcher Megan Franke and her colleagues make the claim that students who have their problem-solving strategies explained to the class by their classmates benefit academically.⁷ Research suggests this happens because teachers push students to further explain their thinking and compare their thinking with others’. When a student’s problem-solving strategy is shared by another student, this raises the status of the student whose strategy was shared. Raising a student’s status helps to build confidence. Having students share each other’s strategies is also a way to have them include others as experts. In this section, we discuss some key strategies for helping students view themselves and others as experts.

Showing the value of building expertise

One strategy that has proven successful in getting students to understand the value of putting in hard work is to teach them about the concept of malleable intelligence, or the idea that the human brain is like a muscle: when you use it, it changes and gets stronger. Researchers at Columbia University conducted a study with two groups of seventh-grade students whose math scores had declined. Both groups of students participated in an eight-week study skills intervention. One group of students read articles about brain malleability, and the other group did not. The group that learned about brain malleability made remarkable improvements in their math scores, while the other group’s scores continued to decline.⁸

To introduce this concept to students, teachers can provide lessons on malleable intelligence. (A link to sample lessons can be found in Appendix F.) Teachers can have students read articles and share what they found most surprising and interesting with their classmates. Students can also work in groups, with a group spokesperson sharing one example of brain malleability that they read about. Each group can then make a poster or PowerPoint presentation to share their information with the rest of the class. It is critical that teachers then continue to refer to these ideas throughout the school year to reinforce that students can learn if they are willing to put forth the effort.

Creating classrooms that inspire confidence

Look at whom your students ask for help. Who gets listened to and who gets dismissed? Students often view their textbooks and teachers as the only sources of knowledge in the mathematics classroom. However, as Gloria Ladson-Billings notes, “There is more expertise distributed across the classroom than there is in any one person.”⁹

Traditional classrooms reinforce the idea that the teacher is the arbiter of knowledge who dispenses to those who dutifully follow their instructions. The culturally relevant teacher, however, does not view knowledge as static, but rather as continuously re-created and shared by both teacher and student. In this approach, teachers should look for opportunities where they can play the dual roles of student and co-teacher. One way of making a class less teacher centered is by striving to never say anything kids can say for themselves. That means allowing students to ask and answer their own questions, to respond to their classmates’ questions, and to repeat and revoice others’ thinking in their own words. Teachers redirect questions asked of them to other students.

This is where it is important to emphasize that the mathematics classroom is a learning community, where every student has a responsibility to learn and to contribute to the learning of their classmates. This is especially important for students who have internalized negative stereotypes about learning mathematics. Sometimes students will do for others things they would not ordinarily do for themselves. The critically conscious teacher capitalizes on this idea to help build the learning community. Because low-status students will often avoid the appearance of looking dumb to their classmates, classroom structures that provide opportunities for them to contribute can invite otherwise reluctant learners to engage in meaningful mathematical activity.

One way to structure this interaction is by assigning roles to students working in mixed-ability groups. To support equal participation, group roles should be designed to be intellectually equal. Before assigning roles to students, the teacher should provide explicit instruction on each role. To include time for students to practice these roles during groupwork, we recommend that one role be introduced per week. Once the class has practiced all four roles, the teacher can communicate the expectation that these roles be used whenever group assignments are given in class. Teachers can assign roles at first and gradually turn that responsibility over to group members.

The following roles have been adapted from Cohen and Lotan’s research [on] complex instruction:¹⁰

• The Coach keeps the group together, making sure everyone’s ideas are heard. They ask questions like, “Did anyone see it a different way?” and “Are we ready to move on?”
• The Skeptic helps students know they will need to provide justifications for their thinking and methods. They probe deeply into other students’ processes, asking questions like, “How do you know that?” and “How does that relate to …?”
• The Accountability Manager organizes the ideas of the group using mathematics principles, reasoning, and connections. They ask questions like, “How do we want to represent our ideas when it’s time to meet with the teacher?”
• The Team Captain checks in with the team to see if they need any mathematical tools while solving a problem. They are the only one allowed to get up from the group to communicate with the teacher or members of other groups. They make sure that questions they ask outside the group can’t be answered by any of the group members, and they have the responsibility of bringing any information from the teacher back to the group.

Another way students may try to avoid looking dumb to their peers is by not asking for help. It is important that teachers create classroom structures to help students overcome this fear, and one way to do this is by using instructional strategies that normalize seeking help. Find Someone Who, outlined below, is a Kagan Cooperative Learning strategy in which students are asked to find someone in the class who can explain to them how to work a problem on a worksheet.¹¹

This activity helps students build confidence in their own and others’ expertise in several ways. Since this activity requires everyone to ask for help, no one has to feel self-conscious about it. It also gives all students the chance to be teachers, as well as learners. This is especially important for low achievers who talk much less in class.¹² When students teach others, they remember approximately 90 percent of what they share. If teachers make themselves available to low-status students to explain how to work the hardest problems on the assignment, the low-status students can become the people from whom others have to get assistance. Seeing the boost in a student’s confidence when they get to explain how to do one of the “hard” problems to the “smart” kids in the class is one of the great joys of teaching.

Find Someone Who

(Sample can be found in Appendix A.)

Setup: The teacher prepares a worksheet or set of questions for students.

Steps:

1. Students walk around the class, keeping a hand raised until they find a partner.
2. In pairs, Partner A asks a question from the worksheet; Partner B answers.
3. Partner A records the answer on his or her own worksheet, and Partner B checks and initials the answer.
4. Partners A and B switch roles and repeat steps 2 and 3, with Partner B asking and recording, and Partner A answering and checking.
5. Partners A and B part and raise a hand again as they each search for a new partner.
6. Students complete steps 1–5 until their worksheets are complete. They sit down when they are finished.
7. In their regularly assigned teams, students discuss answers. If there is disagreement or uncertainty, they all raise a hand to ask an agreed-upon team question.

References

7. Noreen M. Webb, “Engaging with Others’ Mathematical Ideas: Interrelationships among Student Participation, Teachers’ Instructional Practices, and Learning,” International Journal of Educational Research 63 (2014): 79–93, doi:10.1016/j.ijer.2013.02.001.

8. Society for Research in Child Development, “Students Who Believe Intelligence Can Be Developed Perform Better,” ScienceDaily, February 7, 2007, www.sciencedaily.com/releases/2007/02/070207090949.htm.

9. Gloria Ladson-Billings, “V-FF. Gloria Ladson-Billings Cultural Competency,” YouTube video, 3:10, posted by YouthWellness, January 22, 2012, https://www.youtube.com/watch?v=XSE8nxxZN5s.

10. Yekatarina Milvidskaia and Tiana Tebelman, “Rolling Out Group Roles,” Google Docs, accessed January 2, 2021, https://docs.google.com/document/d/1-SA4eIG4oeQ_XPcy51ORVWEkHSb-5FzayLQZBmIuAdU/.

11. Spencer Kagan and Miguel Kagan, Kagan Cooperative Learning (San Clemente, CA: Kagan Publishing, 2009).

12. Elizabeth Cohen and Rachel Lotan, “Producing Equal-Status Interaction in the Heterogeneous Classroom,” American Educational Research Journal 32, no. 1 (1995): 99–120, doi:10.2307/1163215.