Mathematical discourse is so important to building student confidence and understanding - even the students recognize this! When the teacher is acting as the facilitator for discussion, their job is to recognize and empower each student's voice (Buchheister, 2019). That means that sometimes the ones doing the most talking in a whole group discussion are students who are not the most comfortable with math or with sharing their thinking. As we encourage these students to share more, we are helping them build their (and others') understanding of the math, pulling them into the math community we are constructing, and, hopefully, showing that wrong answers are okay and even sometimes help point us in the right direction. Mathematical discourse isn't just the whole group discussion, though. It is also the conversation that pairs or small groups of students are having about their strategies and understanding. Including variety of discussion formats, not just whole group discussions, provides more opportunities for students to be able to share their thinking with one another, which builds their identities as mathematicians (Buchheister, 2019). A student who is not willing to explain to the whole class may be willing to share with a partner. Student participation in partner discussion can also build student confidence in their understanding, making them more likely to want to share during whole group discussions.
I’ve seen that most of my students seem to feel more comfortable now with mathematical discourse than they did at the beginning of the year. I know a large part of what helps students feel comfortable is feeling like they belong to a community of mathematicians, so I continue to work hard to validate the work my students do in being mathematicians and their contributions to our community. Students expressed appreciation of our use of discourse in the classroom to help them build understanding of math concepts, regardless of whether they had self-reported high or low comfort. This shows how important mathematical discourse is for students, and it is something I will continue to prioritize in my math classroom.
The curriculum our district uses prioritizes procedural learning over high quality math tasks and mathematical discourse. Each unit has 1-2 "open response" lessons that encourage the students to solve a task, then for the class to discuss solution paths the students came up with. One-two lessons a month that involve discourse is not enough for students to benefit from the opportunity to build and develop understanding that mathematical discourse provides. Mathematical discourse has been shown through the research to increase student achievement, increase student engagement, and increase equity in the classroom, and my students have shared that discourse has been important for their learning/understanding. Discourse should be happening everyday in math class.
I told my students what my study was about, so they knew why I was videoing our lessons/recording conversations. This, and the fact that I was working with my own students, may have skewed student responses more positively toward mathematical discourse, than if I had asked students from other classes, with whom I do not have a relationship. Also, during the mathematical discourse - I know my students' strengths and weaknesses, which, in turn, influenced who I would call on to share during the discussion. The student interviews were done with pairs of students, in order to have time to talk to more students - so peer pressure of what their friend was saying may have influenced what students shared during that interview time.
Another limitation is the study size. I looked at one class for a period of a few weeks for my EQUIP analysis. I was not able to survey students at the beginning of the year, so when I asked students about their comfort levels for the beginning of the year, I had to rely on student perception/memories.
I am so glad I was able to do this research and have my students participate in it. Through the survey and interviews, I was able to get to know my students better as mathematicians and learn how they saw themselves as mathematicians. I learned that my students had generally positive experiences with mathematical discourse - they find it helpful, and they like being able to turn to peers for support. Student negatives around mathematical discourse are mostly around peer pressure and the fear of looking silly in front of their friends/classmates. Using the EQUIP data, I was able to see where student self-reported comfort lined up with their actual level of sharing during discussion. Some students are obviously much more comfortable sharing than they reported, while others who reported themselves as "very comfortable" rarely speak up in whole group discussions. Looking at these particular students, some are probably wishing they were comfortable with sharing their thinking while the others are confident in their math work/processes, but are uninterested in sharing during group discussions.
All of the students who I interviewed mentioned being afraid of having the wrong answer in front of everyone. When asked if they would share if they knew how to start the problem, but were unsure how to continue working on it, most said they would not. While I have tried to build a culture where mistakes are okay and encouraged in my classroom, fear of others learning about those mistakes are holding my students back. This takes me back to Wood et al. (2019), who said "students often choose to participate, and are allowed to participate, in mathematics to the degree that they are seen (and see themselves) as smart" (pg. 219). One of the authors' suggestions is to "Make '. . . yet!' a norm," saying that using yet "reinforces a classroom expectation that all students (regardless of status) will become more capable over time" (Wood et al., 2019, pg. 220). Encouraging and embracing mistakes, wrong answers, and incomplete solutions is going to become a new norm for me in math class. Students need opportunities to be wrong and see that the only thing that came from it is learning and growth. Hopefully this new norm will help those students who are less comfortable sharing their thinking be more willing to participate in discussions.