While the student surveys gave me a starting point of how students were experiencing mathematical discourse, they could not give me the whole picture. Students were chosen to interview based off of their responses to the survey. I was only able to interview 6 students due to time constrictions. Some students, like Amber and Emory, were chosen because their comfort level with sharing in mathematical discourse remained low from the beginning of the year to now. Others, such as Cristian and Adan, were chosen because their comfort level rose from the beginning of the year to now. Nylah and Damon were chosen because their comfort level started off high and remained that way.
In interviewing my students, several themes became apparent. The first was that students are often afraid of being made fun of or laughed at if they get an answer wrong, even the students who were comfortable with sharing their thinking with the whole class. Another was that students liked mathematical discourse because if they didn't have an answer (or only part of the answer), they knew they could talk to someone who did to help them figure it out. A third theme that came up was that students felt like talking through their math helped them better understand the concepts.
Most of the students I talked with expressed being worried if they got an answer wrong. This was a surprising theme to me, because the math community in my classroom seems fairly strong. Students are encouraged to make mistakes, and I often tell them "Learning happens when things are hard." Students expressed confidence if they were sure their answer was correct. Emory, who had the most responses recorded using EQUIP, said that she was most comfortable "if I’m 100% sure I’m right and I know how to explain the answer . . . [I know] what to say." Cristian said that he felt better when someone else got the wrong answer - "It helps me feel more comfortable because other people get the answer wrong." Amber mentioned people laughing at wrong answers, and when I asked if she had ever been laughed at, she amended her answer to they might laugh "inside their heads." To this, Nylah said that she sometimes saw other students exchange looks if an answer was wrong.
Many of the students appreciated that the mathematical discourse provided them an opportunity to have help figuring out the answer. Damon said, "It's easier to talk to each other. Let’s say he has half the answer and you have half. You work together to get the answer." I asked what if he and his partner had the same half of the answer, and his response was, "Well, you work together, to find the other half of the answer." Nylah spoke about how working with a partner gave her more ideas on how to solve a problem -- "I was listening to what Winston was thinking about, and I was like 'Okay, that could work. But what if we did this? Could this work?'" As Ing et al (2015) saw in their study, my students were also noticing that the ability to engage with others' ideas helped support their learning outcomes better than if they were doing the work independently.
The literature said time after time that mathematical discourse helps students build deeper understanding of concepts -- my students agree. Emory says "When other people say it, I can learn from them. They can help me learn the problem from other points of views." Cristian had a similar idea, "When other people share the problem, it helps me learn different ways on how to get the answer." Adan shared a story of a time when he was confused, and asked his partner to explain their work another way, and after the partner explained again, Adan said, "I was able to understand." As Cobb et al (1997) suggested, my students were constructing understanding through their participation in their mathematical discourse. Students also recognized that talking through their thinking with others helped them realize they had strayed off the path. Damon shared, "Before we went to break, and we were doing a math talk, I didn’t do it on the whiteboard, I did it in my head. When I was talking about it, I was getting confused. Then I redid it and I got the right answer."