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Did student comfort level with mathematical discourse match what was actually happening in the classroom?
Did student comfort level with mathematical discourse match what was actually happening in the classroom?
It often feels like the same 5 or 6 students are participating in our classroom mathematical discourse. How were they adding to the conversation? How was I inviting students to participate in the conversation? Are students who self-reported high levels of comfort contributing more than students who self-reported low levels of comfort? To answer these questions, I turned to an online tool called EQUIP (Equity QUantified in Participation). Through 10 mathematical discourse sessions of about 10 minutes each in my classroom, I was able to use EQUIP to collect data on: who was sharing, what level of thinking were they sharing (answer, procedural, explanation, justification, engagement with other students), and what level of question I was asking as the teacher (answer, procedure, explain, justify, engage with others).
Who shared? Did it match with the Student Survey data?
Who shared? Did it match with the Student Survey data?
Student Comfort Level Compared to Participation Percentage
All names are pseudonyms. The ** next to a name indicates that these students were interviewed. Amos, Zayne, Winston, and Spencer did not participate in the survey.
The data show that a student's comfort in sharing their thinking does not always match up with their willingness to share their thinking. Students who said they were "very comfortable," or comfort level 5, with sharing their math thinking, had an average of 4 responses each. The mean of their responses is only one higher than the mean of responses from the "not very comfortable" group (level 2). Students in the "somewhat comfortable" group (level 3) had an average of 6.25 answers each, while the "comfortable" group (level 4) had a mean of 7.6 answers per student. Casey and Reign both self reported a high level of comfort, but neither participate much during discussions. I believe they both selected "very comfortable" because they want to be comfortable sharing their thinking. Some students may have conflated comfort with sharing their thinking with their confidence in their math abilities. This would account for students like Miles, who has strong math abilities, but low participation, and Emory, who is not confident in her math abilities, but is almost always willing to share her thinking.
I would have expected students who reported being most comfortable sharing their math thinking to have the highest percentage of participation. But it was students at a comfort level 4 who had the most responses (36%), while students who expressed they were "very comfortable" and those who were "somewhat comfortable" (levels 5 and 3, respectively) both gave 25% of the responses. Students who expressed that they were "not very comfortable" (level 2) gave 6% of the responses, while students who did not take the survey gave 12% of the responses.
Participation Percentage of Comfort Level Groups
What types of prompts did the teacher give for discourse? How did that impact how students contributed to the conversation?
What types of prompts did the teacher give for discourse? How did that impact how students contributed to the conversation?
The mathematical discourse in our class mainly moved forward through questioning student strategies and having them explain their thinking (over half of teacher solicitations and student responses). About 18% of my solicitations were for answers - I like to use this as a way to try to get more students to respond, then ask for an explanation of why that answer works. Another 18% of my solicitations were an invitation to respond to other students - agree/disagree or ask clarifying questions. While this seems low, especially as Ing et al. (2015) says that engaging with others' ideas at high levels increases learning outcomes, these were responses to share with the whole group. Typically students are invited to talk to a partner before I ask someone to share with the whole group, so students are engaging with each others' ideas more regularly than is shown through this data.
Student Response Types
All names are pseudonyms. The ** next to a name indicates that these students were interviewed. Amos, Zayne, Winston, and Spencer did not participate in the survey.
Of the 7 students who had 3 or fewer responses, 5 of them responded to an answer-solicitation question. Adan and Casey both reported higher comfort levels (4 and 5 respectively), but I have seen them struggle to participate in math discussions. Asking straightforward questions and looking only for an answer, helps to strengthen their status as mathematicians in the class. As that grows, hopefully so will their authentic participation in mathematical discussions, as seen by Wood et al. (2019).
These data from the EQUIP tool show only part of the story. They do not show the partner conversations that students engaged in before being asked to share with the whole group. They do not show the number of students who raised their hands to answer, but I could only call on one. They do not show why I chose to call on a certain student over another. How much of who I call on is based on wanting to assign mathematical competence to that student to highlight that all students have ideas they can contribute (Wood et al., 2019)? Emory and Cristian have struggled with math, so of course I would call on them when their hand is raised, because I want to build their confidence. Damien moved into the class partway through the year, so calling on him helps build his status and solidify his place in the classroom community. When I noticed Gwen, who has low confidence and struggles with math, had a viable strategy on her board, of course I would call on her to share what she did over someone like Henry, who has high confidence and is able to easily solve math problems.
The EQUIP tool, especially as I used it in this context, measures teacher behavior. I have obviously created space for Emory to be confident to share, despite her lower comfort. But what about students like Danica, Camron, or Casey? They struggle with math and with confidence - the data show that I need to focus more on making space available to them to participate in the whole group discussions. If mathematical discourse opens up math to all students and provides opportunities for all students to be (and be seen as) successful, it only does so the the extent that the teacher provides opportunities for it to do so.
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