Facilitating meaningful mathematical discourse is one of eight teaching practices that NCTM says supports equitable education in the classroom (2014). It takes more than just a teacher to make discourse meaningful - the students are a large part of what makes it meaningful, and so their experiences with discourse are important. Because teachers and students often have different ideas on how things are going in the classroom, I wanted to approach my students and see how they felt about the mathematical discourse we engaged in on a regular basis. I asked students about their feelings around math in general, as well as mathematical discourse through a survey, then used that survey data to choose which students to interview in order to build a more in depth understanding of their experience. The EQUIP tool was used to see how student perceptions lined up with who was actually sharing in discussions.
While I had been using mathematical discourse and conversations around math as a basis for my math instruction all year, I was curious how my students felt about it. Did they see the benefits? Did math feel different this year than it did for them the year before? I also knew I wanted to interview a number of students, and thought the survey would give me a good place to start in choosing who I would interview. I created the survey using Google Forms that students would take on their iPads. Several of my students are emergent readers, so I read the questions aloud to the class and was available to answer clarifying questions. The survey consisted of 11 questions, using either Likert scale or short answer options for answers. The survey was given in early February, so just over halfway through the school year.
Did you like math in 4th grade? (Yes/No)
Why/why not? (Short answer)
Do you like math in 5th grade? (Yes/No)
Why/why not? (Short answer)
How comfortable are you sharing your thinking in math discussions in a small group? (1-5 scale)
How comfortable were you sharing your thinking in math discussions with the whole group at the beginning of the year? (1-5 scale)
How comfortable are you sharing your math thinking with the whole group now? (1-5 scale)
If your score changed, why did it change? If it did not change, just write NA. (Short answer)
Do you feel like your peers respect you as a mathematician? (Yes/No)
How supported by the teacher do you feel when sharing your ideas? (1-5 scale)
How supported by the teacher do you feel when engaging with others’ ideas? (Agreeing/disagreeing with ideas, rewording others’ ideas, asking questions about others’ ideas) (1-5 scale)
The survey was my starting point, but I knew I would need to dig deeper to understand more about how students experience mathematical discourse. Analyzing the data from the survey gave me a list of students who I thought would have useful insights based on their growth/lack of growth in comfort or the reasons they liked or did not like math in 5th grade compared to 4th grade. It was already part of my classroom culture for me to have a few students eat lunch with me once or twice a week, so it probably wasn't intimidating when I asked the students if they would have lunch with me and talk about math. The interviews helped me identify themes of what students found helpful in mathematical discourse and what was still challenging for them. I had four main questions that I used in my interviews, then used clarifying and probing questions to encourage students to elaborate on their answers.
What is hard about talking about math?
What is easy?
Does knowing the people in the class help you feel comfortable during math discussions?
Do you feel like talking about math or listening to others talk about math help you learn?
The survey allowed students to self-report their feelings, and the interviews allowed me to dig deeper into student experiences. I used an online tool called EQUIP to measure how students self-reported comfort in mathematical discussions line up with who was actually participating in mathematical conversations and to what level. EQUIP stands for Equity QUantified in Participation and is the creation of Dr. Daniel Reinholz and Dr. Niral Shah. I recorded 10 mathematical discourse sessions of about 10 minutes each in my classroom, and used 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).