Over the last year, I’ve participated in two cross-level instructional rounds programs through my involvement with the Inquiry into Disciplinary Literacy and Learning (IDLL) network in my county. At one of our meetings, secondary school teachers attend classes at Eastern Michigan University where professors who have been through the Writing Across the Curriculum (WAC) program are working with their students to build their disciplinary literacy tools. This year, I attended a mathematics methods course for elementary and middle school teachers focused on statistics. While math classes tend to be static in my context—answering homework questions from the night before, lecture, and independent practice time—this class was intentionally different, and it helped me and, more importantly, the future teachers in the room, reimagine what math instruction might look like.
Inquiry-Based Approach
“What statistic or calculation could you use here to determine effect size? How would you figure out what to do?”
Seeing the questions that students were working through in class was eye-opening: students weren’t working through huge sets of problems with complex calculations, they were being asked to design problems that would help their future students build knowledge through a process. If you want students to understand how distributions work, have them create multiple data sets and make box plots. Have students talk about how changes in data leads to changes in distribution. If you want to understand how effect size functions, look at studies on prescription drug trials to understand why understanding the concept and how it works is important, as is the connection to something beyond the math classroom. Throughout this process, students were being asked to think about points in the process where their future students might struggle and why; they were being thoughtful about the need to differentiate and to be comfortable with everyone not being at the same place at the same time. Having students design the problems and think through their processes is critical to develop more inquiry-based math instruction. At some level, the answer, while important, is also incidental, especially if we believe the old saying that “math is about learning how to think.” Answers are eventually important, but they won’t matter much unless a student can articulate to another person (or themselves) how they got there.
In the secondary classroom, I could see math classes switching to a short mini-lesson and then having several stations with inquiry problems where students work through different processes that help them continue building their ability to solve complex problems. Students could present out, or they could record themselves using Flipgrid and share their videos with their classmates. Teachers could even have “Big Debates,” which some of our Social Studies teachers use, on the different processes to use, further reducing the emphasis on correctness and turning the spotlight on meaningful reflection and discussion.
Most math classes I took were highly individualistic, and many of those I observe are currently the same. Doing this kind of work requires moving away from traditional grading and assessment structures, but it could be well worth it in terms of building students’ mathematical thinking skills. There’s some group talk—and even group assessment—but it tends to be transactional. Students need to learn how to have ranging, independent discussions in math that are both reflective and process-oriented.
Talk Moves
“I don’t care about the answer. Talk to me about your process for getting there.”
The class started with students talking with each other in small groups about the homework from the last class. Groups quickly assembled and with a command of both math’s academic vocabulary and reflective language, each student was able to carefully and cogently discuss their strategies for solving the inquiry-based problems that they were assigned, and, in my cases, each had a different answer or way of seeing that allowed them to do the work. The ability to use academic vocabulary in an accessible way to explain a process to someone else is incredibly important in teaching math, and this was great practice for new teachers. The reflective talk moves were impressive, too, as students were unpacking not only what they did and how they did it, but why it might matter in a classroom, as they worked to identify areas where students would struggle based on the Common Core-based learning progressions they were studying in class. This became even more apparent in the “Mini Activities” students did throughout the class with breaks for questions and process demonstrations for both the professor and the students using the whiteboard and the document camera.
In talking with the professor, she tries to incorporate these language practices into her instruction so that her students are equipped to do this important work, but, perhaps more importantly, she builds a mathematics space where students can share vulnerability. In a subject area that relies so much on being right, she’s made it acceptable to be wrong and to revise throughout the process of solving a problem. The ability to use reflective talk moves rooted in academic language was representative of a powerful pedagogy that helped students sound themselves out through a process, articulating each step and why they did it. The ability to unpack and discuss a process in a careful, considered way is a hugely important component of teaching mathematics, and being able to share vulnerability throughout can make interaction and instruction more inclusive.
Classes tend to move fast, but it seems worth it for teachers spending time throughout a course on building the academic vocabulary and reflective skills of students, even if it might mean less content.
Conclusion
Some of the professor’s intentional choices in their class are good pedagogy in any content area, like having multiple activities in a 75-minute period that release responsibility to students, but their ability to construct a safe environment where future math teachers can experiment with different processes, practices, and pedagogies was exciting to watch. It’s important for future math teachers to know their content, but I’m hoping they were also taking notes on the teaching that day, too.
Jeffrey Austin 