Imagine yourself sitting in your high school math class. As your teacher is speaking, another student raises his hand to ask a question, and he and your teacher start having their own back-and-forth dialogue about an equation that has been written on the board. Lost in the commotion of what is now going on between the other student and the teacher, you start drifting off. As you drift off, you miss important information that may have answered some of your own questions.
You can probably recall an instant or two when this happened in one of your math classes. This sort of scenario occurs more frequently than teachers are aware. In 2012, Drs. Blake Peterson and Keith Leatham from the BYU mathematics education department observed several classrooms and noticed a trend of situations like this one. These observations had the professors wondering, “How can we help teachers recognize important spontaneous teaching moments in the classroom?”
Over the next five years, they continued to observe classrooms to identify teachable moments. Those observations evolved into the “MOST” project which aims to help teachers recognize these pivotal teaching opportunities. The acronym stands for “Mathematical Opportunities in Student Thinking.” With the help of efforts from teachers all over the nation, Peterson and Leatham hope to enable students to engage in thinking about what other students are asking. “A teacher is not just someone who stands in front of the class and tells. They are someone who facilitate learning,” Peterson said.
In the summer of 2018, Peterson and Leatham initiated the second phase of the project by recruiting 13 teachers from across the country. They wanted to test a new style of teaching that they formulated to accomplish their goal of facilitating more interactive learning. The teachers spent two days together discussing the project and receiving instructions on how to incorporate them into their classroom. They were also instructed to record themselves using the techniques and meet together each week to discuss how those lessons went.
After recruiting the teachers and gathering their results from implementing these practices, Peterson and Leatham analyzed what teaching techniques worked well and called their findings “Building on MOSTs.” In order to instruct schools in the future about the importance of involving students more in the teaching process, they broke these instructions down into four different steps: make precise, grapple toss, orchestrate, and make explicit.
The step of “make it precise” is a mandate to teachers to give direct, obvious, and clear instructions so that students can more easily understand concepts. It is also important that the questions teachers ask are such that students can learn from one another. Instead of asking several variations on the same question, Peterson and Leatham advise that teachers ask one clear and concise question and see how the students respond to each other’s comments.
To grapple with something means you’re working hard to solve a problem. The step of “grapple toss” involves two parts: first, encourage teachers to metaphorically throw questions at students in an effort to second, solve inattention by refocusing everyone’s attention. One example of this type of teaching is when a student asks a question, the teacher can invite the rest of the class to help answer the student’s question. This type of engagement helps enforce student learning and solidify their knowledge by explaining important concepts to their peers.
Once a teacher has involved the whole class in answering a given question, Peterson and Leatham’s observations show that the best way to keep hold of students’ attention is by acting like an orchestra conductor–probing each student for their input and eventually tying the discussion back to the melody, or the main idea of the discussion. This assists the entire class to remain attentive and involved in a discussion.
Finally, “make explicit” means pulling the whole discussion together and clarifying the takeaways. This type of articulation enables students to understand the connection between all the different ideas and clarifies the main points so students walk away not only understanding the concepts, but knowing more about how their peers are thinking.
Undergraduate Camilla Llana has been working on the MOST research project since May 2019. One of her responsibilities is to watch the classroom videos from the 13 other teachers and examine the effects of this type of teaching. “I’ve definitely seen…the importance of [these practices in] the flow of the teaching,” Llana said.
Peterson confirmed Llana’s sentiment when he said, “Being involved in this project gives students a lot of time to look at teaching math from a different perspective. I think it makes them better teachers as a result.” Peterson had an opportunity to observe a few of the students who were previously involved with the project in their student teaching environments. Compared to other teachers who hadn’t been involved, he said they “were so much better at listening to figuring out what students were saying in the moment” and were therefore more prepared to help the students teach each other.
Though these steps seem simple enough, this method of teaching involves a great deal of teacher concentration according to Peterson. While he and Leatham observed many teachers practicing aspects of these steps, they hope to encourage math teachers all over the country to be more conscious of when these teaching opportunities arise.
The efforts of these students, teachers, and professors Peterson and Leatham will pave the way for students in future math classes to not only become more actively involved in the discussion, but learn more from the other students than they ever have before. That’s the most any teacher could hope for.