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Making the MOST Out of Mathematical Thinking

Photo by Alyssa Lyman

Teachers need to take advantage of key moments in a classroom, and Professors Keith Leatham and Blake Peterson have been working to pinpoint these significant teachable moments in the classroom.

“My colleague Blake Peterson and I, for years, have had conversations about what would happen when we went in to see student teachers teaching,” Leatham said. “And these things would happen in the classroom where a student would say something, and we’d be like ‘That’s exactly what you wanted somebody to say. Now what are you going to do with that?’”

Photo by Alyssa Lyman

Leatham and Peterson have named these teachable moments MOSTs, which stands for Mathematically significant pedagogical Opportunities to build on Student Thinking.

These teachable moments are easily identified by professors like Leatham and Peterson, who have been in the field for years.

“Could we define a teachable moment in a way that we could teach student teachers how to recognize them and then how to build on them, how to use them well?” Peterson said.

Student teachers, being new in the field, did not always recognize teachable moments during lessons.

“It would just go right over their head,” Leatham said. “They just wouldn’t notice the significance of the particular things the students said.”

Leatham and Peterson have focused their research on middle and high school teachers. According to Leatham, they have looked at lessons from sixth-grade math classes to AP Calculus.

“We coded 11 classroom videos, and we identified all the teachable moments,” Peterson said. “We identified them and used that to help us refine what this thing is—this teachable moment—and we looked at the attributes of these things.”

They found that although many MOSTs were of a type one might expect—that is students saying something that was incorrect or incomplete—somewhat surprisingly, a substantial number of MOSTs also came from students giving a correct solution, but doing so in a way that brought together ideas in a unique way. They also found that about a third of the MOSTs were related to mathematics beyond the immediate goals of the current lesson. Peterson said he and his team didn’t find a shortcut for identifying MOSTs, but rather confirmed the complexity of identifying such moments.

“We feel like we’ve got a good handle on characterizing these moments and instances we call MOSTs,” Leatham said. “Now what we’re really trying to work on is the teaching practice of building on them, what it looks like to build on a moment, or to take advantage of a moment.”

“In some ways, we feel like this work is providing a vehicle for even really good teachers to get better,” Leatham said.

Although their research has been focused in mathematics, the ideas could be applied to teaching any topic, according to Leatham.

“I think about it in teaching a religion class,” Leatham said. “You’ve got this topic and when somebody shares some idea in class, you can think about what they’ve said with respect to the potential that what they’ve said has for other people to kind of understand some particular idea.”

Peterson, Leatham and their colleagues are currently drafting a follow-up grant proposal. “If that works out, then we’ll have another four years to study how to build on MOSTs and how to help teachers learn how to do so,” said Leatham.