You’re a teacher standing in front of a classroom of 30 fourth graders. You’ve just asked the class a question about fractions, and after a moment of thought, a student shares out an idea that’s partially correct. What happens next?

If you’re a new teacher, you might not be sure. Expert teachers, however, have the ability to better anticipate how different classroom scenarios will unfold, just as expert soccer players watching video of a match can identify, if the video is paused, where the players on the field are and where they’re headed. The expert players developed sophisticated mental representations that allow them to integrate knowledge from a number of different domains – the rules of the game, ball-handling skills, team strategy, experience – and apply it on the field in real-time.

Similarly, expert teachers integrate knowledge from multiple domains (content, instructional pedagogy, student cognition) and apply it in real time in classrooms. That’s what enables an expert teacher to anticipate what other students might do in response to a classmate’s incorrect guess while simultaneously evaluating the various moves she could make and what the consequences of those moves might be. (In case you hadn’t realized this before: teaching is extraordinarily complex.)

So the question for educator-preparation programs: how do you teach teacher-candidates how to do that? How do you help them develop the sophisticated mental representations that will allow them, over time, to know what happens next?

At a recent Deans for Impact convening, we had the privilege of hearing from Elham Kazemi, a professor of math education at the University of Washington, about her experience with using cycles of enactment and investigation as a way to help novice teachers improve their practice and develop those sophisticated mental representations.

Embedded within these cycles are rehearsals, a particular pedagogy of enactment that “approximates the work of teaching by providing a space for [novice teachers] to open up their instructional decisions to one another and their instructor,” according to a 2016 article by Kazemi and co-authors.

This approach allows novice teachers (or teacher candidates) to rehearse instructional moves and decisions that could emerge in a classroom, while receiving real-time feedback from a teacher-educator. Candidates have opportunities to reflect on what good teaching looks like across different domains while practicing the skill of simultaneously responding to what students have said and anticipating what they are going to do next.

At the convening, Kazemi shared her own evolution as a teacher educator, from a more traditional approach early on in her career to the approach she employs today. Earlier versions of her math methods course focused on building candidates’ knowledge about children’s math thinking, under the assumption that once they had the knowledge, they would figure out how to use it. But candidates’ evaluations were blunt: The course was fascinating, but it didn’t teach them how to teach.

“I had to help them think about how to deploy the knowledge,” said Kazemi during the DFI convening.

Now, Kazemi teaches her methods course at a partner school, working with a K-12 classroom teacher. She starts each session by meeting with candidates to plan and rehearse the plan. Then they move into the classroom, where Kazemi and the classroom teacher teach the whole class, taking pauses throughout to think out loud and make their decision-making transparent. Finally, candidates break into small teams to work with students. During the last activity, candidates and teacher-educators pause to ask each other questions, help with next steps or think out loud about decisions.

“It’s one thing to analyze written cases, and notice what moves teachers are making. And it’s another thing to get up yourself and try to ask those questions and figure out how to elicit and respond to people’s ideas,” said Kazemi of the current version of the methods course differs from earlier iterations.

Kazemi and her candidates work with the same K-12 class throughout the course of the semester, which allows them to get to know the K-12 students as individuals and as thinkers. Building relationships with students is an important part of teaching, according to Kazemi, and the current structure of her methods course allows candidates to learn from and with their K-12 students.

“You have to get to know your students as people, not just as thinkers. And you have to understand what motivates them, why they’re there at school, what their families want for them … Those things matter and you have to spend just as much time studying those things as you do the content, the subject matter, that you teach,” said Kazemi.

Kazemi said that in order for her to help candidates improve, she had to create new learning situations that helped her develop a better understanding of her candidates’ mental representations. Teaching them at the university and then sending them off into K-12 classrooms was not sufficient: she couldn’t see how they were internalizing and applying the new ideas they’d learned, and she couldn’t intervene immediately to help improve their practice. It was as though she were teaching players specific skills in practice, but never going to games.

A model anchored in cycles of enactment and investigation isn’t the only way to bridge the disconnect between what candidates are learning in their coursework and what they’re practicing in the classroom; another model is the iTeachAZ program at ASU. But it helps underscores the importance of giving teacher-candidates opportunities for classroom practice and feedback to help them develop rich mental representations that allow them to anticipate what happens next.

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