# High Leverage Practices

Given all that must be accomplished in teacher education programs, we
as teacher educators are faced with choosing how to spend our limited
time. We know we have to help our teacher education students learn
"how" to teach mathematics. We know that choosing "practice-based"
activities is necessary (Ball & Cohen, 1999; Wilson & Berne,
1999; Darling-Hammond, 1998; Lampert & Ball, 1998), but there is no
professional consensus about what it means for a methods course to be
practice-based.

We have to find ways to support our teacher education students, as
beginners, to develop mathematical teaching practice. This challenge is
complicated by the need to maintain sufficient complexity such that
what is being taught and learned in teacher education is actually
usable in real practice. Our goal is to identify slices of practice
that are high-leverage for beginners.

Mathematics methods students struggle in their first year of
teaching to make sense of the practices inherent to mathematics
teaching, choosing difficult practices to try and often giving up. We
conceive of “high-leverage practices” as those aspects of mathematics
teaching practice that are central to supporting the development of
mathematical understanding, generative in nature, and productive
starting places for novice teachers.

Working across these sites and looking then at the other examples
across sites allows us to begin to see some common core elements in
high-leverage practices.

## Choosing a Pedagogical Focus

Janine Remillard allows students to choose their own pedagogical
focus, "Each prospective teacher selected a pedagogical focus from a
list provided to emphasize in their planning and teaching. The purpose
of asking them to identify and work on a single pedagogical focus is to
encourage them to direct their efforts on some aspect of their
developing pedagogies, rather than trying to do everything at once.
Having a single pedagogical focus also made it more likely that
students would focus their attention on the role the four dimensions of
teaching played in shaping their pedagogy."

## Problem Posing

Megan Franke chooses problem posing as a high-leverage practice for our
elementary methods students because it exists in every mathematics
classroom (almost daily), it is critical to lesson development and to
opening opportunities for participation, it supports attention to
issues of equity, and research evidence exists for support.

## Slices of Practice

The Mathematics Planning Group makes explicit their approach to
focusing on an aspect of mathematical practice in ways that support
teacher education students to learn to teach. "In order to make the
complex work of teaching more learnable by beginners, we temporarily
‘slice’ teaching practice into smaller tasks or routines of teaching
that can be articulated, unpacked, studied, and rehearsed." (link)
We agree on the following:

- frequency of the practice in teaching mathematics
- applicability of the practice across different orientations to teaching mathematics
- extent to which the practice could support work central to mathematics
- extent to which work could open opportunities for the learning and achievement of all students
- the accessibility of the practice (e.g., could it be done by beginners?)
- grain size of the practice in relation to the extent to which
preservice teachers could begin to see how the practice works and
develop skills around the details of the practice
- likelihood that beginners would have the opportunity to engage in the practice in their field-based settings

## Summary

Our focus on high leverage practices has pushed us as teacher educators
to rethink our practice, to consider how to support our students in
learning about practice in a way that becomes generative. We have
always been concerned about practice, but we have now found ways to
adapt our practice to support students to learn about the details of
teaching in a way that helps them see what it means to learn in an
ongoing way to perfect one's practice. As we have adapted our practice
we have collected data about our students’ learning, which has
supported continued adaptation and convinced us of the merit of
focusing our teacher education courses on high leverage practices. We
have learned a great deal about what constitutes a high leverage
practice, and about what it means to engage students with high leverage
practices to maximize learning.