Mathematical Understanding for Secondary Teaching

A perennial discussion about teacher development is the optimal content background for teachers. In
recent years, that discussion has taken center stage in the work of mathematics education researchers,
mathematicians, mathematics professional developers, and mathematics education policymakers. Much
of the existing and prior work in this area has been directed toward mathematical knowledge for
teaching at the elementary level. The work described in this volume takes a sometimes-neglected
approach, focusing on the dynamic nature of mathematical understanding rather than on a stable
description of mathematical knowledge, and on mathematics for secondary teaching rather than
mathematics for teaching at the elementary level.
The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based
response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50
events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that
teachers could use-each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We
developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We
call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics
practice.
Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional
developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening
their understanding of secondary mathematics. Mathematics teacher educators and mathematicians
who teach mathematics to prospective and in-service secondary teachers will be able to couch their
mathematical discussions in the Situations-examples that arise from secondary mathematics
classrooms. They will be able to use this volume as they design courses and programs that enhance
mathematics from the perspectives identified in the MUST framework. Policymakers and researchers
can use our MUST framework as they consider the mathematics background needed by teachers.