Mathematical Understanding for Secondary Teaching

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