SECONDARY MATHEMATICS

By ABIGAIL MILLER

CONTENTS EXPLORING ADVANCED MATHEMATICS COURSES AND CONTENT FOR SECONDARY MATHEMATICS TEACHERS PART I EXPLORING STUDENTS’ LEARNING OF ABSTRACT ALGEBRA CONCEPTS CLOSELY CONNECTED TO SECONDARY MATHEMATICS CONNECTING THE GROUP THEORY CONCEPT ASSESSMENT TO CORE CONCEPTS AT THE SECONDARY LEVEL MONSTER-BARRING AS A CATALYST FOR BRIDGING SECONDARY ALGEBRA TO ABSTRACT ALGEBRA WHAT KIND OF OPPORTUNITIES DO ABSTRACT ALGEBRA COURSES PROVIDE FOR STRENGTHENING FUTURE TEACHERS’ MATHEMATICAL KNOWLEDGE FOR TEACHING? PART II EXPLORING MATHEMATICAL CONNECTIONS BETWEEN ABSTRACT ALGEBRA AND SECONDARY MATHEMATICS EXCAVATING SCHOOL MATHEMATICS FORESHADOWING IDEAS IN ABSTRACT ALGEBRA: RE?ECTIONS FROM THE SECONDARY SCHOOL MATHEMATICS CURRICULUM IMPROVEMENT STUDY UNDERSTANDING SCHOOL MATHEMATICS IN TERMS OF LINEAR MEASURE AND DISCRETE REAL ADDITIVE GROUPS ABSTRACT ALGEBRA AND SECONDARY SCHOOL MATHEMATICS CONNECTIONS AS DISCUSSED BY MATHEMATICIANS AND MATHEMATICS EDUCATORS MAKING MATHEMATICAL CONNECTIONS BETWEEN ABSTRACT ALGEBRA AND SECONDARY MATHEMATICS EXPLICIT: IMPLICATIONS FOR CURRICULUM, RESEARCH, AND FACULTY PROFESSIONAL DEVELOPMENT PART III EXPLORING APPROACHES TO SECONDARY TEACHER EDUCATION: ENGAGING IN ABSTRACT ALGEBRA IN RELATION TO DEVELOPING DISCIPLINARY PRACTICES MAKING CONNECTIONS FROM THE SECONDARY CLASSROOM TO THE ABSTRACT ALGEBRA COURSE: A MATHEMATICAL ACTIVITY APPROACH LEARNING MATHEMATICAL PRACTICES TO CONNECT ABSTRACT ALGEBRA TO HIGH SCHOOL ALGEBRA FROM EQUATIONS TO STRUCTURES: MODES OF RELEVANCE OF ABSTRACT ALGEBRA TO SCHOOL MATHEMATICS AS VIEWED BY TEACHER EDUCATORS AND TEACHERS USING GEOMETRIC HABITS OF MIND TO CONNECT GEOMETRY FROM A TRANSFORMATION PERSPECTIVE TO GRAPH TRANSFORMATIONS AND ABSTRACT ALGEBRA DEVELOPING A STRUCTURAL PERSPECTIVE AND ITS ROLE IN CONNECTING SCHOOL ALGEBRA AND ABSTRACT ALGEBRA: A FACTORIZATION EXAMPLE BUILDING A COHERENT RESEARCH PROGRAM THAT LINKS ABSTRACT ALGEBRA TO SECONDARY MATHEMATICS PEDAGOGY VIA DISCIPLINARY PRACTICES PART IV EXPLORING APPROACHES TO SECONDARY TEACHER EDUCATION: ENGAGING IN ABSTRACT ALGEBRA IN RELATION TO PEDAGOGICAL PROBLEMS IN TEACHING SECONDARY MATHEMATICS EXPLORING AN INSTRUCTIONAL MODEL FOR DESIGNING MODULES FOR SECONDARY MATHEMATICS TEACHERS IN AN ABSTRACT ALGEBRA COURSE GROUPS TO THE RESCUE: RESPONDING TO SITUATIONS OF CONTINGENCY SOME APPLICATIONS OF ABSTRACT ALGEBRA TO HIGH SCHOOL TEACHING: TASK DESIGN AND POLYNOMIAL INTERPOLATION IMPACT OF ABSTRACT ALGEBRA ON TEACHERS’ UNDERSTANDING OF AND APPROACHES TO INSTRUCTION IN SOLVING EQUATIONS BLUE SKIES ABOVE THE HORIZON