Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers (eBook)

Nicholas H. Wasserman is an Assistant Professor of Mathematics Education at Teachers College, Columbia University. Previously, he taught mathematics for six years at the secondary level, in both a large public school in Austin and a private school in Manhattan. His scholarly interests focus on mathematics teachers' knowledge and development, particularly on how advanced content knowledge is relevant for teachers and influences secondary classroom teaching and practice. Dr. Wasserman's research has led him to examine how knowledge of Abstract Algebra becomes influential for the teaching of numerical and algebraic concepts in school mathematics. He is also collaborating with faculty from Rutgers University and Temple University to develop an instructional model for designing tasks in a real analysis course with secondary teachers in mind. His related interests include: combinatorics education, both at the secondary and undergraduate levels; as well as how the use of dynamic technologies can influence mathematics teaching and learning.

Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers.- Connecting Group Concept Inventory Results to Essential Topics at the Secondary Level.- Applying familiar algebraic properties in unfamiliar settings: Supporting connections between school algebra and rings and fields in abstract algebra.- Commentary chapter.- Making visible, and using, the Abstract Algebra already latent in the secondary curriculum.- Foreshadowing ideas in abstract algebra: Reflections from the Secondary School Mathematics Curriculum Improvement Study.- Abstract Algebra and Secondary School Mathematics Connections Identifying and Discussed in Textbooks and by Mathematics Educators.- Commentary chapter.- From equations to structures: Linking abstract algebra and high-school algebra for secondary school teachers.- Learning mathematical practices to connect abstract algebra to high school algebra.- Forms of knowing advanced mathematics for teaching: Considering abstract algebra.- Using algebraic structures for developing secondary students' understandings.- Restructuring Understanding of School Algebra by Building a Transition to Abstract Algebra Structures: A Principle-Based Approach.- Commentary chapter.- Making connections from the secondary classroom to the abstract algebra course – a mathematical activity approach.- Designing tasks in abstract algebra that begin and end in secondary teaching practice.- Group properties to the rescue.- Impact of abstract algebra on teachers’ understanding of and approaches to instruction in solving equations.- Commentary chapter.-