Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

ISBN-13: 9783319992136 / Angielski / Twarda / 2018 / 461 str.

Nicholas H. Wasserman

Opis

Secondary mathematics teachers are frequently required to take a large number of mathematics courses - including advanced mathematics courses such as abstract algebra - as part of their initial teacher preparation program and/or their continuing professional development.

Spis treści

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.-  

O autorze

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.

Blurb

Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. 

This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. 

Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.