Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics—and their progression across elementary, middle, and secondary mathemat...

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Bibliographic Details
Published inCanadian journal of science, mathematics and technology education Vol. 16; no. 1; pp. 28 - 47
Main Author Wasserman, Nicholas H.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.01.2016
Routledge
Springer Nature B.V
Subjects
Abstract Reasoning
Algebra
Arithmetic
Common Core State Standards
Content Analysis
Demonstrations (Educational)
Education
Educational Practices
Elementary Secondary Education
Engineering/Technology Education
Equations (Mathematics)
Knowledge Base for Teaching
Mathematical Concepts
Mathematics
Mathematics Education
Mathematics Instruction
Qualitative Research
Science Education
Teaching Methods
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Summary:This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics—and their progression across elementary, middle, and secondary mathematics— where teaching may be transformed by teachers’ knowledge of abstract algebra are developed. In each of the four content areas (arithmetic properties, inverses, structure of sets, and solving equations), descriptions and examples of the transformational influence on teaching these topics are used to depict and support ways that study of more advanced mathematics can influence teachers’ practice. Implications for the mathematical preparation and professional development of teachers are considered.
ISSN:1492-6156
1942-4051
DOI:10.1080/14926156.2015.1093200