Abstract
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.
Résumé
Cet article se penche sur l’influence potentielle de certains aspects de l’algèbre abstraite sur l’enseignement de l’algèbre scolaire (et l’algèbre élémentaire). En utilisant les normes nationales d’analyse, on développe quatre domaines primaires communs dans les mathématiques scolaires, ainsi que leur évolution au travers des classes de mathématiques élémentaires, intermédiaires et secondaires, lorsque l’enseignement peut être modifié par les connaissances de l’enseignant en algèbre abstraite. Dans chacun des quatre domaines (propriétés arithmétiques, inverses, structure des ensembles et résolution d’équations), des descriptions et des exemples de l’influence transformationnelle sur l’enseignement de ces sujets sont utilisés pour décrire et soutenir l’idée que l’étude de mathématiques plus avancées peut influencer la pratique de l’enseignant. Les conséquences pour la préparation mathématique et le perfectionnement professionnel des enseignants sont examinées.
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Wasserman, N.H. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction. Can J Sci Math Techn 16, 28–47 (2016). https://doi.org/10.1080/14926156.2015.1093200
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DOI: https://doi.org/10.1080/14926156.2015.1093200