Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

• Autores: Nicholas H. Wasserman
• Localización: Primus: problems, resources, and issues in mathematics undergraduate studies, ISSN 1051-1970, Vol. 24, Nº. 3, 2014, págs. 191-214
• Idioma: inglés
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• Resumen

  • Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic thinking is discussed by way of an example of an abstract group. Results of this approach in a mathematics for teachers course are presented, with K-12 teachers (n=12) having increased their content knowledge both about arithmetic properties and abstract algebra, as well as having their teaching beliefs and intended practices influenced. Implications for classroom teaching about a vertical slice of the K-12 curriculum related to algebraic structure are examined.