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This chapter presents several frameworks for thinking about the history of mathematics and mathematics education. One is the intentions of the creators of the mathematics in question and our intentions for teaching it. Another is three "windows" for viewing mathematical concepts: geometric representations, algebraic representations, and numerical and tabular representations. After a brief summary of the social history of the 17th century, especially the factors that influenced the development of mathematics, Marshall McLuhan's tetrad is introduced for analyzing the effects of a new technology. Finally, David Dennis's "Context, Content, Critique" framework for using history in mathematics education is introduced. This framework gives the structure of each of the chapters of the book.

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How Did We Get Here (and Where Should We Go)?

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  • 发表日期：

    2026年

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  • David J. Carrejo,
  • David Dennis,
  • Susan Addington

摘要

This chapter presents several frameworks for thinking about the history of mathematics and mathematics education. One is the intentions of the creators of the mathematics in question and our intentions for teaching it. Another is three "windows" for viewing mathematical concepts: geometric representations, algebraic representations, and numerical and tabular representations. After a brief summary of the social history of the 17th century, especially the factors that influenced the development of mathematics, Marshall McLuhan's tetrad is introduced for analyzing the effects of a new technology. Finally, David Dennis's "Context, Content, Critique" framework for using history in mathematics education is introduced. This framework gives the structure of each of the chapters of the book.