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Knowing Ratio and Proportion for Teaching

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Part of the book series: Advances in STEM Education ((ASTEME))

Abstract

Ratio and proportion have been part of school mathematics since the earliest manifestations of anything like school math in the Middle Ages. In this paper, I compile and comment on statements from primary sources of the last 2300 years to exhibit ideas that appear to have influenced the treatment of these topics in schoolbooks today. Historical sources clarify many points about the contemporary curriculum, supporting the contention that an understanding of history of ideas concerning ratio and proportion is an important component of knowledge of mathematics for teaching.

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Notes

  1. 1.

    The Library of Congress holds authenticated reproductions of the original letter, which may be viewed on the internet.

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Acknowledgements

This paper was prepared for Mathematics Matters in Education: A workshop in honor of Dr. Roger Howe, at Texas A & M University, March 26–28, 2015. I’d like to thank Dick Stanley for getting me interested in ratio and proportion many years ago during the Noyce-Dana Project (2008–2009), for continuing to challenge me about these topics, and for discussing the contents of this paper with me. NSF Grant 0928847 (Louisiana Math and Science Teacher Institute, LaMSTI) supported work on which the present paper is based. Unpublished manuscripts prepared by the author for the Noyce-Dana Project, the Klein Project, and in LaMSTI were used as sources for parts of this paper. I would like to thank the three anonymous referees for their suggestions, which have led to significant revisions and improvements.

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  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA

    James J. Madden

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  1. James J. Madden
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Correspondence to James J. Madden .

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Editors and Affiliations

  1. Department of Teaching, Learning and Culture, Texas A&M University, College Station, Texas, USA

    Yeping Li

  2. Department of Mathematics, University of Nebraska – Lincoln, Lincoln, Nebraska, USA

    W. James Lewis

  3. Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana, USA

    James J. Madden

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Madden, J.J. (2018). Knowing Ratio and Proportion for Teaching. In: Li, Y., Lewis, W., Madden, J. (eds) Mathematics Matters in Education. Advances in STEM Education. Springer, Cham. https://doi.org/10.1007/978-3-319-61434-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-61434-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61433-5

  • Online ISBN: 978-3-319-61434-2

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