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Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?

Author(s): 
Po-Hung Liu (National Chin-Yi University of Technology)

Over the years, the journals of the National Council of Teachers of Mathematics (NCTM) have published numerous articles on the history of mathematics and its use in teaching. These journals have included Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher, each of which was published through May 2019. In January 2020, these three journals were replaced by NCTM's new practitioner journal, Mathematics Teacher: Learning & Teaching PK–12 (MTLT). Thanks to the efforts of Convergence founding co-editor Frank Swetz, NCTM has allowed Convergence to republish (in pdf format) up to two articles from Mathematics Teacher annually since 2015.

One of the editors’ picks for 2022 is an article by Po-Hung Liu, in which he discussed five reasons for using the history of mathematics in its teaching:

Po-Hung Liu, “Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?,” Mathematics Teacher, Vol. 96, No. 6 (September 2003), pp. 416–421. Reprinted with permission from Mathematics Teacher, © 2003 by the National Council of Teachers of Mathematics. All rights reserved.

(Click on the title to download a pdf file of the article, “Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?”.)

The author recently reflected on his motivation for writing this article:

Honestly, during my college days, I was never satisfied with the ways professors taught and how I learned mathematics. Whether in advanced calculus, linear algebra, topology, or other courses, every subject was taught the same way, one proof after another. What makes mathematics so boring? It was not until I came into contact with the history of mathematics that I understood how mathematics has evolved into what it is today. As I indicated in this article, answering why the history of mathematics should have a place in school mathematics is difficult, because it is subject to your personal definition of teaching and your view of mathematics. Therefore, I provided five main reasons for integrating the history of mathematics into teaching, including cognitive, affective, and humanistic aspects. Among these aspects, in my view, the humanistic aspect is the most critical. The main utility of the history of mathematics lies in the humanization of mathematical knowledge, which in turn can not only cultivate an attitude of appreciating mathematics, but also trigger students' mathematical thinking. Over the years, I have been practicing the ideas I mentioned in this article to help my students to gain mathematical insights. I am convinced that teaching without the history of mathematics would not be a problem, but with the history of mathematics it would make a difference.

Some additional articles detailing how Prof. Liu has incorporated the history of mathematics into his own teaching include:

T.-S. Chen and P.-H. Liu, “Analysis of the Metaphorical role of Mathematics in Students’ Writing,” in Teaching Interdisciplinary Mathematics, edited by T. Sibbald, pp. 9–28, Champaign, IL: Common Ground Research Networks, 2018.

P.-H. Liu, “When Liu Hui Meets Archimedes: Students’ Epistemological and Cultural Interpretations of Mathematics,” Problems, Resources, and Issues in Mathematics Undergraduate Studies, Vol. 24, No. 8 (2014), pp. 710–721.

P.-H. Liu, “The Role of Mathematics in the Renaissance Sciences and Arts,” Humanities and Social Sciences Review, Vol. 2, No. 2 (2013), 107–111.

P.-H. Liu, “History as a Platform for Developing College Students’ Epistemological Beliefs of Mathematics,” International Journal of Science and Mathematics Education, Vol. 7, No. 3 (2009), 473–499.

P.-H. Liu and Margaret L. Niess, “An Exploratory Study of College Students’ Views of Mathematical Thinking in a Historical Approach Calculus Course,” Mathematical Thinking and Learning, Vol. 8, No. 4 (2006), 373–406.

About NCTM

The National Council of Teachers of Mathematics (NCTM) is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. In addition to its practitioner journal Mathematics Teacher: Learning & Teaching PK–12 (MTLT), the council currently publishes a mathematics education research journal, as well as an online journal for teacher educators (jointly with the Association of Mathematics Teacher Educators). With 80,000 members and more than 200 Affiliates, NCTM is the world’s largest organization dedicated to improving mathematics education in prekindergarten through grade 12. For more information on NCTM membership, visit http://www.nctm.org/membership.

Other Mathematics Teacher Articles in Convergence

Patricia R. Allaire and Robert E. Bradley, “Geometric Approaches to Quadratic Equations from Other Times and Places,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 308–313, 319.

David M. Bressoud, "Historical Reflections on Teaching Trigonometry," Mathematics Teacher, Vol. 104, No. 2 (September 2010), pp. 106–112, plus three supplementary sections, "Hipparchus," "Euclid," and "Ptolemy."

Richard M. Davitt, “The Evolutionary Character of Mathematics,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 692–694.

Keith Devlin, "The Pascal-Fermat Correspondence: How Mathematics Is Really Done," Mathematics Teacher, Vol. 103, No. 8 (April 2010), pp. 578–582.

Jennifer Horn, Amy Zamierowski and Rita Barger, “Correspondence from Mathematicians," Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 688–691.

Seán P. Madden, Jocelyne M. Comstock, and James P. Downing, “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics,” Mathematics Teacher, Vol. 100, No. 2 (September 2006), pp. 94–99.

Peter N. Oliver, “Pierre Varignon and the Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 316–319.

Peter N. Oliver, “Consequences of the Varignon Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 5 (May 2001), pp. 406–408.

Robert Reys and Barbara Reys, “The High School Mathematics Curriculum—What Can We Learn from History?”, Mathematics Teacher, Vol. 105, No. 1 (August 2011), pp. 9–11.

Rheta N. Rubenstein and Randy K. Schwartz, “Word Histories: Melding Mathematics and Meanings,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 664–669.

Shai Simonson, “The Mathematics of Levi ben Gershon,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 659–663.

Frank Swetz, “The ‘Piling Up of Squares’ in Ancient China,” Mathematics Teacher, Vol. 73, No. 1 (January 1977), pp. 72–79.

Po-Hung Liu (National Chin-Yi University of Technology), "Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?," Convergence (June 2022)