Word Histories: Melding Mathematics and Meanings

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.

The editors’ first pick for 2020 is an article that describes the etymologies for common mathematical vocabulary in algebra, geometry, functions and discrete mathematics, and suggests ways in which instructors can use these word origins to enrich student learning:

Rheta N. Rubenstein and Randy K. Schwartz, “Word Histories: Melding Mathematics and Meanings,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 664–669. Reprinted with permission from Mathematics Teacher, ©2000 by the National Council of Teachers of Mathematics. All rights reserved.

(Click on the title to download a pdf file of the article, “Word Histories: Melding Mathematics and Meanings.”)

Figure 1. Word cloud utilizing vocabulary from “Word Histories: Melding Mathematics and Meanings.”

The co-authors describe their motivations for studying and writing about the origins of technical vocabulary as follows:

Our students, whether at K–12 or college, have often expressed puzzlement or dismay when asked to learn mathematical terms. They fret because, among other things, terms are unfamiliar, polysyllabic, and seemingly out of alignment with words sharing the same roots. We have found that discussing word origins is often a pathway that sheds light not only on the etymology, pronunciation, and meaning of the terms, but also more broadly on mathematics and its history. We believe that instructors who are knowledgeable about linguistic origins of mathematics words can share those origins and engage students in mathematical history at the same time as content and meanings. We hope instructors and students find this article informative and intriguing. We also hope you may want to learn more in multiple related articles that we have written, many of which are available online.

For those who wish to take the authors up on their invitation to undertake further etymological explorations, the following select bibliography of their other works can start you on your journey:

Rheta N. Rubenstein and Randy K. Schwartz, “The Roots of the Branches of Mathematics,” Math Horizons, Vol. 6, No. 3 (Feb. 1999), pp.18–20; reprinted in Deanna Haunsperger and Stephen Kennedy, eds., The Edge of the Universe: Celebrating Ten Years of Math Horizons (Washington, DC: Mathematical Association of America, 2006), pp. 105–107.

Randy K. Schwartz and Rheta N. Rubenstein, “Arabic from A (Algebra) to Z (Zero),” Math Horizons, Vol. 7, No. 1 (Sep. 1999), pp. 16–18.

Rheta N. Rubenstein and Randy K. Schwartz, “The Duplicity of Two,” Math Horizons, Vol. 7, No. 4 (Apr. 2000), pp. 25–28.

Rheta N.  Rubenstein, “Word Origins: Building Communication Connections,” Mathematics Teaching in the Middle School, Vol. 5, No. 8 (Apr. 2000), pp. 493–498.

Denisse R. Thompson and Rheta N. Rubenstein, “Learning Mathematics Vocabulary: Potential Pitfalls and Instructional Strategies,” Mathematics Teacher, Vol. 93, No. 7 (Oct. 2000), pp. 568–573.

Randy K. Schwartz and Rheta N. Rubenstein, “Conics: The Truth, The Whole Truth, and Nothing But,” Math Horizons, Vol. 8, No. 4 (Apr. 2001), pp.23–26.

Randy K. Schwartz and Rheta N. Rubenstein, “Another Verse, Changed from the First,” Math Horizons, Vol. 9, No. 2 (Nov. 2001), pp.26–28.

Rheta N. Rubenstein and Denisse R. Thompson, “Understanding and Supporting Children’s Mathematical Language Development,” Teaching Children Mathematics, Vol. 9, No. 2 (Oct. 2002), pp. 107–112.

Rheta N. Rubenstein and Randy K. Schwartz, “Functioning Meaningfully,” Math Horizons, Vol. 10, No. 2 (Nov. 2002), pp.27–29.

Rheta N. Rubenstein and Randy K. Schwartz, “Circles: Around, About, Across, & Through,” Math Horizons, Vol. 11, No. 2 (Nov. 2003), pp.20–23.

Randy K. Schwartz and Rheta N. Rubenstein, “The Bows and Arrows of Trigonometry,” Math Horizons, Vol. 14, No. 1 (Sep. 2006), pp. 26–27.

Rheta N. Rubenstein, “Focused Strategies for Middle-Grades Mathematics Vocabulary Development,” Mathematics Teaching in the Middle School, Vol. 13, No. 4 (Nov. 2007), pp. 200–207.

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.

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.

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.

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

Frank Swetz, “Seeking Relevance? Try the History of Mathematics,” Mathematics Teacher, Vol. 77, No. 1 (January 1984), pp. 54–62, 47.

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

Patricia S. Wilson and Jennifer B. Chauvot, “Who? How? What? A Strategy for Using History to Teach Mathematics,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 642–645.