The High School Mathematics Curriculum—What Can We Learn from History?

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 Robert Reys and Barbara Reys, in which they reviewed several of the major programs for reform in American mathematics education that appeared between 1894 and 2010:

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. Reprinted with permission from Mathematics Teacher, © 2011 by the National Council of Teachers of Mathematics. All rights reserved.

(Click on the title to download a pdf file of the article, “The High School Mathematics Curriculum—What Can We Learn from History?”.)

The authors recently reflected on what they learned while preparing this article:

This article provides a summary of some conferences and reports that focused on educating secondary school students in the United States. An examination of this information shows a mixed bag of outcomes and recommendations. Some called for more mathematics, others called for less mathematics. Some called for a specific order of high school mathematics courses—i.e., algebra-geometry-more algebra—others called for integrated mathematics—i.e., how mathematics is organized and experienced in most other countries. Some called for a common core of mathematics to be learned, others didn’t agree with the common core. Some called for more thoughtful and effective use of technology in promoting mathematics learning. While calls for change are the constant element in these discussions of mathematics curriculum and teaching, it is rare to find complete support for them among professional organizations, parents, and mathematics teachers. A reminder that change is hard, and pleasing everyone about anything in education is very difficult. Awareness and knowledge of this history in mathematics education may be helpful to those confronted with current and future challenges related to mathematics curriculum and teaching at the secondary level. 

About the Authors

Robert Reys is currently Curators Distinguished Professor Emeritus in the College of Education & Human Development at the University of Missouri, where he has been teaching for more than 50 years. He has authored or co-authored more than 250 articles in professional journals and co-authored or edited more than 30 books. In 2008 he received a Lifetime Achievement Award from NCTM. He is also a competitive tennis player and tennis official.

Barbara Reys is currently Curators Professor Emerita in the College of Education & Human Development at the University of Missouri. Her career-long interest has been in “standards-based” mathematics curriculum reform. She has co-authored or co-edited at least 23 books and 145 journal articles and book chapters. In 2016 she received a Lifetime Achievement Award from NCTM. The couple have been awarded numerous grants for researching mathematics education, and they founded the STaR Program for early-career mathematics educators in higher education.

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.

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, “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.