Bringing Historical Methods for Astronomical Measurements to the Classroom

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 include Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher. 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 2019 is the article “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics,” in which co-authors Seán P. Madden, Jocelyne M. Comstock, and James P. Downing describe activities that combine basic mathematical concepts with student-collected data to arrive at answers to astronomical questions that have been studied for centuries:

Seán P. Madden, Jocelyne M. Comstock, 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. Reprinted with permission from Mathematics Teacher, © 2006 by the National Council of Teachers of Mathematics. All rights reserved.

(Click on the title to download a pdf file of the article, “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics.”)

Co-author Comstock now teaches 11^th-grade General and Honors Physics as well as an elective in Earth Sciences focused on Natural Disasters for 11^th- and 12^th-graders. She has been teaching in the K–12 education system since 2001. She recently reflected on the scientific goals that she had for her students which contributed to the writing of this article.

I had been teaching one of the two Astronomy classes at Frontier Academy for three years when Dr. Madden approached me about writing an article for Mathematics Teacher on the activities we had done together in those classes. It was our primary goal to show students that the activities that we did in class actually related to things in the real world, and were not just random tasks we had chosen. The “Poles” article was the second Mathematics Teacher article collaboration that Dr. Madden and I completed with James. Both articles shared ideas we had developed for comparing data collected in real time by our students with data collected by scientists like James.

The World Year of Physics 2005 Eratosthenes Project, sponsored by American Association of Physics Teachers and American Physics Society, allowed teachers to collect and share data with a teacher using the project at another school. The data collected by my students were shared with those of a teacher in Carlsbad, New Mexico. We each collected data with our students from shadows at local noon and calculated the radius of the Earth just as Eratosthenes did. I felt like this exchange was the precursor to writing the Mathematics Teacher paper, as it was another opportunity for our students to see that physical measurements which they were able to make and mathematically process really do provide actual scientific information that others can see and use. This project was also a real eye opener to the past for these students, who learned about the history of these types of measurements and what they meant to science. I still wear the pin that the World Year of Physics 2005 organizers gave us for participating on my jacket lapel.

I have continued to use these activities every time I have taught a class in Astronomy and I sometimes also use them in my Honors Physics coursework. I am so grateful to both Dr. Madden and James for including me in these experiences, and am happy to share any additional thoughts on these activities with my peers.

In addition to the references in the paper “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics,” readers who are interested in learning more about the history of early astronomy may find the following of interest:

• Christián Carlos Carman and James Evans, "The Two Earths of Eratosthenes," Isis, Vol. 106, No. 1 (March 2015), pp. 1–16.
• Duane Roller, Eratosthenes’ Geography. Fragments collected and translated, with commentary and additional material, Princeton: Princeton University Press, 2010.
• Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton: Princeton University Press, 2009.

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. It publishes five journals, one for every grade band, as well as one on the latest research and another for 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.

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, “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.