Using primary sources in teaching, even in teaching math

Primary sources should provide a significant portion of our information. History teachers know this, of course, but it’s rare among math teachers. Even though my major academic interests are math and linguistics/languages, I was deeply affected by the best course I took in high school, which was AP US History. That was hundreds of years ago (well…actually…only 51 years ago) so I’m sure the course has changed since then, but here’s what my teacher did back then: in each unit of the course, he would give us a list of several primary and several secondary sources, and our job was to read all of them and to see how well the authors of the secondary sources did or did not explain the primary ones. Sometimes they contradicted each other! All of this was great training for my subsequent years as a college student and then as a teacher.

coverSo what does this have to do with math teaching? Well, fast-forward to 1994, when I assembled a self-published book for use by ninth-graders at Boston University Academy. Titled Classical Mathematics for Today’s Learner, and unofficially subtitled Sources and Problems, the book included excerpts from the writings of ancient Egypt, and ancient Babylonia, and especially ancient Greece. So I was naturally receptive to an article I saw the other day in Education Week. Here is an excerpt:

Over the next five years, as many as 1,000 college students will be asked to grapple with the original writings of mathematicians like Euclid and Archimedes in a project that many experts say has good utility in high school math classrooms as well.

Under a $1.5 million grant from the National Science Foundation, seven university math professors are writing lesson plans around primary sources—common practice in history and English classes, but rare in the math world—which they’ll then pilot with students around the country.

The idea, based on earlier grant-funded work, is that understanding the origins of important mathematical concepts will help students fully grasp and remember them later, and that exploring mathematicians’ motivations will be inspiring for students.

Yes! Although this project focuses on students studying pre-calculus and calculus in eleventh and twelfth grades, the idea certainly meshes well with what I did with younger students.

[Kathy] Clark, who taught high school for 12 years, periodically used primary sources with her students and found them beneficial. “That’s a missed resource in high school teaching today,” she said. “I hardly see math students in high school open a book for anything other than math exercises. It perpetuates this notion that math is just a bunch of exercises you do—you crunch numbers and solve for x.” Through primary sources, students learn to “tear apart the mathematics and the meaning and put it together at the end.”

Sounds good to me! I’ll have to find out more about this. I will close with these familiar words from Pythagoras by way of Euclid:

ἐν τοῖς ὀρθογωνίοις τριγώνοις τὸ ἀπὸ τῆς τὴν ὀρθὴν γωνίαν ὑποτεινούσης πλευρᾶς τετράγωνον ἴσον ἐστὶ τοῖς ἀπὸ τῶν τὴν ὀρθὴν γωνίαν περι εχουσῶν πλευρῶν τετραγώνοις.


Categories: Math, Teaching & Learning, Weston