When visiting a large art museum one commonly finds groups of schoolchildren accompanied by their teachers admiring and studying paintings, sculptures, and other works of art from centuries past. Their teachers or guides draw the students' attention to the artist's techniques: mastery of color, tone, interplay of light and shadow, and even the significance of the scenes described. Under this directed scrutiny, a painting or statue becomes a testimony to its creator's genius and offers some understanding of the period in which the artist lived and functioned. Learning takes place. This learning is both cognitive and affective. So, too, are the mathematics problems of history. They, in a sense, are intellectual and pedagogical works of art that testify to an expression of human genius. But, unlike the museum pieces, these problems can actually be possessed by the viewers through participation in the solution processes. Questions originating hundreds or even thousands of years ago can be understood and answered in today's classrooms. What a dramatic realization that is!
Historical problems and problem solving, as a topic in itself, can be the focus of a lesson, but such problems are probably more effectively interspersed among classroom drills and homework assignments. Teachers who like to specify a “problem of the week” will find that historical problems fit the task nicely. Ample supplies of historical problems can be found in survey books on the history of mathematics or in the Convergence feature, Problems from Another Time. The seeking out and employing of historical mathematical problems in classroom instruction is a rewarding and enriching experience in which mathematics teachers should partake.
Lieske, G. Spencer. “Reader Reflections: Right Triangle,” Mathematics Teacher 78 (October 1985): 498-99.
McMillan, Robert. “Babylonian Quadratics,” Mathematics Teacher 77 (January 1984): 63-65.
Swetz, Frank J. (editor), "Problems from Another Time," Convergence (2004).
Swetz, Frank J. and T. I. Kao. Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China. Reston, VA: National Council of Teachers of Mathematics, 1977.
Wikenfeld, Morris. “Reader Reflections: Right Triangle Relationships,” Mathematics Teacher 78 (January 1985): 12.
This article is a revised version of an article that appeared in Mathematics Teacher 82 (May 1989), pp. 370-377, and it appears in Convergence by permission of the National Council of Teachers of Mathematics.