Journal Entry for 3/15/2011

Applicable problems in the history of mathematics – practical examples for the classroom

Teaching Mathematics and Its Applications
Volume 26 Issue 1

Abstract:
This text has been centered on two main ideas: the specifications of a good problem
to be introduced in a classroom; and according to Freudethal’s view, the importance
of teaching the students how to apply mathematics in their own real life problems.
Putting these two ideas together, we may conclude that historical real world
problems fit the classroom, as in modeling and changing them into the mathematical
language: 1-certain amount of interpretation and presentation is needed, 2-their
solutions require application of certain mathematical concepts according to
students’ knowledge 3-their solution could be related to the main real problem by
students and 4-presentation can capture and hold the interest of a student. At the
end, Al-Bruni’s measurement of the earth’s circumstance has been brought as an
example of the problems with such specifications.

This article deals explicitly with notions that I have been toying with since the start of this class. As someone who has always preferred pure mathematics to applied mathematics, it is sometimes challenging for me to provide applied problems for my students that will not overwhelm them with complexity. I do, however, recognize that applied problems can and do serve as a valuable touchstone for students’ learning.

This article considers the value in both real world examples but also in examples of historical real world problems. The former are useful because they provided an immediate connection to students, but I think that it is with the latter that we might achieve a more robust success. Problems out of historical mathematics have the virtue of having been done over and over again; so all of the kinks should have been worked out of them. They are also, generally, more sophisticated in their use of techniques. While calculators and computers have been a great boon for the study of mathematics, men and women accomplished amazing things for centuries without their use.

The article provides a detailed example of one such historical solution to a daunting problem: how does one calculate the circumference of the earth? The construction is accomplished through an ingenious use of plane trigonometry, geometry, and some nearby mountain. The solution, while technical, is something that any careful trigonometry student should be able to follow and, given appropriate resources, reproduce.

While I am unlikely to use this specific example in my own teaching, I think it would behoove me to begin incorporating other historical examples into by teaching in the future.