As a math teacher I am often asked during class (and sometimes during parent-teacher interviews), “What is this useful for?” This is an excellent question as it leads not to a final answer, but to more interesting questions: What qualities make something useful? Is the value of an activity in its usefulness? How does one know what the usefulness of an undertaking is prior to knowing what will come of it in the future?
Think of Heinrich Hertz who discovered radio waves in the 1880s, an undertaking which eventually led to such useful inventions as wireless internet and air travel. But at the time he completed this work, he had no grasp of any “usefulness” for radio waves. Hertz was simply trying to understand the strange predictions of the mathematics of electromagnetism.
Like Hertz, students need to know that curiosity and a drive for knowledge are good in themselves. This is precisely why it was such a pleasure to watch over 70 students from Grades 9 to 12 write the University of Waterloo Canadian Senior and Intermediate Mathematics Contests this past Wednesday. Students who took on this difficult task participated in the joy of problem solving and the good of challenging themselves. It is impossible to name or count the multitude of potential ways their work may in time become “useful.”