Conveying the beauty of mathematics
Teaching methods need improvement, Elaine Wisenthal Milech says.
There is no dispute that, to quote a recent headline, “our math teaching needs fixing” (Montreal Gazette, May 27). However, the solutions advanced — trying to emphasize mathematics as a series of algorithms, focusing on one way to do a problem and limiting the discovery approach — are part of the problem, not part of the solution.
I have spent my career in mathematics education, have witnessed many curricular reforms, observed countless mathematics classes and continue to work with students who struggle. The main issue for these students is that little makes sense to them.
Students already feel that mathematics is just a series of rules to be followed, something created to make their lives difficult. They do not appreciate how it developed and, yes, even continues to develop, and they certainly do not see the relevance of the concepts they are being taught.
A strong mathematics curriculum is definitely a good starting point, and I believe the Quebec program is a very strong one, though a few adjustments should be made.
However, what really needs to be addressed are teaching methods. Among other things, teachers need to have strategies for explaining concepts in a variety of ways, and know how to help students differentiate between similar ideas and how not to fall in the trap of oversimplifying concepts with weak students.
Students definitely need to know their basics (one cannot go far in mathematics without knowing the multiplication tables); however, they need to be shown the beauty of mathematics, its history and its applications. Sadly, too many mathematics teachers do not know the origin of some of the concepts they teach and rarely can answer students’ burning question: “when am I ever going to have to use this?”
Often, students are told that pi is 3.14 and are given a formula to find the circumference of a circle. It is certainly more effective to provide circular rulers (the paper ones at IKEA are great for this) and have students measure circumferences and diameters of many different circular objects to discover the mathematical formula on their own. This makes the concept more understandable and amazing to the students, besides having the added benefit of letting them see how mathematics is sometimes discovered. Sections of the Jewish scripture, comprising parts of the Christian Old Testament, hint at the number pi: “And he (Hiram) made a molten sea, ten cubits from the one rim to the other it was round all about, and ... a line of thirty cubits did compass it round about. ... And it was an hand breadth thick” (First Kings, Chapter 7, Verses 23 and 26). What an enriching classroom discussion can be had about units of measurements, their development and an early reference to pi, let alone any religious topics!
Senior mathematics stu- dents are taught about “conic sections.” They are rarely shown a cone taken apart to create these sections and are almost never exposed to the wonders of whispering galleries. A whispering gallery is in the shape of an ellipse (a conic section), and when a visitor stands at one focus and whispers, the line of sound emanating from this focus reflects directly to the focus at the other end of the gallery, where the whispers may be heard. When I tell weak students about this, they are truly intrigued and then are more open to studying the characteristics on an ellipse.
Teachers often complain that they lack time to finish mathematics programs, so do not have the luxury of these kind of approaches. However, current approaches require constant re-teaching of topics that were never retained. Taking the time to explore, appreciate and understand mathematical concepts will free up time to do a much better job.