I have always wanted to start an Algebra II class in a very different way to show the students that mathematical notation is not Math. It just describes and helps us communicate Math.
I want to print off one page of sheet music and set it on the Algebra II students’ desks and immediately start talking about Major keys and Minor keys and how to do inverted note transformations. The whole time I will be firing off definitions of deceptive cadence, Gavotte and Klangfarbenmelodie. Then I would assign them homework that is designed to have them practice the transformations over and over again. I would do all of this without ever letting them hear the music.
Unfortunately, Math class can become this type of experience for many students. How often do we as teachers throw a worksheet on the projector to introduce a new concept and then walk through the worksheet showing the student how to manipulate the letters and numbers on the page while firing off definitions of standard deviation and variance and think that they have just taught Math?
Math textbooks are perfect examples of presenting the notation first. I was reading my son’s Algebra II textbook and the very beginning of the chapter begins with the words
“An exponential function has the form y=abx where a<>0…”.
Most people look at that sentence and think that it is gibberish. As a Mathematician, I look at that sentence and I actually see the graph and think of a real world business situation that it can represent. I feel the flow of the numbers and the elegance of it getting infinitely close to “0” as it goes to the left. I hear the music. Just as a conductor can hear the music in his head when he reads a score, most math teachers hear the music just by reading the “notes”. Unfortunately, most students cannot do this.
I have not taken a lot of music classes, but one of the best ones I have ever taken is one given by Professor Robert Greenberg on Beethoven’s symphonies. In each lesson, he starts out by playing a whole movement of the symphony and then leading a discussion about how it makes us feel and what do we hear in the music. He then plays small chunks of the music and shows, using musical notation and definitions, how Beethoven is able to accomplish such amazing work.
Math class should be a similar experience, but teaching students to hear the music of math is much harder than Professor Greenberg has getting his students to hear the music. All he has to do is turn the stereo on and the sound flows around the room.
Even though it is hard, Math teachers must find ways to let the Math music flow around the room. What student wants to just manipulate letters and numbers and memorize steps? You want to know why many students say “I hate Math”? It is because they do not hear the music, all they are doing is writing notes.