All three of my children are musicians. I watched them all grow from beginners, barely able to make a sound that one could describe as musical, to confident and talented performers. I think about what might have happened if they had learned music the way we typically teach math. It might have looked something like this:
Treat math lessons like a violin concerto.
- First, we teach the individual notes, one at a time, until students know them all and can accurately produce them on an instrument.
- Then we teach the notations so that students can accurately reproduce various rhythms and patterns.
- We follow this with practice of all of the various dynamic and articulation markings that tell players how loud or soft to play, and how to smoothly or harshly to play the individual notes.
- Next we start playing scales. First we rehearse the C-major scale until it is mastered. Then D-major, E-major, and so on through the other nine major scales.
- Then there are minor scales. You’d think there would be twelve of these also, but there are actually three different kinds of minor scales, meaning there are a total of 36 when you consider every key.
- But wait, there’s more! There are five other “modes” of scales with different patterns. Then there are chromatic scales, pentatonic scales, and on and on.
- Once students have completely mastered all of their notes, notations, markings, scales, and other technical aspects of music, then (and only then) are they permitted to tackle “real” music.
Thankfully we don’t teach music this way. My children were given real songs to play almost as soon as they could make a sound with their instrument. Certainly some of the music was a bit contrived, limited by the constraints of the students’ skills, but it was mixed in with recognizable, authentic music that students knew from their experience in the world.
There’s an important element missing, though. Making music is nearly always a collaborative effort of multiple people. Even the “singer-songwriter” who writes and performs her own songs usually has some other musicians involved in performances and recordings.
This is true in good music instruction, too, and my kids got to experience it. They had the opportunity to play with performing groups within weeks of starting. Everything was about being able to produce a real performance. No one expected professional quality outcomes, and the music was simple, but it was recognizable and felt real to both the kids and the audience. And the teacher emphasized the experience and the musicality and the group process above technical proficiency.
Math can take a lesson from music. But what does this look like in a math classroom? Just as it is not possible to learn how to play an orchestral work without learning to play with an orchestra, it is not possible to learn how complex problems get solved in the real world without having complex problems to solve with collaborators. We can take away three lessons from this:
- Teach math with problems, not just exercises; that’s the music
- Students need to learn math with others, not in isolation
- Don’t expect professional level outcomes, but coach them in that direction
Treat math lessons like a violin concerto, and soon you and your students will make music with your math.
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Gerald Aungst has more than 20 years experience as a professional educator, specializing in digital technology, mathematics, and gifted education. In his various roles as a classroom teacher, gifted support specialist, administrator, curriculum designer, and professional developer, he has worked to create a rich and vibrant learning culture. He is also passionate about improving learning opportunities for all students. Gerald is a founder of AllAboutExplorers.com and ConnectedTeachers.org.