On Mathematics Education and Music Education

Last month, Jordan Ellenberg wrote about the Proof School, wondering, “ought there be a school just for math kids?” He is not entirely sold on the idea but later notes that there are schools just for music kids. What are the parallels between music education and math education? Are they fundamentally different? Ellenberg thinks that success in mathematics doesn’t require, or necessarily benefit from, the single-minded dedication that many musicians give to their instruments at an early age.

Coincidentally (I assume), around the same time, Conrad Wolfram wrote a post about what mathematicians can learn from music education. He disagrees with the idea that doing calculations by hand is similar to practicing a piece of music, a necessary step towards becoming a mathematician/musician. Unlike practicing music, Wolfram says, “practising hand-calculating doesn’t relate to the real-world outcomes in any direct way. It’s not akin to practising a piece of music because the real-world outcome is disconnected.”

This connection between mathematics education and music education has been made several times, especially in mathematics education circles. Paul Lockhart’s famous Mathematician’s Lament starts with an analogy between math education and music education. We would be appalled if music students weren’t allowed touch their instruments until they had been through years of training in how to write sheet music, but Lockhart and many others fear that this is how we approach math education.

These posts about math and music education got me thinking. Until my junior year of college, I didn’t know whether I wanted to do math or music as my career. I had a viola performance scholarship, but I probably wasn’t cut out for a performance career. I loved music theory as well and considered going to graduate school in that subject before ultimately deciding in favor of mathematics.

A mathematician plays viola. My musical education had an impact on my mathematical training in  ways I don't quite understand. This picture from my senior viola recital was taken by Gary White.

A mathematician plays viola. My musical education had an impact on my mathematical training in ways I don’t quite understand. This picture from my senior viola recital at Baylor University was taken by Gary White. In it, I am playing Hindemith’s viola sonata opus 11 no. 4, one of my favorite pieces for viola.

Before I went to graduate school, my music education and math education were very different from each other. In math, there was a right answer or a wrong answer, and when I finished all the problems on my math homework, I was done with it for the day. In music, there was never a finish line. There were performances, but even after those, I had more music to learn and more practicing to do. Even if I felt good about my performance, I knew there were things I could improve. I never felt like I had practiced “enough.” More practice was always better. In that way, my music education was a better preparation for graduate school in math than my math education was, at least up until my last two years of college. When I read this interview with biochemist and Nobel Prize winner Thomas Sudhof, I saw the same idea. In response to the question, “What was your most influential teacher, and why?” Sudhof responded: “My bassoon teacher, Herbert Tauscher, who taught me that the only way to do something right is to practice and listen and practice and listen, hours, and hours, and hours, and hours.”

But the ideas about the importance of practice and perseverance I (and Sudhof) got from my music training are not specific to music. If I had been an accomplished athlete, actor, or painter as a young person, I probably would have learned similar lessons from those endeavors. I think there is, however, a real connection between the way I approach music, both in terms of performance and in terms of music theory, and the way I approach mathematics, but I have trouble putting my finger on it. Yes, musical rhythms are connected to fractions. (Malke Rosenfeld of the math/dance education blog Math in Your Feet just wrote about using music to teach fractions.) Yes, musical intervals are related to ratios of frequencies of vibrating strings and therefore to number theory. In fact, rock star math graduate student Robert Schneider of the Apples in Stereo and Emory University has used his mathematics background to develop a new tuning system and microtonal scale. But I think the connection is deeper than that. I can’t pinpoint it precisely, but music and math both deal with structures in ways that feel similar to me.

So where does that leave my thoughts about math education and music education? I do think the mind-body connection in music performance is fundamentally different from mathematics education, which can be done while lying in bed, not moving a muscle. And I think Ellenberg is right that early dedication to music is much more important than early dedication to math. And I am convinced that my music education did influence my mathematical development, even if I can’t pinpoint how. But would a more math-intensive curriculum earlier on have done more for me than my music education ever could? I went to a math and science program for my junior and senior years of high school, but it was important to me that I could take courses outside of math and science and continue taking viola lessons. As commenters to Elllenberg’s posts point out, magnet schools offer courses outside their specialty areas, so students at the “proof school” will not be deprived of literature or history. The school will just emphasize mathematics more than most schools do. I probably wouldn’t have been interested in even that amount of specialization at age 12, but middle-schoolers who already know they are interested in pursuing mathematics professionally probably have a lot to gain from getting a solid foundation before college.

I know there are a lot of musical mathematicians and mathematical musicians out there. Do any of you have more concrete ideas about how your pursuit of one discipline has influenced your pursuit of the other?

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10 Responses to On Mathematics Education and Music Education

  1. JSE says:

    Just to make it clear, I wouldn’t say I’m “not entirely sold” on the Proof School; I think the school sounds terrific. What I’m not entirely sold on is the idea that it should be exclusively for “math kids”; I hope kids who love math will go there, and be welcome there, even if they primarily identify as “art kids” or “physics kids” or “punk rock kids” or whatever. And I expect that’ll actually be the case, but the phrase “a school just for math kids” might suggest otherwise.

  2. George Woodrow III says:

    People learn music because they want to. Most people learn maths in school because they have to.

    I, too, am in both the music and maths camps — degrees in both music and mathematics. I think that the type of open-ended process of learning music is also available with the fine arts (drawing, painting, sculpture, etc.). It could be available for maths as well, but I think that the current educational system does not see it that way.

  3. Malke Rosenfeld says:

    This is all really interesting to read. I posited recently in a new article (now up on my website) that the true connections between math and dance (and, by extension, music) is really in the processes of making/doing both math and dance. I’m curious to know if that might be part of it for you. I’m also curious to hear more if/when you discover the structures that are similar between both disciplines.

    And I hope that it was clear in my post that I find connecting fractions to music to be a superficial activity in terms of math learning. I was interested in sharing Nick’s ideas b/c they pointed to a deeper, more interesting, and more musical experience.

  4. Ot says:

    This discussions greatly overlook the fact that music can be modeled with mathematics as any part of the natural world. Good examples are the work of Stevin, Gallilei, Mersenne, Lewin, Klumpenhouwer, Tymoczko or Mazzola, to name a few.

    Now, as far as I am concerned, many music teachers I have had say that definitely there are “right” and “wrong” ways of playing music. And, once you are “I was done with it for the day” with mathematics, you did not practice Polya’s dictum of thinking about the solutions again. And again. And again, ad infinitum.

  5. Eric Lawton says:

    If and only if there is a mathematical (or, better, scientific) proof that most potential students will be better off in the long run.

  6. miranda says:

    thi is really good idea for attract students by mathematics.. because some students like me are really go far from mathematics but we love music.. if both are get at same place than surely i attend mathematics class.

  7. María Norlov says:

    Personally, I think one of the biggest problems with maths education at the moment is that the ONLY emphasis on why maths is good – at least throughout secondary school and sixth form – is the practical application of it. I don’t mean that this isn’t important – because for many people this is their draw to maths. But for me, I am drawn to maths because it is a chance to learn for the sake of learning; to know more, to understand more, and hugely; to create. The beauty of mathematics is having all this knowledge you’ve learned, and then coming to understand it to the point that you can use it to create something else. Something new. Something beautiful. I don’t think this side of maths is really existent at all within the general education system. I think that’s sad.

    Great blog – really interesting concepts! 😉

  8. Daisy Wendy says:

    This information very helpful and provides valuable information to us. I have read some good stuff here.

  9. Marley Mozart says:

    Thank you for your article. I do believe Music and Math are highly related and the more we encourage young people to participate in music at an early age–the more developed the brain and more opportunity for children to use higher level thinking and analytical skills. It is no doubt sight reading a musical piece on the piano or instrument requires more brain power. And music theory is full of mathematical elements.

    Also, it is said that when a musician sight reads a piece for the first time on their instrument, the brain lights up in a scanner more than an epileptic seizure. So many neurons and synapsis are utilized during this process and audio, visual, and kinesthetic areas are tapped. Music is an opportunity for All people to develop the love of music and enjoy life more fully.
    Marley Mozart

  10. Stepanov Sergey says:

    Where Math meets Music
    Kids of new generation should have different methods of training .They capable to perceive information faster, with cross-modal processing ,activating all senses at once : visual perception, audio analyzers , neuromotor functions.
    Stepanov Ukraine

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