Math Course Assignment
Mar. 22nd, 2010 08:46 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageThe assignment was to try something completely new for five hours over the last few weeks, and write about where the math was to be found in this new thing, and how learning it gave you insight into your students' issues with trying new things in math.
Fortunately,
I am a decent amateur musician. I play the piano, I sing, I play the recorder well enough to teach it to grade fives, and I’ve been conducting choirs of various descriptions for half my life. But I have never given serious thought to trying a rhythm instrument until recently. That’s mostly because the type I was most familiar with was a snare drum, and the sound of those leaves me feeling frazzled and over-stimulated. Since I didn’t like the tone of the instrument, I had a vested interest in staying away from it.
Then a few weeks ago, a good friend of mine (who also happens to be a mathematician and scientist by trade – I don’t think it’s a coincidence) introduced me to an African djembe drum. He brought two with him to a drum circle we were both attending (it was an event within a larger event) and offered me one to learn on.
Always before when I’ve learned music, I’ve started with a combination of aural and visual. I read music to play the piano and don’t know how to play by ear. I prefer to read music to play the recorder, though I’m getting better at playing that by ear. A choir leader always works from a score. The visual learning mode is deeply ingrained in my musical education.
Drumming is different. I started drumming by watching my friend as he demonstrated certain basic beats. A djembe is a big wooden drum with an animal skin; it has a deep and musical tone to it when struck in the centre and a much sharper tone when hit on the edge. I loved the sounds it made and the physicality of it, the immediacy of the rhythm, with nothing between me and it. The drum circle allowed me a freedom of expression on the drum that no other instrument had ever matched for me; there was no right or wrong way to play, just a beat to be followed. I lost myself in it faster than I have ever lost myself in any new musical endeavour. I followed my friend’s lead, added what he added, experimented with different angles and tones and sounds, and generally discovered an instrument I’m going to love.
So I bought a drum, and had my friend come over to show me some more tricks. He went for some more complex rhythms, which again I picked up easily.
The next step, as far as my musician’s training would have it, was to learn to read drum notation. So I googled hand drum rhythms – and figured out where I was going to have to work at this. The notations look nothing like music in any form I’d ever seen it before. When I looked closer, of course I saw time signatures I recognized, but the format was so different that I had to look several times to figure them out. Furthermore, they weren’t sorting themselves out on screen the way they had sorted themselves out in my head. I was picturing the measures as being very quick – close to 200 beats per minute, I suspect – while the drum notation was taking what I thought were four measures and putting them into one. I had to realign what I knew about rhythm on the piano with rhythms where fractions of fractions of fractions are the order of the day. I couldn’t read it.
Faced with this frustration, I scaled back a bit, to the rhythms I’d already learned orally and kinesthetically. I was still making mistakes on them, but the mistakes were the kind that didn’t stand out. I got my friend to link me to sites that had the same rhythms in standard drum notation that we’d already worked on, so I could connect what I’d learned orally to the visual format I was having trouble with. I worked through a few of the variations, the way I’ve always taught my music students to do it: by counting beats and fractions of beats. Unlike every other rhythm exercise since I started learning the piano at the age of seven, this one didn’t seem right to me. For the first time, the counting was counter-intuitive. I persevered until I could get the rhythm on the page to match up with the one in my head. Once that single rhythm came clear, I stopped. I’ll go back to it tomorrow and see if I can add to that rhythm and figure out how it would be written.
The math of music seems so obvious to me that it seems odd even to have to spell it out. I learned fractions via the mantra, “Four beats in a measure, and a quarter note gets one beat” a good three years before I came across them in school. Drum rhythms are more complex, but they’re really just more interesting equivalent fractions. The back-and-forth of the drum circle, with its call-and-response format, also made me suspect it could be connected to algebraic equivalencies without too much difficulty. I will have to remember to ask my friend if he’s ever worked that through; he’s the kind of guy who tests mathematical theories in his spare time, so he may have. In any case, once I get a little more proficient with it, I will see about taking my drum into class with me to demonstrate aural and kinesthetic fractions to my students.
The problem-solving required to make the notation match up with the intuitive pounding of the drum reminded me that students often have a connection they can make to a new math topic, and they can often sense that there’s a connection there that they’re missing, but they need help and problem-solving strategies to make the connections come clear. Math is a way of describing reality with numbers, but the numbers can seem counter-intuitive, too abstract to matter in the face of the all-encompassing reality. The ability to step back and analyze that reality, to apply abstract concepts like numbers and fractions and equivalence to it, is a skill we must teach and reinforce and reward when we see it.
Fortunately,
I am a decent amateur musician. I play the piano, I sing, I play the recorder well enough to teach it to grade fives, and I’ve been conducting choirs of various descriptions for half my life. But I have never given serious thought to trying a rhythm instrument until recently. That’s mostly because the type I was most familiar with was a snare drum, and the sound of those leaves me feeling frazzled and over-stimulated. Since I didn’t like the tone of the instrument, I had a vested interest in staying away from it.
Then a few weeks ago, a good friend of mine (who also happens to be a mathematician and scientist by trade – I don’t think it’s a coincidence) introduced me to an African djembe drum. He brought two with him to a drum circle we were both attending (it was an event within a larger event) and offered me one to learn on.
Always before when I’ve learned music, I’ve started with a combination of aural and visual. I read music to play the piano and don’t know how to play by ear. I prefer to read music to play the recorder, though I’m getting better at playing that by ear. A choir leader always works from a score. The visual learning mode is deeply ingrained in my musical education.
Drumming is different. I started drumming by watching my friend as he demonstrated certain basic beats. A djembe is a big wooden drum with an animal skin; it has a deep and musical tone to it when struck in the centre and a much sharper tone when hit on the edge. I loved the sounds it made and the physicality of it, the immediacy of the rhythm, with nothing between me and it. The drum circle allowed me a freedom of expression on the drum that no other instrument had ever matched for me; there was no right or wrong way to play, just a beat to be followed. I lost myself in it faster than I have ever lost myself in any new musical endeavour. I followed my friend’s lead, added what he added, experimented with different angles and tones and sounds, and generally discovered an instrument I’m going to love.
So I bought a drum, and had my friend come over to show me some more tricks. He went for some more complex rhythms, which again I picked up easily.
The next step, as far as my musician’s training would have it, was to learn to read drum notation. So I googled hand drum rhythms – and figured out where I was going to have to work at this. The notations look nothing like music in any form I’d ever seen it before. When I looked closer, of course I saw time signatures I recognized, but the format was so different that I had to look several times to figure them out. Furthermore, they weren’t sorting themselves out on screen the way they had sorted themselves out in my head. I was picturing the measures as being very quick – close to 200 beats per minute, I suspect – while the drum notation was taking what I thought were four measures and putting them into one. I had to realign what I knew about rhythm on the piano with rhythms where fractions of fractions of fractions are the order of the day. I couldn’t read it.
Faced with this frustration, I scaled back a bit, to the rhythms I’d already learned orally and kinesthetically. I was still making mistakes on them, but the mistakes were the kind that didn’t stand out. I got my friend to link me to sites that had the same rhythms in standard drum notation that we’d already worked on, so I could connect what I’d learned orally to the visual format I was having trouble with. I worked through a few of the variations, the way I’ve always taught my music students to do it: by counting beats and fractions of beats. Unlike every other rhythm exercise since I started learning the piano at the age of seven, this one didn’t seem right to me. For the first time, the counting was counter-intuitive. I persevered until I could get the rhythm on the page to match up with the one in my head. Once that single rhythm came clear, I stopped. I’ll go back to it tomorrow and see if I can add to that rhythm and figure out how it would be written.
The math of music seems so obvious to me that it seems odd even to have to spell it out. I learned fractions via the mantra, “Four beats in a measure, and a quarter note gets one beat” a good three years before I came across them in school. Drum rhythms are more complex, but they’re really just more interesting equivalent fractions. The back-and-forth of the drum circle, with its call-and-response format, also made me suspect it could be connected to algebraic equivalencies without too much difficulty. I will have to remember to ask my friend if he’s ever worked that through; he’s the kind of guy who tests mathematical theories in his spare time, so he may have. In any case, once I get a little more proficient with it, I will see about taking my drum into class with me to demonstrate aural and kinesthetic fractions to my students.
The problem-solving required to make the notation match up with the intuitive pounding of the drum reminded me that students often have a connection they can make to a new math topic, and they can often sense that there’s a connection there that they’re missing, but they need help and problem-solving strategies to make the connections come clear. Math is a way of describing reality with numbers, but the numbers can seem counter-intuitive, too abstract to matter in the face of the all-encompassing reality. The ability to step back and analyze that reality, to apply abstract concepts like numbers and fractions and equivalence to it, is a skill we must teach and reinforce and reward when we see it.
(no subject)
Date: 2010-03-23 03:27 am (UTC)(no subject)
Date: 2010-03-23 08:34 am (UTC)(no subject)
Date: 2010-03-23 03:27 am (UTC)(no subject)
Date: 2010-03-23 08:36 am (UTC)typo
Date: 2010-03-23 03:28 am (UTC)oven?
Re: typo
Date: 2010-03-23 08:35 am (UTC)Re: typo
Date: 2010-03-23 11:17 am (UTC)Or you could post an erratum. Maybe they've never gotten one before and will have to strike a committee to deal with it.
-- hendrik