Guest Post: Music Teaching, UIL, and the Problem with Skills

Editor’s note: Although I’ve been thinking of you during my time away from the blog, grad school + new baby make it terribly difficult to sit down and write. Lucky for me (and now you) the astounding Marshall Escamilla has agreed to share some thoughts on teaching music. Visit his twitter and say hello!

    In order to understand what goes in the world of music education–particularly at the secondary level–you have to understand the world of competitions. In Texas, we have something called UIL, which is an organization that mostly takes care of competitive sports, but that also happens to deal with competitive music. As someone who spent most of my life playing music, I found the idea of competitive music to be extremely strange when I first moved here and started teaching. But that’s neither here nor there.

If you watch the following video, you can get a pretty good idea of the kinds of things that happen at a music competition:

If you don’t care to spend 10 minutes watching this video, or don’t understand what’s going on in it, let me elaborate a little bit. This is a middle school band at a sight reading competition. They’ve been given a piece of sheet music that they’ve neither heard nor seen before, and for the first 7 minutes (or so) of the video, their director is instructing them on how to go about learning this piece of music. After that, they play a scale to warm up, and then have one shot to play through the piece. That set of tables off to the right of the screen is a group of judges, who are listening carefully to their performance and, ultimately, giving them a score on it. The sight reading contest is one part of the bigger picture of the UIL competition, as bands are also evaluated on individual pieces that they’ve prepared all semester–or, sometimes, all year.

In most typical programs, UIL competitions are really the centerpiece event. Directors are judged primarily by how their kids perform at contest–both by their peers and their employers. In other words, it’s a really, really big deal.

Now, I think it’s actually fun to watch a group of middle schoolers that are so thoroughly trained go through an activity that then comes together so beautifully into actual music. It’s also fun to watch an excellent teacher at work. She clearly enjoys what she does and is obviously terrific at it.

And that’s all great.

But then, you should also watch this:

Most of the tunes the Carter Family learned when they were young probably they learned in church. I’d be willing to bet that most of their learning came from singing together in a communal setting. Even those songs they learned from songbooks might have looked more like this than anything like traditional music notation. The bottom line is that as much of a storied career as the Carter Family enjoyed, they would not have succeeded at a UIL competition.

Of course, the Carter Family isn’t alone in this regard. In my years playing around Austin, I’ve met scores of professional musicians–including some very successful ones–who can’t sight read worth a damn. There’s no shortage of successful professional musicians who know next to nothing about music theory. In fact, I would say that at this point most people making their living in music don’t know anything about theory or sight reading.

So what gives? Why is it that this set of skills that are so highly valued in school music programs are so non-essential in the “real world” that most professionals in the field don’t even have a basic proficiency at them, let alone anything close to the mastery displayed by the 8th graders in that first video? There is no equivalent to this phenomenon in any other professional field. I suppose you can imagine a successful engineer who hasn’t fully mastered multivariate calculus (maybe?), but to find one who can’t add or subtract?

The only possible explanation is that there must be a set of skills that most professionals do have that are more important for predicting success in the field than their ability to read or understand music theory., I’d also be willing to bet that the skills that June Carter gained by singing with her family in church–namely, a thorough knowledge of repertoire, an ability to learn by ear, and an intuitive understanding of how music works–are probably much more important.

I don’t want to knock the very, very hard work of any of my colleagues in the field of music education, but when I see stuff like that I can’t help but wonder what’s missing from that picture. Have the kids in this ensemble ever once been asked to play music without a chart in front of them? Have they ever–once–improvised a melody or a solo?

The answer to both of those questions is almost certainly no. With the intense emphasis on preparing for contest, pretty much any other form of music learning outside of the “traditional” Western-art music approach has been crowded out. And to tell the truth, based on my experience at music education conferences, there’s precious little interest in pursuing those forms in any serious way.

And the thing is that those non-traditional forms of learning music are, actually, a whole lot more traditional than the model that depends on sight-reading. It’s really only in the last 150 years or so that any form of music making has existed that didn’t rely heavily on playing by ear and improvisation. Outside of the realm of Western Art music (e.g., folk music, jazz, rock and pop, “world” music), those two skills are of foremost importance.

The thing about non-Western Art music skills is that they are a hell of a lot harder to assess at a contest. Sight reading is great in that way. You can give an adjudicator a chart; they listen to the students play; they mark it up when they hear anything that differs from what’s written on the page.

Though music competitions may seem to a layperson like any other kind of school competition–you know, like football, or debate team–what they really are is a kind of standardized test. They function as a way to measure whether a music teacher is effective at his or her job, and when overemphasized they have a similar effect on learning that overemphasis on testing does. It causes educators to narrow their focus into a tiny realm of types of learning that are deemed acceptable; it causes educators to emphasize rigor and precision over joy and motivation; it crowds out student interests that won’t (can’t?) be assessed.

Marshall Escamilla started the music program at the Khabele School, where he’s been teaching music for the past 11 years. You can read his other random musings at mescamilla1980.wordpress.com
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Thinking quickly

I’m going to ask you a question about pizza, but I’m going to trust that you won’t look below until you agree not to do any calculations. By calculations, I mean on paper, in your head, or on a machine.

So don’t break our circle of trust.

Seriously, just move on if you’re tempted to cheat.

Ok, got the stragglers out of here. Without calculating, answer the following question

The largest pizza at East Side Pies has is fairly big. It’s 18 inches across. What is the area of the pizza?

a. About 254 sq inches
b. About 1017 sq inches
c. About 56.5 sq inches
d. About 740 sq inches

I…. couldn’t resist doing the mental estimation. It didn’t come to me naturally.

Now the rest is of this post is obviously speculation. I imagine that the rate of correct responses is somewhere in the 25-33% range, that is you might be able to rule out one of these questions pretty quickly. However, I don’t think there would be much difference if you asked a 4th grader or a high school junior.

If I have no real intuition about many, many little squares of pizzas, what does that say about my ability to “do” mathematics? To me, it shows how being able to calculate an area of some generic shape is a lower level of skill. If we made a Bloom’s taxonomy for math classes, I think calculation should be like level 2.

Transversals, KenKen, and the Art of Making Puzzles

I’ve taught Geometry for four years now, and this year I’m completely writing my own course notes, essentially a textbook. I burned the boats, so to speak. And yes, it is because I’m a crazy person. But, also the books cater to these state standards which can be so very mind numbing. if I were to read through the TEKS (Texas standards for you outside the good nation), I would see dregs like this:

“111.41.C.5  Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to: (A)  investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.”

If the numbers at the beginning didn’t get you, the inane droning of vocabulary might have. But you know what? Puzzles in Geometry are badass. Kids like to do them, I like to assign them, they’re stretching, and they actually match up with class standards.

In the Beginning

Sometimes I start with low-level, accessible puzzles like this one from KenKen.com. They have to use some logic, some elimination, but nothing so taxing that they’re spent.

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What I’ve noticed is that the “easy” (in quotes because it is banned in my classroom) problems generally only have one difficult spot – once a particular square is filled in, the rest of the puzzle becomes rapidly finished. Old Windows users, think of Solitaire when all the Aces through the 8’s are already moved to the winning area – from that point on it’s just a click party.

Back to Geometry

In that light, when I see puzzles like this… they’re a little on the soft side.

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There’s not really any conundrum. The only way I can really have fun with a puzzle like this is by letting all the students solve for angles 2, 7 and 8 and then telling them they’re wrong (unless they’ve explicitly assumed two lines are parallel). So it’s off to Google (or Bing if any sponsors are reading this) to find better puzzles.

From the Discovering Geometry page we can see this one is an upgrade:

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This puzzle is interesting to look at. Most of the students can solve these pretty quickly – they’re accessible and they can check themselves by looking at groups of angles that form circles. They feel great when they finish, but they’re not the most cognitively demanding puzzles. We can reinforce some vocabulary (what’s the relationship between angle f and the angle with 64 degrees?), but the only other meta question for me that really comes up is: Which angle is the easiest to find first? Or, how many angles does it take to get to angle c?

In my estimation, there are only a couple of points where kids can get productively struggle – probably around getting angles d and c.

So I keep searching, when I come across this:

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Ok, here we have something interesting. If I was in my first year teaching this class, I might explicitly give them some of the angles (say, angle b is 40), and ask them to solve for the others. If I’m really devious, I might try to sneak in some Algebra components (what if angle f equals 4x and angle a equals –8x +20??), but I’ve been hearing some powerful arguments against that.

Now that we have a diagram, and I’m in a safe place in terms of my job, we can start to ask a different type of question, one that I’ve never asked before…

How many angles must you be given in order to find all the other missing angles?

I’m no Christopher Danielson, and I don’t know much about Hiele levels of proof in Geometry, but this is the kind of question that I’d like to give to students more often. The discussion was fascinating. About half of the students were convinced that you only needed one angle. The other half were convinced you needed two angles. Even though we haven’t used the word “similar” in class once, after talking with others, most students became convinced that angle a and f were congruent, as well as b and ace, and acb and e.

I can still play the devil’s advocate pretty well – even if the entire class was convinced the number of angles needed was “two”. I can simply give them angles a and f and say “gotcha suckers”. 

Yes, I have academic standards to which I am accountable. But this underlying level of communication, this “System 2” thinking where students move from instinct to a prolonged, effortful attempt at problems is my main focus.

I haven’t done it yet, but this problem is going to be on their next assessment. I haven’t even begun to work it out for myself because I’m interested in how students approach it.

“What information do you need in order to solve for all of the numbered angles in the figure below?”

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Other thoughts:

How  does one make a good KenKen puzzle anyway? What makes one “easy”, “medium” or “hard”. I share with you the rabbit hole of information I’ve come across, or I could say – have you ever tried to make one?

Why are you lying to me Kia?

I bought a new car for the first time in  my life back in May of 2012, a Kia Optima. I had been driving the same Ford Explorer since I was a senior in high school… around February of 2002.

I know nothing about cars, and a little less about buying big expensive things. And, I am way too influenced by television. So when the NBA playoffs come around and I watch roughly 9,000 hours of games, my mind succumbs to ads like this:

or this

  

 

Owning a new car has been completely badass. My old car didn’t have fancy new inventions like Bluetooth calling, steering wheel controls or passenger seat belts. So I’ve really been digging it.

However, one new addition has really caught my attention. In the dashboard I have an electronic display that not only tells me the odometer’s readout, but also

  • My overall rate of fuel consumption (miles per gallon)
  • A mysterious “trip B”
  • My almost-instantaneous-fuel-consumption-rate (super curious to know what interval of time they’re using to calculate)
  • My estimated number of miles I can drive before I have to start pushing

I had no reason to doubt the face value of my overall fuel consumption rate reading. After all, the car knows how many miles I’ve driven and how much gasoline it can hold… But I started noticing a discrepancy earlier this year. So I began logging the readouts of the odometer, the gallons it takes to fill up, and the readout of the MPG from the dashboard. Here are my findings.

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(Note: The one entry with (???) comes from me forgetting to record that one).

Some aspects/questions of this table are extremely striking.

  • Notice how not once does the MPG indicated by the dashboard dip below the actual performance of the MPG.
  • Notice how large the discrepancy is between the two columns. Theoretically (and it’s not a lot of mathematics involved), they should be the same.
  • What factors are driving (no pun intended) the large variance of the difference between calculated MPG and the readout MPG?

And the last question that comes to mind: Is this a conspiracy? When I purchased the car, Kia advertised 24 mpg in city, and 35 mpg on the highway. Obviously, there are factors (A/C use, temperature, tire pressure, driving style, etc) that affect those numbers. But none of those have to do with the data points that the car should be using. The car should only be calculating how many miles were driven on how much fuel. Did Kia deliberately manipulate the calculations to offer drivers a better indication of fuel economy than is actually being performed?

Once, Harvard professor H. L. “Skip” Gates said, “Conspiracy theories are an irresistible labor-saving device in the face of complexity.” I don’t want to jump to the conspiracy theory just yet. But what could be the cause of such a large discrepancy of MPG? Is my Kia lying to me or is there some Mathematics that I’m missing?