Learn the New By Improving the Old
The power of dynamic repetition
The best group class I ever attended didn’t have a dedicated teacher. Students could come and go as they pleased. There was no curriculum. Explanations were rare...and generally not that useful anyway. More than a few students drank alcohol throughout.
How did I learn so much in jam sessions? (And what does this have to do with math?)
The terror helped.
I’d be standing in the player line, listening to some alto absolutely shred Stablemates. Asking myself, “What was that first chord change? How long is this A section? Where does it go in the bridge? Is the drummer going to do that while I’m playing?” I better figure it out fast, because in just a few moments, all those eyes and ears will be on me.
Or, even worse, they won’t. They’ll realize I can’t play, that I’m one of those players.
In case you’ve never been to a jam session, this is how it works: There’s generally a house band (drums, bass, piano or guitar, a horn player). They’ll call a tune, usually a “standard” – something that people have played for decades, like All The Things You Are or Straight, No Chaser. The house band will play the melody and the horn player will take the first solo. All the other horn players will wait in line for their turn. The rhythm section members each solo at the end, and then everybody plays the melody one more time.
It couldn’t be more different from the math classes I attended growing up: One teacher ran each class, specifying every question we worked on and in what sequence. Every concept was explicitly explained. Attendance was mandatory.
But I think that I was basically in the same position in both classes, learning-wise. At any given time, I knew some things and was trying to learn others. I was successful when I was able to connect the known and unknown, usually by noticing a similarity between the two, or by strengthening the known little by little until (somehow!) what confused me before seemed obvious. This is how math works: fractions lead to ratios and proportions and percents; arithmetic leads to basic algebraic expressions, then simple equations, then more complicated equations.
And it’s how musical improvisation works too. Stablemates is considered a much harder song than All The Things You Are, but they have a lot in common. The underlying rhythms of the bass, drums, and piano are the same. Any individual chord in one song can be found in the other. Most of the harmonic progressions (sequences of chords) are very similar. Stablemates has a few tricky aspects: it moves through some keys I don’t play in that often; the form is a little weird (not the usual AABA). But if you really know All The Things You Are, it’s not going to be that difficult to learn Stablemates, even if it’s bewildering the first time you hear it.
In math, ellipses are often considered harder than parabolas, but if you truly understand one concept, it won’t take long to learn the other. This has been the case for every “difficult” math concept I’ve ever learned: learn the old stuff better and the new stuff is easy. Learn parabolas really well (and linear equations, and the pythagorean theorem, and translations) and you won’t have a problem with ellipses.
Learning old stuff much better is one of the great (and very underrated) benefits of test prep. You aren’t learning new material – as I argued here, students have already seen 95% of the concepts by the time they take the SAT. Rather, you’re learning fundamental skills much more thoroughly – from multiple angles, in combination with many other skills. When you strengthen those skills and fill in all the gaps, it’s much easier to solve difficult problems. I can’t tell you the number of students (including one just a few days ago) who have told me that math “is a lot easier this year” once they’ve been working on standardized tests for a while, even though they are usually taking preCalculus and Calculus, classes that are often thought to be “beyond” the algebra and geometry of the SAT.
In their best forms, jam sessions and test prep both include the same key elements:
Fundamental material: The exact form of the material may differ from the forms you encounter in real life, but its substance is universally helpful. Mechanical engineers and family budgeters and business forecasters may face problems that look very different from SAT questions, but the principles that help them solve proportions and linear equations will help them solve their ‘real life’ problems too. When I took a gig with a Spanish singer/guitar duo, or played with a funk band, or improvised descants at church, all of the music was composed of the same building blocks I’d encountered at jam sessions.
Dynamic repetition: When you wrestle with these same fundamentals in different settings – different players, different tempos, and different songs in the case of music; different words, different numbers, different combinations of concepts in the case of math – the fundamentals just start to seem like one thing. Percents are percents. Chord changes are chord changes.
Immediate feedback: If you get lost in a tune during a jam session, it’s very obvious. People look at you funny. They may even attempt to help (by gesturing when you’re at the top of the form, for example), which somehow makes it even more embarrassing. But that embarrassment is good for you – it makes you want to learn. Bad test scores serve this same purpose – nobody likes bad scores, but they do let you know what you need to practice.
Jam sessions shared one other similarity with my math classes: I wasn’t always excited to go. I wanted to play original music, not some Tin Pan Alley song that was written before my parents were born. Some of the musicians were incredibly annoying – horn players taking long solos, singers trying to scat, drummers thinking they were Elvin Jones during my solo. And I didn’t actually get to play that much – maybe only 10 or 15 minutes out of a 2-hour session.
The rest of the time, I was just waiting around, listening to other players take their turns with the same song on repeat, sometimes for 30 minutes straight. But that’s where most of the learning happened. I’d hear many, many solutions to the same ‘problems’ – different instruments, played by different people, with very different skill levels, executing (sometimes) different ideas, all grappling with the same chord changes and rhythmic textures. After a while, you start to fill in the gaps. It’s easier to make connections. And the new stuff…doesn’t seem that new (or terrifying) any more.