Scaling the mentor–apprentice relationship
Meet Practica Musica, an electronic tutor for music theory and ear training. Let’s not talk about its aesthetics; instead, I’ll use it to focus a couple topics broadly relevant in education.
From brush strokes to big picture
Practica Musica features a massive collection of interactive activities, organized by goal and ordered along appropriate difficulty curves. A few examples include: syncopated rhythm reading, chord progression ear training, correction of inscribed melody from audio playback, and rhythmic dictation. The publisher’s site hosts videos of some activities; the pitch error exercise is representative.
Now picture you’re some teenager with a guitar and inappropriately long hair. Your uncle gave you this app for your birthday, but see, you just want to write some rockin’ hooks. This blather about figured bass looks terrifically dull.
This stuff is not Hanon’s Virtuoso Pianist, though. It’s not an eating-your-vegetables proposition. These exercises aim to build intuition. You’re not going to be recalling what your music theory book says about harmonic progressions when you’re writing a hit single. Your internalized knowledge will puppeteer you toward natural results.
I applaud the diverse suite of exercises in Practica Musica, but it’s hit upon a common and decisive educational pitfall: a hazy path through the doldrums of boring intermediate goals to the student’s true desires on the other side. Inspiration is step zero. The student must understand how his hard work will pay off.
Practica Musica’s publisher mitigates the situation with a companion textbook that links the exercises into something like a narrated curriculum. But the textbook is utterly static, ignoring the incredible benefits explorable explanations can have in students’ understanding.
For instance: inline with its description of altered chords, the textbook could let the student drag a triad’s notes around on a staff to see and hear its variations. Or he could “scrub” through a progression by running his mouse over the chord letters “I IV V I”. Exercises which test concepts introduced in the book could be directly integrated in layout—or even made required to proceed—rather than passively referenced.
Responsive testing
One Practica Musica exercise tests aural identification of major thirds, minor thirds, perfect fourths, and perfect fifths. If you consistently misname minor thirds, it will play them more regularly. And it won’t let you proceed until you’ve answered a few correctly in a row.
Contrast this to an Algebra student who is being tested on his exponents but does not understand that 62 × 64 = 66. Regardless of whether he passes or fails the test, this represents a fundamental gap in his knowledge that may never be directly retested. Each subsequent exam will build upon this concept (less and less explicitly) until the student has either figured out his missing understanding or flunked out.
What if our tests were dynamically generated in response to each student’s strengths and weaknesses? How many struggling students missed just one fundamental concept—but so long ago that neither they nor their teachers understand the root of their confusion?
The Khan Academy has experimented with these ideas in classrooms. In his TED talk, its founder Sal Khan claims:
You see students who took a little bit of extra time on one concept or the other, but once they get through that concept, they just race ahead. And so the same kids that you thought were slow six weeks ago you now would think are gifted. And we’re seeing it over and over and over again. It really makes you wonder how much all of the labels maybe all of us have really benefited from were really just a coincidence of time.
We can respond to students’ progress even more effectively by exploiting spaced repetition and related techniques: present troublesome material repeatedly, but with increasing intervals between each exposure modulated by success rate. The exact curves remain controversial but could be approximated by machine learning.
From mentor to classroom
I’m convinced that mentor–apprentice education is the best way to learn most subjects. Unfortunately, it doesn’t scale at all. But if we understand what, specifically, makes this approach so effective, maybe we can emulate the results in classrooms.
A mentor will be exposed far more directly to his apprentice’s excitement and frustration. His student’s emotions, combined with his empathy, all but force him to paint the path I described through the doldrums of beginnerhood. To provide inspiration. A classroom teacher could do that, too; I just don’t think it’s recognized as a goal or component of their curricula.
Likewise, a student’s weak spots are much more apparent in one-on-one tutelage, and the format encourages a naturally flexible curriculum schedule. Exam metrics and automated reporting could enable classroom teachers to identify problem areas, and tools for responsive testing could address students’ individual issues by personalized spaced repetition.
Often I wonder: what would happen if just one classroom could have a dedicated software engineer who would shadow the teacher and build tools full-time to help him?
