Understanding systems
Some time ago I read an article on what makes a good tutor.1 I cannot find the article again, but in the process of writing this I came across the book Improving Academic Achievement, which has a chapter that may have inspired that article: The Wisdom of Practice: Lessons Learned from the Study of HIghly Effective Tutors; Lepper and Woolverton; Academic Press; 2002. It explicated many of the things I do when tutoring, so obviously I thought it was a great article. When I had a side gig as a private tutor, I covered mostly maths and physics, so that’s how I’ll frame things in this article. The same thing applies to other fields too, but it might be harder the further away from maths they are.
The main thrust of the lost article (as I remember it) was that effective tutors are highly empathetic to the level of motivation of their student, and they quickly adjust the lesson to that. That’s it. That’s the main thing good tutors do differently. If motivation decreases, they switch to lighter content, or even transition into non-lesson conversation. If motivation increases, they ramp up the difficulty of the lesson. Tutoring is, say, 80 % motivation management.
Okay, but that undersells it a little. Lesson difficulty is not fixed for any topic; it depends on the student. Annoyingly, it even depends on the student’s level of motivation! The tutor must somehow know what is going to be difficult and what is going to be easy for their student, in every specific situation.
Here’s how I figured it out when I was tutoring. A lesson with me consisted basically of me repeatedly (a) selecting an exercise for the student from their book, and then (b) watching the student work through it.2 You can guess why motivation management is a big part of this! It sounds very monotonous and boring unless done right.
Selecting an exercise for the student is a really fun activity. There needs to be some thematic variety to break the monotony of the lesson. But then the exercise should also be just at the limit of the student’s abilities at that moment, and ideally it should also end up revealing a flawed mental model of theirs. This meant I could only tutor students in subjects I was good at, because I had to quickly skim the exercises and visualise the steps to solve them, to find one in which a flawed mental model would be exposed.
I knew which flawed mental models the student had because that’s what happened in the watching-them-work step. As the student performs the motions, they continuously emit clues as to the mental models running in their head. Sometimes there is something subtly weird about what they do – even if the result works out in the end – and that’s a potential flawed mental model. If I observed something weird, I would choose the next exercise to bring that specific mental model to the forefront. Most of the time, that exercise reveals there was nothing wrong at all, but sometimes the student does something very wrong in that exercise, confirming the suspicion.3 This is also why, with new students, I would start out by going through a bunch of different exercises. Open a random page in the book, do one exercise there, then switch to another random page. The goal of this is for me to calibrate catalogue of mental models the student uses, and find out which are good and which need improvement.
The student needs to find out about their flawed mental model too, of course. Many of my students had a learned response to check the solutions in the back of the book as soon as they had attempted to solve an exercise. I really, really wanted to tear out the solutions pages from their books and throw them in the rubbish bin. Looking at the solutions is not a good way to learn.
When the student had attempted to solve an exercise, I would ask them if they believed their answer was correct. Whatever they answered, I would then ask them to verify their own solution.4 Then why did I ask? The strength of their belief indicates how much work it will take to rip out bad mental models. When we believe incorrect things strongly, we use our incorrect beliefs as knowledge shields to reject the correct belief. It takes more work to get at a misconception when it is used as a shield. How to verify one’s solution is rarely taught in school, so early on with a student I would have to ask more leading questions at this stage. There are three main ways to do it:
- Use a different approach to solve the same problem, and see if they come out to the same answer.
- Perform a feasibility check by coming up with loose, intuitive bounds for the answer that would be reasonable for the solution.
- Recursively: in a multi-step solution, start with the step one is most uncertain about, and verify that step in isolation. Continue the depth-first search until confident in all steps.
Being able to verify one’s own solution is a critical skill, and none of my students had it before I started working with them.
This interacts with motivation management. It is often demotivating for the student to finish a solution attempt when the tutor recognises early on that they are barking up the wrong tree, and that they will fail to verify their solution. In those cases, I would sometimes step in and ask for immediate verification.5 To keep the student on their toes, I would also ask for immediate verification even when nothing at all was wrong. I also recognise that some errors are unproductive (simple slips of the mind) and some errors are productive (reveal a fundamental misunderstanding.) These should be treated differently. Unproductive errors can usually be ignored entirely (and this is another reason to prevent the student from reading the solutions in the book!) or, if they’re going to cause problems, be casually corrected right away. On the other hand, productive errors are a great starting point for discussion.
There is an underlying current here. The student learns in part through the sheer volume of exercise. Without the tutor managing motivation, they would not be doing as many high quality exercises as they are. But they also learn to verify their solutions and diagnose their problems. They learn the right questions to ask to figure out if they are wrong. This is a critical skill that’s – for some reason – not emphasised elsewhere.
Of course, the tutor already needs to do this: they need to continuously form hypotheses about their student’s knowledge, and need to select questions to ask to figure out if they are wrong. Nobody teaches the tutor about their student’s understanding – they have to figure that out on their own. What’s amazing about this skill is that it is transferable. It works when trying to learn anything.
When I was a ta in computer networking and security in university, I would walk around to provide assistance during lab hours. A student might observe something unexpected on their systems, and call me over. I would ask, “What do you think happened?” Sometimes they needed to be convinced they would not be in trouble for giving me an incorrect answer, but eventually they’d respond with a guess.
Then I’d ask, “Okay, and what else could you do that would have a known consequence only if that is true?” Usually, they could think of a way to verify their hypothesis. They’d perform that action, and discover if their guess was wrong or right. If it was wrong, we’d go through the loop again.
I never taught them anything. They figured it out on their own.
This is how experienced people understand systems: they continuously form hypotheses about how the system works, and then they deliberately place themselves in situations which have a chance of invalidating their hypotheses.
I describe tutoring as “giving students an opportunity to reevaluate their assumptions, by asking the right questions to expose the critical mechanisms from their invidial perspectives.”
That’s how tutoring works, but it’s also how to debug broken code, how to learn how a network is put together, and how to learn to drive a race car. That is how to learn.