Understanding systems

Some time ago I read an article on what makes a good tutor.11 I cannot find<br>the article again, but in the process of writing this I came across the book<br>Improving Academic Achievement, which has a chapter that may have inspired<br>that article: The Wisdom of Practice: Lessons Learned from the Study of HIghly<br>Effective Tutors; Lepper and Woolverton; Academic Press; 2002. It explicated<br>many of the things I do when tutoring, so obviously I thought it was a great<br>article. When I had a side gig as a private tutor, I covered mostly maths and<br>physics, so that&rsquo;s how I&rsquo;ll frame things in this article. The same thing applies<br>to other fields too, but it might be harder the further away from maths they<br>are.

The main thrust of the lost article (as I remember it) was that effective tutors<br>are highly empathetic to the level of motivation of their student, and they<br>quickly adjust the lesson to that. That&rsquo;s it. That&rsquo;s the main thing good tutors<br>do differently. If motivation decreases, they switch to lighter content, or even<br>transition into non-lesson conversation. If motivation increases, they ramp up<br>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<br>topic; it depends on the student. Annoyingly, it even depends on the student&rsquo;s<br>level of motivation! The tutor must somehow know what is going to be difficult<br>and what is going to be easy for their student, in every specific situation.

Here&rsquo;s how I figured it out when I was tutoring. A lesson with me consisted<br>basically of me repeatedly (a) selecting an exercise for the student from their<br>book, and then (b) watching the student work through it.22 You can guess why<br>motivation management is a big part of this! It sounds very monotonous and<br>boring unless done right.

Selecting an exercise for the student is a really fun activity. There needs to<br>be some thematic variety to break the monotony of the lesson. But then the<br>exercise should also be just at the limit of the student&rsquo;s abilities at that<br>moment, and ideally it should also end up revealing a flawed mental model of<br>theirs. This meant I could only tutor students in subjects I was good at,<br>because I had to quickly skim the exercises and visualise the steps to solve<br>them, to find one in which a flawed mental model would be exposed.

I knew which flawed mental models the student had because that&rsquo;s what happened<br>in the watching-them-work step. As the student performs the motions, they<br>continuously emit clues as to the mental models running in their head. Sometimes<br>there is something subtly weird about what they do – even if the result works<br>out in the end – and that&rsquo;s a potential flawed mental model. If I observed<br>something weird, I would choose the next exercise to bring that specific mental<br>model to the forefront. Most of the time, that exercise reveals there was<br>nothing wrong at all, but sometimes the student does something very wrong in<br>that exercise, confirming the suspicion.33 This is also why, with new<br>students, I would start out by going through a bunch of different exercises.<br>Open a random page in the book, do one exercise there, then switch to another<br>random page. The goal of this is for me to calibrate catalogue of mental models<br>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.<br>Many of my students had a learned response to check the solutions in the back of<br>the book as soon as they had attempted to solve an exercise. I really, really<br>wanted to tear out the solutions pages from their books and throw them in the<br>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<br>believed their answer was correct. Whatever they answered, I would then ask them<br>to verify their own solution.44 Then why did I ask? The strength of their<br>belief indicates how much work it will take to rip out bad mental models. When<br>we believe incorrect things strongly, we use our incorrect beliefs as knowledge<br>shields to reject the correct belief. It takes more work to get at a<br>misconception when it is used as a shield. How to verify one&rsquo;s solution is<br>rarely taught in school, so early on with a student I would have to ask more<br>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<br>to the same answer.

Perform a feasibility check by coming up with loose, intuitive bounds for the<br>answer that would be reasonable for the solution.

Recursively: in a multi-step solution, start with the step one is most<br>uncertain about, and verify that step in isolation. Continue the depth-first<br>search until confident in all steps.

Being able to verify one&rsquo;s own solution is a critical skill, and none of...