I think there’s a way you can assign grammar and math questions that yields roughly the same benefits as index fund investing: higher ‘returns’ for your students, less work for you. I can’t tell if others agree – in fact I think many may not! – so I thought I’d explain it and see what everyone thinks.
The theory behind index funds is that the market as a whole goes up a lot over long periods of time, so if you can just invest in the market itself (or in a basket of stuff that performs very similarly to the market), then you can enjoy a great financial return without doing much work.
Of course, there are some very skilled investors who can regularly beat the market. Someone may know a lot about a certain sector, or develop an insight that has eluded millions of other investors. But *most* people who attempt to beat the market end up spending a lot of time analyzing companies, following trends, and indulging hunches…only to receive a lower return. They would have made more money if they’d just thrown their investment in an index fund and forgotten about it.
In my analogy, the ‘stocks’ are the specific question types, and the ‘money’ is time. I want to invest my (and my students’) time in questions with three attributes: 1) likely to show up on the test 2) likely to be missed by a student 3) not hard for a student to learn. If a question has those three qualities, I don’t need to know anything else about it. It is my tutoring version of index fund investing: I will spend homework and session time on these questions blindly, without any further research or thought.
In effect, I’m trying to maximize expected values for the questions my students work on. If something has a 100% chance of appearing on the test, the student doesn’t know that concept at all, and I can teach it to them in five minutes, with minimal required follow-up, then that’s a fantastic use of our time. On the other hand, if it has a 2% chance of showing up, or they already know it, or it’s going to take hours and hours to teach it and retain it, then it’s not worth our time.
So how do you curate these questions? I believe it’s better to mostly outsource this. Don’t pick individual questions – just put a collection of high value questions in front of students and respond to the ones they miss. For those dreading the inevitable product placement…I won’t even mention my product. There are lots of ways to do it. Practice tests are themselves a form of this. So are redos. From the little I know about Anki and Quizlet, I think you could rig them to do this as well. You basically just need these components: 1) a high-quality pool of questions 2) a way to filter unwanted questions based on student responses.
There are some great tutors who can effectively ‘beat the market’. Some of them may be reading this post! These tutors meticulously tag questions from real tests, log student results, analyze those results by various tags, then produce targeted assignments for their students. And they get great results.
However, that approach takes a ton of work, and it wasn’t worth it for me. The questions I spent hours cobbling together were not any better than my ‘index fund’ questions. I actually experimented with this for a long time. I would think of 20 questions I wanted a student to work on, and then I’d generate 20 ‘index fund’ questions and see which group was better. And the index fund questions were always at least as good or better. They always included important questions that I thought we’d covered but hadn’t, or that I’d meant to check up on but hadn’t.
The problem is this: it is impossible to know the exact ‘learning state’ of a student. Do they remember the percent increase variation you taught two months ago? Do you need to teach them everything about noun/verb agreement, or just a couple variations? Have they ever been taught the powers of i? They should have learned basic versions of SOHCAHTOA…but did they actually? And if you don’t know the student’s learning state, you can’t calculate the expected return for spending time on it, no matter how right it might feel to dig in that matrix question they just missed.
Tutors out there – I’m curious to hear what you think! Are you willing to fire your intuition and hire a rule-based system?