As a tutor, I have the responsibility of helping students with their various classes that are difficult for them. I am supposed to work with the student in order to answer their questions. That’s the deal, at least in my view.

I’ve been thinking a lot though about what my actual job needs to be. Am I giving the students a false sense of what I’m actually going to provide? Should I be clear about what I expect I can do? Usually, I assume that since a student has sought me out, what they want is for me to make them better at the subject. I think that’s a fine desire, but I don’t know if I can really do that.

(Just to be clear, the tutoring I’m talking about is with regards to mathematics and science classes. Therefore, think problems, equations, mathematics, and so on. It’s usually less about theoretical concepts and more about actually calculating things.)

I’ve written about this before, but in my mind there are two “kinds” of learning that you’re supposed to do in class. The first level is conceptual, and it basically means you understand the idea of what you’re learning. For example, knowing the concept of the derivative means that you’re comfortable with the idea that it’s the slope of the tangent line to a curve at a specific point. You might also understand that it’s essentially done using a limit of bringing essentially two points on a curve arbitrarily close to each other. Knowing this also means you have an understanding of what a limit is. All of this is on the conceptual level.

The second level is then (for lack of a better word), the “calculating” level. This level involves – you guessed it – actually calculating and doing problems. Returning to our example, this would mean calculating $frac{d}{dx}(arctan(x))$ or $x^3e^{4x}$. It would also mean doing word problems that involve the derivative in some way. While the first level gives you an understanding of what you’re doing, this level gives you and understanding of how you do it.

Both levels are important, but we all know that the one that is actually tested on at school is the second level. It’s great to understand the idea, but if you can’t actually calculate or solve a problem, you’re “punished” by way of failing the test. Therefore, the level that is the most “useful” is the second one.

The fear I have is that students enter tutoring sessions with me expect to become fluent at the concepts they struggle with (which means improving on the second level), while simultaneously only going to one session a week with me for perhaps an hour. Now, I don’t want to say that nothing gets done in an hour, but I can say that most students will not be able to improve their second level by just dedicating one hour a week with a tutor. It’s a great start, but it’s not enough. Why? Because improving the second level requires one thing: practice. And lots of it. Much more than can be done in a single hour.

That’s why students need to work on problems when they aren’t with me. Just like learning a language, they need to practice regularly and frequently. That’s the way they will improve.

So how do I see my job? I see it as an opportunity to strengthen a student’s conceptual understanding (the first level), as well as giving a student the tools to make calculations and problem solving go faster (the second level). This means I like to spend a good chunk of time on hammering home the ideas of what a student is doing (instead of just saying it’s what they need to do and leave it at that). Additionally, I’ll then help a student go through several examples where they attempt the question and I try to give helpful feedback.

What I don’t like doing is simply a bunch of problems where calculations are made and no discussion or conceptual thinking is involved. This means that once I’ve looked at a type of problem with a student, we will probably move on to something else and not do a bunch of the same type of problem. The reason is simply that I want to spend as much time as possible laying the foundation for the student. Actually building it requires time on their own, working at their own pace and doing a lot of examples. I see myself as someone who will point them in the right direction, but won’t hold their hand all the way until their destination. That’s a kind of time investment that both I and the student can’t do, so I rather focus on giving the student a clear picture of what to do. using this system, I think I can give students the best chance possible to succeed, but the key is that they have to buy into the process by practising on their own as well. Without that, I can’t be an effective tutor (and I’ve experienced this difficulty before).

When I first started tutoring, I simply went and didn’t think of how I was going to help the student. I thought that I would answer their questions, and be there to check their work to make sure they are doing things correctly.

Now though, I’ve seen a glimpse of what works and what doesn’t. I realize that I can’t give them the skills of solving problems with ease. At least, not without them investing time outside of our tutoring sessions. Therefore, I’ve come up with a new way to evaluate a potential student who wants tutoring. I think that I’m going to tell them something along these lines:

What I am able to do is help you get a conceptual understanding of the subject, as well as the best ways I know to solve problems. However, what I need from you is a commitment to practicing on your own time. I can show you all the best techniques in the world, but you won’t ever really be comfortable with them unless you practice outside of this time. If you can do that, then I can be your tutor.

What I’m hoping this does is send a signal to those who are serious about improving. I need a person who is ready to work hard and improve. That’s the key, above else, to improving. My job to set them on the right track, and their job is to do the work to improve. I won’t be going into tutoring blind anymore, because I’ve learned that it’s not on me, ultimately, which helps them to succeed. It’s on the student.