### A Tutor’s Job

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.

### Time For Reflection

When you’re going to school, it’s all too easy to dedicate an enormous amount of time to your studies. This is particularly true if you are in a difficult program and want to get the best marks possible. When you have your mind set on getting a certain average, it doesn’t always seem that unreasonable to push other things in your life aside in order to achieve that goal. I know this because I am in a constant struggle to stop myself from doing that, and I can see the effect it has on others that I know.

The problem is that we aren’t machines. After a while, we do get tired. I can’t keep on studying for hours and hours. After a while, I burn out, and I doubt it is only me. We can’t be hyper-focused on one thing all the time. Apart from getting tired and not having enough energy to focus anymore, there’s also the issue of stress. I’ve seen firsthand how stress can affect those who spend a lot of time on schoolwork. The most dangerous example of this is when students start skipping out on sleep in order to finish homework. I am saddened each time I hear of this, because it points to a shortcoming in how they’ve set up their lives. If one is cutting their sleep in order to finish schoolwork, their situation is not good (and I can imagine some scenarios where students don’t have a choice, but those are not what I’m referring to here).

It shocks them when I say I go to bed so early (compared to them), and that in the mornings I run for over an hour on average each day. They don’t get how I can still get my homework done, or how I choose to go to bed before a big test even though I didn’t get a bunch of time to study for it.

To me, the answer is simple: the best way for me to achieve my goals is to treat my body and mind well. That means taking a break from schoolwork at regular times and doing other things I enjoy. That’s why I go running each day and go to bed early. Running gives my body something to do and my mind a chance to just wander. It’s cathartic in a way. I’m not forced to think about school or methods of solving problems (though that is what I sometimes do). More often, I can just focus on the effort, which is a nice change of pace and one that I deem absolutely necessary for my well-being.

Therefore, my best advice to those going to school is this. Study regularly and become knowledgeable at your subject, but never sacrifice your time spent away from studying in order to do more school work. Without giving yourself something else to do to rest and recover, you risk burn out, which will be much worse than taking a regularly scheduled break.

### Interdisciplinary

I have to be honest: I’ve often not taken other disciplines seriously because I’ve always seen physics as the “purest” science there is. That means I would disregard biology, chemistry, geology, and social science, as well as the arts and humanities at large. I think the two other fields which I did have a certain affinity too was mathematics and computer science, since they were about rigorous logic. Other than that, I found the other fields mildly interesting at best, but never something to take too seriously.

Obviously, this shows how blind I was to the world in general. I had projected the somewhat arbitrary categories of education to the universe, even though it wasn’t at all a good reflection. It’s not that I thought that the other subjects weren’t useful or important, but I didn’t see any use for me to care about them. They were subjects for other students to worry about, because I wasn’t going to waste my time doing them.

This narrow view of the world was one I’ve thankfully grown out of. As I read more about science, I’ve started to see how all the subjects we have can be important to the world. Furthermore, I’ve seen how interconnected they all are. It’s nice and all to separate the sciences into their own domains, but at one point, everything boils back down to physics, so there’s a definite link between the sciences. Additionally, disciplines such as computer science are useful to physics, mathematics, biology, chemistry, and basically every other branch of science. With the massive amount of data we’re acquiring in experiments now, it’s so important to be able to know the ins and outs of programming and how computers work in order to do your experiments.

What’s also interesting is how many disciplines are blending into one another. Physics isn’t just in a bubble. There’s biophysics, geophysics, physics in the medical setting, and plenty of other examples in industry. Heck, a lot of theoretical physics couldn’t be done without having some knowledge of how computer programming works. Likewise, you can find these “blends” of disciplines within biology, chemistry, and other sciences. We don’t have silos anymore.

The other thing to think about is that some of the most interesting problems in science today will probably be achieved by merging different sciences. Just to give one example, the idea of consciousness being information-processing can be tackled on the side of living organisms, but it can also be looked at through the lens of AI and computer science. Of course, if this is true, it will be interesting to analyze the various particles and properties needed in order to exhibit what we call consciousness. This isn’t a one-discipline problem. It’s something that many of the sciences can tackle.

This is why I’ve been trying to do more to learn about other disciplines as well. It’s fantastic to learn more about physics, but I think it’s equally important to look at subjects like biology and chemistry, as well as computer science sand mathematics. I’m not saying that I want to become an expert in all of these disciplines (besides, an expert would only be on one branch of that discipline), but I want to see how the sciences connect together. I think it’s my duty as a scientist to make sure I keep myself knowledgeable about other fields in addition to my own.

And lastly, the arts and humanities. While I respect the wonderful work they do, it’s not an area that I find myself as interested in, at least professionally. I’m a person of science, and so I tend to stick within scientific fields, though I can see the use of philosophy (however much I may dislike some aspects) as an important part of discussing how we govern and build an ethical and just society in the future.

The point I wanted to share here is that school makes it too difficult to be aware of the various disciplines outside of your own. My classes are solely in physics, mathematics, and the odd computer science course. Therefore, I don’t learn about biology, chemistry, or any of the social sciences. As such, the picture I have in my mind of these fields is woefully wrong (I’d imagine), since I have little to no exposure. I think this is a problem, and so I try to address it by reading books and following smart authors in other fields who can bring me information on things I’ve missed from my own education. Of course, it doesn’t mean the information will be useful to me (in the sense that I’ll use it in my life in what I do), but I think there’s something great about being able to know a little about various disciplines. As long as I stay mindful of how little of a picture I’m getting from these small bits of information, I can develop a more fleshed-out story of what science has taught us, and that can only be a good thing.

Remember, as you go further into school, your work gets narrower and more focused. Don’t forget about everything else that is going around you, because you will really miss out if you ignore it all.

### Playing With An Idea

When we learn new concepts in class, I think we tend to focus on what we’re taught, confining ourselves to the scenarios that were introduced in class. To be fair, that’s not a bad strategy, since most professors are only going to test the material that was explicitly seen in class. As such, there’s an implicit sort of agreement that students are not going to see any “surprises” on the test (not the euphemism).

But even though that’s true, I think there’s a huge benefit to looking at more than just the scenarios and cases that are outlined in class. In particular, I think it’s a useful practice to look at the edge cases of a concept, as well as alterations on the regular scenarios you’ve seen in class.

Just to give a brief example, consider the regular kind of differential equations you see in an introductory course. During this course, one learns about the various techniques that can be used to solve differential equations. One usually learns about integrating using the integrating factor and integrating via separable equations before they start learning about the characteristic equation.

If you were boring and didn’t like exploring, you’d cleanly separate each use case out and find ways to identify when one method should be used versus another. Or, you could be like me and try to skip the first techniques that I learned and try to apply the characteristic equation to first order differential equations, for example. It was here that I was able to try and see how the different methods could work and produce the same answer for a given equation. It also helped me gain an intuition about which methods are better for a problem.

Being good at a certain subject in mathematics or science can seem to others as though you have a magical ability to see things they don’t. One way to hone this ability is to explore different ways you can go about answering the same question. This may seem boring and repetitive at first, but the real reward is in the potential application of this experience to future problems. When you encounter a new problem that has given others pause, you might be able to solve it because you’ve already explored different ways to tackle a problem, and one of those ways can you help you out.

If you want to be good in mathematics and science (at least, on the theory side), it’s always a good idea to work on answering questions with multiple methods.