I adapt to the needs of each individual student. Some students are better visual learners, and some need more "active" means of engagement. I also make sure to get to the root of why a student might be having trouble. Often it's not the calculus that's hard; it's the missing algebra skill underneath that needs a little bit of practice.

First thing I'm going to do is just make sure the student and I are comfortable with each other. I can see if we have any common interests that will help us relate a little more, and hopefully create a friendly atmosphere. After that, I'll dig into what they're working on, and ask if there's a particular problem they feel like they're having with the subject. As we explore those issues, I can figure out where the underlying problems are and get to work fixing those to make the subject a little easier for my student.

The most important result for me is making sure a student fully understands what they're trying to learn. While some tricks and shortcuts might be useful to learn eventually, it's critical that they actually understand what it is they're doing, rather than just trying to get through the problem. To get to that point, I always make sure the basics are in place. Often a student is struggling with a complicated problem because they lack a basic skill they missed at some point. Once those basic skills are built up, I focus on letting the student guide themselves through the problem, rather than just telling them the answers. The more they're talking, and they less I talk, the better things are going.

The most important thing is a sense of progress. I would remind a student of what they've managed to learn so far, and how they're better than they were before. If they have positive test or homework results, I would also point to those as a way of showing how things are working and improving.

The first thing I'm going to do is make sure they understand the underlying basic skills first. It's possible a student is getting hung up because they don't know how to progress through a problem, even if they know what they're trying to do. Beyond that, I would revisit simple examples and build up to more complicated situations from there. This not only helps develop that skill, it also builds up confidence, and that's often just as important.

The best way to deal with complicated passages and unknown vocabulary is to try to identify context clues. I would have the student point out what parts of a sentence or paragraph they do know and guide them to relate that to the specific portions they don't understand. I would also offer simple synonyms for complicated words in some situations.

First and foremost, I want to be friendly and welcoming. I also want to make sure I don't seem judgmental just because a student doesn't understand a particular concept. Building that rapport will make the student more accepting of my advice, and will make me seem more like a friend rather than a harsh teacher.

Building up confidence is key. If they're struggling with something, I'll revisit earlier skills and simpler examples that they can use to prove to themselves that they can handle these new problems. I also need to make sure I'm excited, too. If I'm enthused by what they're doing and the progress they're making, the student is more likely to be excited as well.

It's understandable that a student will sometimes fib and say "Yeah, I get the problem.” If it's a subject they really don't enjoy, there might be some pressure to move on so they cannot have to think about it anymore. I would make sure to cover an extra example in those situations, and I would make the student solve it on their own to prove to me they're ready to move on.

Start simple, and build up from there. A complicated problem can seem overwhelming, but often the problem just comes down to a few different ideas put together, each of which the student already understands. By revisiting those concepts individually, and showing how they come together, the student can feel less intimidated, and by extension feel better equipped to handle complex problems. Positive reinforcement also goes a long way. Never complain about how "slow" they're solving a problem. Instead, I would make sure to acknowledge any progress, even in small amounts.

The best way is to ask the student directly. "What are you working on right now?" "What's giving you issues?" "What do you think you need some help with?" As I begin to work through problems and examples, I'll assess whether there's some basic skills which might be lacking. If I see that there's something simple that can be easily fixed, I'll always be happy to pause things on the current subject to refresh on an older one.

In the beginning, I would take a generalist approach to tutoring. Once I see the student having trouble understanding one of my explanations, I'd shift to try a different approach. There's a few different directions I could go, and every student is going to respond a little differently. Some students need to hear the problem phrased in a different way. Some of them might need some visual representation of the problem rather than just hearing or reading it. Once I figure out what works best, I can make a note of it and stick to it, even teaching the student how to "coach" themselves when they see a complicated problem.

I would be equipped with the standard paper, writing materials, and calculator. That's just the basics, however. I would also try to have a whiteboard or similar material available to draw on. I'd also keep a notebook available where I keep notes about the student themselves, things like what they've been working on, what they're struggling with, and what kinds of methods work best to help them understand concepts.