There are many ways to solve a problem. Understanding is key, not memorizing a recipe.

After getting to know each other briefly, I like to see where they first started struggling in that particular class. Because math builds on itself, it's often difficult to jump straight to the current material if its base is not understood. It's also great if we can review some graded homework/tests so I can see how they work and what their class is expecting.

There are two main skills to help independence: critical thinking and learning how to study. Critical thinking will come naturally through greater understanding of the math. Learning how to study will come from working together with the textbook, class notes, and technology. We will work on how to read math texts interactively and find what works for them individually.

The best motivation is understanding the material and seeing its applications. When you see that you can do it and don't feel lost in class, it's so much easier to keep at it. Knowing why and how it's used in the real world also helps keep things from seeming futile.

First is attempting a different angle. There's often many ways to look at a concept, and all it takes is for one to stick, and the rest will come more easily. This can be as simple as using different terms or visuals, or as involved as interacting with something. If that doesn't work, it's often important to see if they understand everything that skill/concept is based on. The problem may be something less obvious not being fully understood from earlier.

This is common with math texts, and it is important to take things slowly, and to be interactive with it. A math or science textbook should never be open without a piece of paper next to it solving the problems alongside. Reading something together can help, and learning where to question "what do they mean by this?" Rephrasing in their own words as we read along can greatly help comprehension.

Watching someone solve something themselves, with them explaining why an action is taken and me guiding them towards the right direction. This way, they develop their own methods without hitting dead ends. Sometimes I will solve a problem, asking them to guide me to what they would do next, and that can also be helpful for them to step back and see what they are doing at a distance.

Sometimes showing a neat/useful trick the subject provides can be really helpful, or showing how it connects to a topic they are interested in. People are often surprised how much math and physics are intertwined with their favorite hobbies.

Seeing them solve a problem without any guidance from me, and explaining why they took each step throughout. Taking problems they've solved and changing key parts to see if they understand how the problem has evolved.

It's important not to overlook improvements. When they get something right and it's clicking for them when it didn't before, they need to know and it should be applauded. That way, when they hit another roadblock, they know they can get through it, just as they did before. It can also help to let them know how myself and others went through many of the same difficulties and that it gets better.

Listening to them, and looking over their work. Most people have an idea of their needs, and sometimes a secondary area can be observed when going through their work or working with them.

It depends on the need. I try to bring in more visuals or more lecturing or interaction depending on their preferred learning style. It's about what they are most comfortable with, so they are more open and can understand more easily.

Mostly writing things out, however it is often useful to use calculators, web resources, and their textbook.