I think the most important thing in trying to master a subject is to learn to understand and that this is especially true in math.

Much of the teaching of modern math has just become the repeated use of a growing set of memorized tools to solve problems that often seem useless.

In reality, math, and every other subject is so much more, and if you can begin to understand just what you are doing, the memorization comes naturally (or is even unneeded).

In the first session with a student, I would start by attempting to measure their current ability and to determine what outcome they are hoping for.

From there, I would orient future sessions to working towards that goal from wherever we started.

Working with them, I would try to see what methods of learning best work for them so that they can apply them on their own.

As someone who struggled with motivation during my early years of high school, I understand it can be hard. There doesn't seem to be an easy answer to the question, but I would do my best to show them the rewards of learning more and of setting goals and reaching them.

By stepping back until we have reached a concept the student is certain of, and from there building back to what the student had difficulty with. Given how so much of education (and especially math) builds, it is important to have a solid base, and from there working towards new concepts and skills.

The short answer would be that "it depends on the student," but in general I would likely suggest trying to find something lighter that the student enjoys to read, and encouraging them to read more at that level.

This would hopefully increase their reading ability over time until they are ready to start with higher level material that may not be as enjoyable to read.

Starting off every new concept or idea by having the student work out a problem about it, and having them very explicitly explain every step they took to arrive at their answer.

This is helpful in two ways. If the student gets the correct answer, it helps to reinforce the process and gives them a better understanding of what they are doing.

If the student is having difficulty, then I can see exactly where they are having problems and work with them to "remove the roadblocks."

It simply isn't possible for every student to be excited about every subject, but I think it is certainly possible for everyone to see the rewards in what they are doing and the pleasure of reaching their goals.

As I stated for another question, having a student very explicitly work through challenging problems involving the material helps me to see that they understand it well.

Additionally, having the student explain the material back to me is also a great way to see that they understand it. If they are confident enough to explain it themselves, they know it.

By starting with less and lighter subject matter and slowly adding in more difficulty. This allows the student to feel that they are building their skills without "jumping off the deep end" and overwhelming them with a difficult problem to start.

I think it's important the student feels engaged with, and not someone that I am just working with. I will of course watch them work, and try to see the gears turning in their heads, to understand where they have problems, but I will also just ask them what they are having problems with.

My having a keen eye is no replacement for good communication throughout the process.

By watching how they work, I can alter the way I explain material or how I work with them.

一种奇怪的轶事;当我处理我的问题am struggling with I like to write them on a whiteboard. While there is no functional difference between writing it on a piece of paper or writing it on the whiteboard, I suppose there is just something comforting about having it all laid out in front of me.

It's the little things like this can be bring a student from having a good understanding to possibly having a great understanding.

It would depend slightly on the class level, but generally the textbook assigned for their class is the greatest tool they have. It has hundreds of problems for practice, and the class, especially at the high school level, is often tailored directly to the book.

除此之外,如果我看到他们的书是insufficient or I am working with someone for a higher level class (such as calculus), I will bring additional (generally more difficult) practice problems to work through together.