I don't think that there is any great mystery as to how best to teach.
You must have an excellent understanding of the subject material, and you must be
able to engage the student.
We learn things by hearing about them, reading about them, and/or doing them. By far, the most important
factor in that equation is the doing.
That is why I try to actively engage the student. I am not going
to be talking or lecturing for the entire session.
The goal is to get the student to solve the problems, not me.
a classroom setting, the teacher can really only force the interaction of one student at a time, leaving the other 29 students
as mere listeners and watchers.
I encourage students to think out loud in trying to solve problems. If they don't know
where to begin, or get stuck, I can suggest the first or next step and work them through it to the ultimate solution. Math
must be learned in steps. You must know algebra to do geometry, and geometry to do trigonometry; and all three to do calculus.
Everyone is different and learns
at a a different pace. I can go at whatever pace that benefits the student. If they are having trouble in one particular area,
I can work with them in that area until they understand it, and then advance to the next level.
In a classroom with 20-30 other students, the teacher wouldn't have the same advantage. They would
have to go at a pace determined by the average of the class. This can be most unfortunate for some, because with math, if
you get lost, you generally stay lost.