My philosophy

 I cannot help but think of the words "Another brick in the wall"! This is because learning math is like building a wall: one brick builds upon the previous one, and if a certain brick is missing, causing a hole in the wall, the whole wall starts crumbling. So I teach math by starting at the beginning, and making sure that the bottom bricks are all there before I build on them. And if I find a hole in the wall, I will go back and fill it in before trying to build on it. It is important to start at the beginning, and learn things in the right order. And it is important to understand what you are learning. It makes all the difference.Math often gets taught with lots of rules to be memorized, with none of these rules actually making any sense to the student. In my work I often get surprised comments from students, saying "This is so much easier than following all those rules!" and "This makes so much more sense now!" Indeed, if you understand math, there is very little to memorize, and it actually becomes easier and much more enjoyable.Not everything that we call "math" is actually math, though. A big part of doing math is just using ordinary common sense and reasoning - an ability that all humans have and which I've seen demonstrated even in very young children. It never ceases to amaze me how beautifully elementary school children can reason! (Even, and maybe especially, Grade 1's.) But it seems to me that we manage to teach that innate human capability right out of students and by the time they reach high school, their brains are switched off and they seem to be incapable of reasoning any more. A part of my job is to reawaken that ability.One other thing that I try to do is to show students how all of the math that they learn are connected. Math tends to be taught as many separate, loose standing topics. It seems that every chapter has to do with something new, and something that has nothing to do with the preceding work or the work that follows. And after the chapter is done, it is easily forgotten. This is not how math works in the real world! So I show my students how everything is connected and how one can use any of the many seemingly different parts in solving problems. By keeping the work connected and always alive in their minds, I also prevent further holes from forming in the wall.