A lot depends on a teacher's excitement about his or her subject. I think Singapore does well because they invest in good teachers. I think the best idea for schools is to hire teachers in math that have Ph.D's in math, not in education. This applies to learning Torah also. I had the benefit of learning from "Alter Mirer's" people that had been in the Mir in EUROPE. And in school I had the benefit of a great music teacher, Mr. Smart, who was amazingly talented and able to turn high school students into a great orchestra.
Whether in the USA or Israel,- all teaching degrees are worthless. You want to teach math or whatever?--get someone who is good at it.
My main teacher at the Mir, Reb Shmuel Berenbaum was a very deep thinker, but never wrote anything. The classes were in Yiddish, and the later ones were recorded. It would be great if someone would translate them and publish them in Hebrew. During his life, he was considered the most difficult to understand of any rosh yeshivah. People everywhere I went said, ''If you can understand Reb Shmuel Berenbaum, you can understand anything.'' [I think you can get something of a taste of this in the Avi EZRI of Rav Shach.]
