[taxcontrol]

My trig teacher started us with fractions and ratios. Spent three weeks on it till we were bored out of our minds. We kept hanging in because he had the day that we were going to start Trig marked on the calender. So we actually started Trig 3 weeks late.

When the day came, he drew a circle and told us that all of trig can be expressed as the ratio between the adjacent, opposite and hypotenuse sides of a triangle. You could hear the whole class go .... “oh wow” as the light bulb came on.

We finished the year 3 weeks ahead of schedule because we “got it” up front. And in my mind, the review of fractions and ratios was WELL worth the effort.

[notbuyingit2]

Sounds like you had a great teacher who really understood his subject.

[Vigilanteman]

What you described is basically how they teach math in Japan. Thin texts books. Lots of drills. Multiple ways to solve problems. My daughter took one of those standard tests in Japan and was pretty much average, just slightly below the 50th percentile. We moved to the United States next year, one of the better school districts in the state, she takes the same type of test and suddenly she's in the 92nd percentile for math.

Go figure.

Below the college level, the Japanese don't even divide trig, algebra and geometry into separate subjects. It is all one continuous flow. They even learn basic calculus in high school, not all that different than what I needed to earn a graduate degree in economics.