Earlier I mentioned that teaching mathematics is improving. There are two ways this has happened:
1. Technology and techniques of teaching have improved. Problems that were once difficult to solve are now solved easily with a calculator. The calculator has not made it easier for the students, it has meant they can be taught more. Instead of spending time teaching students how to use trig tables I am teaching how to solve problems using trig. To all of those people who grumble that things like the graphing calculator have made math easy, I ask, “Do you really want to go back to log trig tables?”
The online homework systems are very good and getting better. Used properly, they help students tremendously.
Classes are moving away from the lecture mode and towards having students spend class time doing problems. People do not learn algebra by watching people do it any more than the can learn to shoot baskets, drive a car, or play the piano by observation only.
2. Content has become more relevant. I never want to teach a problem that starts out “Five years ago, John was twice as old as Mary.” Who cares? There are more problems involving real data. It is perfectly reasonable to give actual population data and ask the students if the data looks more like linear or like exponential growth. Then they find appropriate model and project the population to a future year. Of course this is a simplification of real life, but it comes closer to being relevant than the age problems.