> not everyone has to be destined to be a teacher. It is important to know that you are not (if you are not), and to thoroughly appreciate those who are.
Well, this should be understood, but it's not. Especially in the current academic setup the professors - experts in the field - should have the skill to transmit their knowledge to students. Unfortunately, many spectacularly fail. They'd better focus on research and leave the job of teaching to more able individuals.
My pet peeve is linear algebra. You can present it in an extremely boring way, and this is what most professors do. It's like they wanted to make this fascinating subject as repulsive as possible. Maybe you could get away with it 50 years ago, but now we have all the tools and areas of application that make teaching linear algebra in the old way a crime.
Linear Algebra was another one I had a tough time with until I found the right "teacher."
Gilbert Strang's MIT Open Courseware series to the rescue. He wrote the textbook I was using and was also pretty entertaining. My college professor made the concepts sound terribly complicated, but Strange made them highly approachable and interesting.
> I am convinced by the experience of others: It is good for students to work in small groups. There are so many reports about the success of this idea that it has to be accepted as valuable. It will be implemented in different ways, and the comments from Ithaca about group projects are representative:
> "The approach changed the students' attitudes toward mathematics. The projects engage the curiosity of the good students and challenge them, but this does not come at the expense of average and weaker students. In fact, cooperative work with good, motivated students bolsters the others.'
> "A common fear about groups is that one student may do nothing but still get the same grade as the members who did all the work. This has not been a great problem . . . (others say the same). Students experience cooperative learning. They talk to each other about mathematical ideas and they form friendships with other mathematics students."
> I personally believe that we too often lose sight of the human part of learning mathematics.
Well, this should be understood, but it's not. Especially in the current academic setup the professors - experts in the field - should have the skill to transmit their knowledge to students. Unfortunately, many spectacularly fail. They'd better focus on research and leave the job of teaching to more able individuals.
My pet peeve is linear algebra. You can present it in an extremely boring way, and this is what most professors do. It's like they wanted to make this fascinating subject as repulsive as possible. Maybe you could get away with it 50 years ago, but now we have all the tools and areas of application that make teaching linear algebra in the old way a crime.