I note in my local newspaper (The Bellingham Herald. 5/18/09)an article that reports that the local school district has been using a sub-standard mathematics in the schools. I'm not sure what sub-standard means as it was not fully explained in the article. I suspect the school district will return to the more direct and rote method of instructions in mathematics. I have mixed emotions however. I suspect somewhere in the research and other articles that students in other lands are scoring higher then our children in mathematics. It is a pretty standard commentary that is made from time to time.
The problem that I see is that, at least in my local town, we were teaching the children how to discover mathematics and then we test for straight learning of numbers. You teach the children to do one thing but you test for another. And then you get upset because the kids don't do well on your test.
I want to digress for a moment. I taught for thirty two years at my university....my field of study and research was Instructional Technology. Basically it was how to use technology in the teaching/learning situations. This was at a time when computers were just coming into prominence in education.
I had students of all types who were interested on how to use computers in teaching....both undergraduate students and graduate students wanted to know more about how to use computers. Not only did I have both undergraduates and graduates in class, I also had students from foreign countries.....India, Canada, Lithuania, and Indonesia and a few countries I have forgotten. Let me say at the onset that Canada has an excellent educational system. They train their teachers well. And those teachers do a good job. In some areas they do a better job of teaching then we do in the United States....but then I think we do better in a few areas as well. It's a mixed bag.
But excluding Canada, it is my opinion that the foreign students that I had were very bright, intelligent and wonderful people but they did not work well on problem solving. If I gave an assignment, they wanted to know each step of the way. I did more "hand holding" with foreign students then with American students. The American student was able to think through the steps to the solution of the assignment and carry them out. Most of my foreign students could not.
For example.....in one class I wanted students to make color lift transparencies for use in teaching a class. I had several Indian grad students who wanted to know what they were going to teach, which overhead transparencies they would need and how to start. I remember telling them to pick something they would be teaching and this left them in a quandry. Their ability to imagine themselves teaching a subject was very difficult.
My Indonesian students were even more of a problem to teach. They were so use to working in a group that they could not study a subject and bring a report to class to share with the others. They had to do it all together. Now I am not unhappy with my Indonesian students--it was a cultural style of learning an I had to adjust my assignments so they could work together. Margaret Mead, the great sociologist and anthropologist would have loved to study this differences.
My Indian students were very, very bright. They could memorize entire pages of information. With multiple choice and fill in the blanks, they would beat the American students time after time. But when I asked on a test of how they would use something in an educational setting, they couldn't do it.
Returning to my original theme, American students are much better at analyzing the situation, deciding upon some action and then completing the task. Many foreign students are not up to this type of learning.
So when we compare our American students in mathematics with foreign students one has to know what the test are testing. Rote knowledge or problem solving? It is my gut feeling that our students can hold their own quite well in Mathematics.....they might not score well, but they will understand what the goal is and how to get there.
The mathematical argument goes on. If your checkbook is close to coming out correct, be sure to thank your math teacher in your prayers.