ScottPowell wrote in response to a sample trig quiz that was posted: >Wow does this sound like a really exciting summer;-) Do they have the >option of doing thousands of these problems? I am sure there future client >will be really impressed with the fact they can expand cos(A-B). Give that >man a bonus!!
This story has a point, I hope: My husband was commenting at dinner one night about a fellow worker who was in danger of losing his job due to a downsizing of the organization.(We all know about downsizing. It's where people lose their jobs so that corporations can continue to pay phenomenal salaries to the top management and keep the stockholders happily making money.) The organization is involved in commercial use of scientific research in geology. He was offered a slightly different position but he had to pass an examination in mathematics in order to qualify for that position. It was not an advanced math exam: just what we would call arithmetic and understanding the basic operations as applied to scientific notation, the meanings of prefixes like milli, pico, nano, deci, centi and so forth. This man was frightened. He had been perfectly competent in his former scientist-support position. But that position was simply being eliminated. Now he needed to demonstrate an easy facility with mathematics...Yes, the company has computers...very expensive, elaborate and all over the place computers. But his employer felt it was essential that he demonstrate competence in basic mathematics in order to be allowed to continue to provide for his family by working at this company. When I heard of his plight I offered to work with him in order to prepare for this exam. You can be sure we did lots of problems quite repetitively. I also tried to *focus* on the meaning of the operations. But he needed to know efficient algorithms to get correct answers fast. He needed to memorize the terms that he would need to communicate accurately with the community. It wasn't fun. He worked very long and hard at it. But it was more fun than "losing his home and not eating".
Was he unique in this experience? I don't know. Did he at one time think he wouldn't need all that stuff like sin, cos(A-B)? I would guess, probably.
This is a reality that I try to keep before me as I work to implement change in mathematics instruction. Yes, keep the focus on understanding and meaning. Help people to see that they can construct mathematics. Teach so they are in control of the material they are learning. But then carry that understanding forward to some form of completion, with competence, accuracy, efficiency and rigor. With the necessary shift in focus toward problem solving and constructivism some (myself included) have lost sight of the necessity to carry the job to completion. Where that line of completion is at this time I am not quite so sure. I'm still thinking about this.
Lucille L. Peterson Math Leadership Program Bank Street Graduate School of Education Tel: 212-875-4665 610 West 112th Street Fax: 212-875-4753 New York, NY 10025 E-mail: firstname.lastname@example.org