In a message dated 97-06-29 11:03:36 EDT, you write:
<< We -- mathematics teachers at all levels -- learned well and succeeded by being taught by the lecture method. It's very efficient: the teacher lectures, the student wants to learn what's being lectured about, he/she studies and asks questions about what he/she doesn't know, the lecturer answers the questions (by lecturing) etc. etc. Some people can learn this way and we are them. We like to teach that way because we learned well that way. It's difficult for us to consider (even as a point for discussion) that this may not be the "best" way. But we are not everyone. The second sentence in this paragraph contains a lot of assumptions which just do not apply to the majority of high school students in math or many other areas.
Lin McMullin Ballston Spa, NY >>
Thanks for your message. Your observation is indeed accurate in terms of my experience. I might also add that we were GOOD math students and we found the study of mathematics INTERESTING. If we had not really ENJOYED mathematics, I do not think we would have decided to become mathematics teachers. Many of our studnts neither like mathematics nor are they necssarily good at it. I think that many math teachers "love" mathematics and we can't understand why our students lack interest. Consider what it was that motivated us to enjoy mathematics and you will surely find that what motivated us is quite different than what it takes to motivate our current students.
Your last sentence is particularly intersesting because I have found at times that students are not really interested in anything. Our generation, for example, collected stamps, coins, stickers, and for the most part had hobbies. We had something personal to connect our learning to and something that we were proud of.
Getting back to the discussion of Calculus Reform, I must add that Calculus was the first math course in which I really began to see what math was used for in the real world. It is often hard to show this in the earlier math courses because the students do not have enough of a foundation to really understand real world problems much less solve them with real data. I think that technology has made the teaching of Calculus (and higher level mathematics courses) more accessible if it is used appropriately. I recall taking a college level statistics course and the difficulty we had in visualizing moment generating functions. That experience would not have occurred if I was taking the course now. We now have an opportunity to make concepts clear that at one time were very difficult to visualize.
In this sense, some degree of reform is needed. We as teachers need to become more familiar with how to use technology appropriately in the classroom. This is no easy task. Our methods of teaching and our assessments will also need to change as a result. This last note has nothing to do with the ability level of our Calculus students. This change is needed because we now have additional tools that we can use to facilitate learning.
I agree with Martha Green's comment that "Even the "worst" HS calculus student has got to be a better than average student or he/she never would/could have arrived at "college level" math while in high school! " But I do think that many more high school students that do not take Calculus would be capable of being successful in Calculus if the points I made in my long posting were addressed. And yes many of our Calculus studnts are weak in Algebra. And again, I claim that we have three options - we can continue to say that the Algebra teacher should not have passed them, we can attempt to raise standards earlier on, or we can address this issue as part of our discussion of Calculus Reform. Options 2 and 3 can be (and I would suggest should be) done simultaneously so that eventually our students will have a stronger foundation in Algebra and we can devote more time and resources to the study of Calculus as we should.
Deanna M. De'Liberto Assessment Specialist in Mathematics Hazlet, NJ (732) 888-9339