Summary and Challenges

At the urging of the mathematical community, the National Science Foundation began its efforts in undergraduate curriculum reform with calculus, which was seen to be the capstone course for secondary mathematics and the keystone course for collegiate mathematics. This strategy for eventually influencing all of the secondary and tertiary curricula in mathematics is working. Calculus reform is a viable movement that has turned out to be highly consistent with the NCTM Standards, and therefore with the emerging reform of school curricula.

Reformed calculus courses are leaner in terms of the number of topics in the syllabus, but much richer in actual content. They have been enriched by balanced emphases of symbolic, numeric, and graphical representations, by reading, writing, and speaking as learning and assessment tools, by use of appropriate technologies (calculators and computers), and by extended and realistic problems.

Calculus reform has come to mean reform of pedagogical methods as much as reform of the curriculum. Most reformers are beginning to pay attention to the literature on learning, which contains a strong constructivist message: Listening to lectures is not an effective way to learn -- but active involvement, especially in small group activities, is. The same literature also tells us that we can set high expectations for our students, and, with proper support, they will achieve those objectives. Finally, this literature tells us of the importance of posing problems that are interesting and meaningful to our students at their current stage of development -- not problems that would be interesting or meaningful only if they had already achieved some higher level of mathematical sophistication.

Technology, ranging from inexpensive scientific calculators to powerful symbol manipulation systems, is playing an important role in shaping both content and methodology -- content because the existence of technology alters the relative importance of specific techniques, and methodology because technology offers opportunities for creating new learning environments (e.g., laboratories).

Now that many of us are beyond the first flush of excited volunteers, we are finding a lot of resistance and negative reaction from students who don't want us to shake up their comfortable relationship with "math," no matter how distasteful that relationship may be.

Reform in calculus instruction places fundamentally new demands on us as teachers. We have to be open to new ways of relating to students in the classroom -- indeed, be willing to become novices again. Administrators have to invest new resources in developing the teaching faculty, providing for an appropriate faculty-student ratio, and supporting workshops and other means of upgrading skills. Furthermore, we have to devote more of ourselves to teaching as a profession, engaging in dialogues on matters of pedagogy, forming support groups, and -- perhaps most important -- valuing the profession for which we get paid. The rewards are worth it: We may not ever agree that we get paid what we are worth, but nothing quite matches the thrill of seeing students' eyes light up when they really understand.

There is good news and bad news, both from that great philosopher of the comic strips, Pogo. The bad news:

The good news:

| Introductory page |
| Movement | Methodology | Content| Students | Instructors |
| References | Bibliography |