8. Renewal in Calculus Courses

It would be foolish to pretend that reformed calculus courses were designed to implement the messages of cognitive psychology or neurobiology. Very few of the developers a decade ago had any knowledge of these subjects. Rather, we had some instinctive ideas about what to try. Some of those ideas were reinforced by our experiences and became the basis of our courses. Some ideas didn't work and were quickly forgotten. This is selection at work -- but, in order for it to work, we had to challenge our prior knowledge.

Virtually to a person, reformers became committed constructivists, even though few of us knew that word (in the cognitive sense). In varying degrees, we discovered empirically all seven principles of good practice. Our best materials are the ones that encourage students, singly or in groups, to complete the learning cycle -- often. Our best programs incorporate in some measure all seven of the skill groups identified by employers. And we have learned appropriate ways to use technology to serve learning objectives.

The reader interested in theories underlying renewed calculus courses, planning and implementing such a course, and assessing student learning should start with [14]. For additional help on using cooperative learning groups, see [8], and for constructive suggestions for coping with institutional barriers, see [13].


| Title page |
| Reform or Renewal? | Students | Problems |
| Cognitive Psychology | Brain Research
| Technology and Learning | Technology and Curriculum |
| References |