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In the four-month period following the Rethinking the Preparation for Calculus conference in October 2001, there were three other invited conferences regarding the undergraduate mathematics curriculum.
CRAFTY's Curriculum Foundations Summary Workshop (November 2001), organized by Bill Barker and Susan Ganter and supported by the NSF and the Calculus Consortium for Higher Education . CRAFTY (the MAA committee on Curriculum Renewal Across the First Two Years) had previously organized a series of 11 workshops in which leading educators from 17 different quantitative disciplines came together to discuss and inform the mathematics community of the mathematical needs of their students today. The summary workshop was held to unify the suggestions from the individual workshops.
The Forum on Quantitative Literacy (December 2001), organized by Bernard Madison, sponsored by the Woodrow Wilson Foundation and funded by the Pew Charitable Trusts .
Reforming College Algebra (February 2002), organized by Don Small on behalf of the MAA Task Force on the First College Level Mathematics Course and supported by the Consortium of Historically Black Colleges and Universities .
Each of these conferences focused on the mathematical needs of students in courses below calculus. Although the CRAFTY Curriculum Foundations Workshop did not look at these courses specifically, the recommendations from most of the quantitative disciplines were directed at courses such as college algebra and precalculus, because these are the courses that provide the mathematical foundation for students in most other disciplines.
The calculus reform movement of the last decade or more has led to major changes that include an emphasis on geometric and numerical ideas as a balance to symbolic manipulations, student projects, realistic applications via mathematical modeling, the use of technology, and a more active learning environment. These efforts were intended to transform calculus into a pump, not a filter.
But if we are to change calculus, we must also consider how we “fill the tank”; that is,
how do we increase the numbers of students who proceed on to calculus?
how do we improve the mathematical experience of both those students and the ones who have no intention of going on to calculus?
Each year approximately three-quarters of a million college students take some variety of precalculus course; yet only a small fraction of them ever go on to start calculus. Most of those who do take calculus display a singular lack of retention of the material they were taught and often cannot complete calculus. This is a dreadful indictment of the effectiveness of traditional precalculus courses. They neither motivate the students to go on in mathematics nor adequately prepare them when they do continue, especially in view of the changing curricula in calculus and also the client disciplines.
Several years ago, Richard Riley, secretary of education in the Clinton administration, challenged the mathematics community to address the problems of articulation in mathematics education between high schools and two- and four-year colleges. Riley called for this national initiative, through the National Research Council, because of the growing breakdown in the once smooth transition between high school and college mathematics, as well as the differences between mathematical experiences in different colleges when students transfer from one institution to another.
In large measure, many of the problems with mathematical transitions are due to the rapidly growing reform movements in mathematics education, both at the secondary level and at the college level. NCTM's efforts to promote a school curriculum based on their Standards documents are bearing fruit around the country, as described in other articles in this volume. Instead of the relatively uniform secondary curriculum that most of us went through, many schools across the country have implemented a variety of reform curricula that provide students with very different content and very different teaching and learning environments.
There is a major emphasis on conceptual understanding, not just routine manipulation;
There is an emphasis on realistic problems, not just artificial template problems whose solutions are to be memorized and regurgitated;
There is an emphasis on mathematics via discovery, not mathematics as a collection of facts and procedures to be memorized;
There is an emphasis on the use of technology;
There is an emphasis on writing and communication and working collaboratively.