How best to teach undergraduates has for some time been an important question for many portions of the physics community. The American Association of Physics Teachers (AAPT) has been actively working on the undergraduate curriculum since its founding in the 1930s through committees, meetings, local outreach efforts, and its monthly American Journal of Physics (AJP). Sputnik stimulated a number of programs. The American Physical Society (APS) established a Forum on Physics Education that has become influential and signals the involvement of the research community. An Introductory University Physics Program, funded by NSF, has resulted in several innovative and well-tested course syllabi and texts. Much of the recent activity has been built on the results of the rapidly growing area of physics education research, which now has its own supplement to the AJP. Among the current mantras of the field are:
"It doesn't matter how well I teach, what matters is how much the student learns,"
"Start from where the student is," and
"Really try to understand what is in the mind of the student."
It was in this context that a ten-member physics panel gathered for the first Curriculum Foundations workshop, at Bowdoin College, on October 28-31, 1999. The panel had a vigorous discussion, and in the end found significant areas of agreement on most of the topics on the agenda. To give a sense of the results we reproduce below selected excerpts from the panel's report. (The full report can be obtained at http://academic.bowdoin.edu/math/faculty/barker/dissemination/)
"For success in introductory physics, we believe that it is most important for students to be able to think operationally within the context of a few fundamental mathematical concepts. ...[T]he most important factor is that students gain enough active understanding that they are able to think through and solve a wide variety of problems involving the fundamental concepts in a wide variety of contexts."
"Conceptual understanding of basic mathematical principles ... is more important than esoteric computational skill. However, basic computational skill is crucial."
"Mathematics instruction is worthwhile not only in developing problem solving skills but also in exposing students to 'how a mathematician sees the world.' In the words of workshop participant Tony French, "Mathematics has a point of view, a rigor, that we value but wouldn't attempt and can't afford in the introductory physics classroom."
"Courses should cover fewer topics and place increased emphasis on increasing the confidence and competence that students have with the most fundamental topics."
"There was significant agreement regarding the topics needed by students taking introductory physics courses. There was also significant agreement about the priorities among these topics. This is summarized in the table below."
"Technology should not have a major effect on what mathematics is learned in the first two years. Computers are most helpful for visualization, and for handling problems that are otherwise impracticable. Most instructors of introductory physics are not using symbolic manipulation packages. Spending time in mathematics courses teaching students to use such programs does not directly help in introductory physics courses. However, knowledge of such software is helpful once students enter upper level physics courses."
"The impact of mathematics teaching reform on the performance of students in physics courses has not yet made itself felt. However, there is great potential synergism between mathematics education reform and physics education reform."
Workshop participant Ernst Breiten-berger made a strong encapsulating statement: "The learning of physics depends less directly than one might think on previous learning in mathematics. We just want students who can think. The ability to actively think is the most important thing students need to get from mathematics education."
Guy Emery, who is Professor of Physics Emeritus at Bowdoin College, was the local organizer for the CF Workshop in Physics at Bowdoin College. He spoke about the workshop at the CRAFTY panel on the Curriculum Foundations Project at the New Orleans meetings in January.