3. Problems with American Collegiate Education in Mathematics

What was wrong with mathematics education in colleges and universities in the 1980's that led to a perceived need for reform? Many have described the turned-off students and jaded faculty in our classrooms and lecture halls, usually with the intention of blaming someone -- teachers at a lower level, society, administrators, or the students themselves. A more constructive description appears in a recent essay [13] from the Pew Higher Education Roundtable, a product of discussions among a group of 35 science and mathematics faculty, administrators, foundation officers, and program directors. Their thesis is that there is broad consensus on what constitutes effective science education, but institutional barriers to change have thus far prevented widespread implementation. We quote selected parts of their description of the problem. In the following paragraphs the word ''science'' is shorthand for ''science, mathematics, engineering, and technology,'' all of which have had similar problems with education -- with similar solutions.

"The traditional approach is to conceive of science education as a process that sifts from the masses of students a select few deemed suitable for the rigors of scientific inquiry. It is a process that resembles what most science faculty remember from their own experiences, beginning with the early identification of gifted students before high school, continuing with the acceleration of those students during grades 9 to 12, fostering in them the disciplined habits of inquiry through their undergraduate majors, and culminating in graduate study and the earning of a Ph.D. Forgotten ... are most students for whom a basic knowledge of science is principally a tool for citizenship, for personal enlightenment, for introducing one's own children to science, and for fulfilling employment. Forgotten as well are those students who will become primary and secondary school teachers and, as such, will be responsible for the general quality of the science learning most students bring with them to their undergraduate studies. ...

''Although it is widely recognized that an inquiry-based approach to science increases the quality of learning, introductory-level students are often not given to understand what it means to be a scientist at work. ...

''... science faculty have at times openly acknowledged their tendency to gear instruction to the top 20 percent of the class -- to those students whose native ability and persistence enable them to keep pace with the professor's expectations. The fact that others are falling behind and then dropping out is seen not as a failure of pedagogy but as an upholding of standards.''

In short, when we use ourselves as models for our students, we get it all wrong. Hardly any entry-level mathematics and science students are like us. In particular, most students in most calculus courses are in their last mathematics course. And these students are not our replacements. Rather, they are the next generation's parents, workers, employers, doctors, lawyers, schoolteachers, and legislators. So it matters to our profession how they regard mathematics.

It's not hard to trace how we got to be so out of touch with the needs of our students. Those of us educated in the Sputnik era were in the target population of that ''traditional approach'' described above -- just at the end of a time when it didn't matter much that the majority of the college-educated (an elite subset of the whole population) didn't know much about science or mathematics. As we became the next generation of college faculty, the demographics of college-going broadened significantly, new money flowed to support science more generously, and broad understanding of science became much more important. The reward structure for faculty was significantly altered in the direction of research -- away from teaching -- just when we were confronted with masses of students whose sociology was quite different from our own.

This oversimplifies a complex story, but the response of the profession was to water down expectations of student performance, while continuing to teach in the only way we knew how -- as we were taught. We created second-tier courses (e.g., calculus for business and life sciences), we wrote books that students were not expected to read, and even in our ''mainline'' courses we dropped questions that we didn't dare ask on our tests. The goal for junior faculty was to become senior faculty so we wouldn't have to deal with freshman courses. Along the way, we produced high-quality research and excellent research-oriented graduate students to follow in our footsteps. But seldom in our graduate or professional careers was there any opportunity or incentive to learn anything about learning -- in particular, about how our students learn.

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