A contemporary analysis of the content of mathematics for liberal education at the college level.

摘要

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a survey to determine the present content of such courses.The review contains an analysis of the purpose of liberal arts education. Educators and other thinkers, past and present, are quoted to reveal their views on mathematics education and liberal education in general. The consensus is that mathematics should be included in a liberal education because it provides practice in logical reasoning, because it is important knowledge both as an end in itself and as a foundation of the sciences, because it is an important tool in allowing citizens to deal with current issues, and because it has an aesthetic value of which students should be made aware. Several different approaches to the liberal arts mathematics course are identified. The course has been influenced by other mathematics courses, including discrete mathematics, finite mathematics, and elementary teacher-training. Other trends include humanistic mathematics, mathematics and Western Civilization, multicultural mathematics, history of mathematics, quantitative literacy, applications of mathematics, and modeling.The survey examined all colleges and universities in three states, California, Pennsylvania, and Ohio, to determine the enrollment, topics taught, and textbooks used in liberal arts mathematics courses. 173 institutions out of 211 in California offer such a course, 120 out of 135 in Pennsylvania, and 74 out of 103 in Ohio. The most popular topics were found to be probability, statistics, geometry, combinatorics, finance, functions, graph theory, and logic. Popular textbooks include those by Angel, Bennett and Briggs, Blitzer, Burger and Starbird, COMAP, Johnson and Mowry, Miller, and Tannenbaum.It is concluded that the objectives of a liberal education have influenced the approaches to the liberal arts mathematics courses as well as the choice of topics.