Active learning will engage the student's mind to construct meaningful knowledge of lasting benefit. Instead of repetitive remedial work, the student will be challenged to explore exciting areas of mathematics that are recognized steps along the pathway to professional stature. Many such students are quite capable of advanced work in science and mathematics, but need to have their interest rekindled. To attract these students to the collegiate study of mathematics, many institutions have introduced innovative courses in quantitative reasoning, workshops in elementary mathematics, and first-year mathematics seminars as alternatives to the traditional precalculus course. Much of this exploration takes place naturally in liberal arts colleges where the environment encourages curricular innovation.
Few students learn a mathematical idea well the first time they encounter it.
Reinforcement and broad support are crucial to students' success in mathematics, as well as in science. Enhancing self-esteem, especially in those who may have not had a strong school mathematics background, requires effort from the whole campus community. Few students learn a mathematical idea well the first time they encounter it. Science faculty need to recognize this need for multiple exposures as a natural part of all learning processes, and not as a failure of the student to learn or of the mathematics instructor to teach. Students' mathematical self-esteem can be destroyed as easily in a science class where ridicule rains on those who have forgotten a key formula as in a mathematics class where the lecturer takes far too much for granted.