FEBRUARY 1994 Supersedes all previous printings
MATHEMATICAL REASONING (MAR) (Foundation Studies)
Mathematical Reasoning: A course that develops a student's understanding of mathematics and mathematical problem-solving.
- A course in mathematical reasoning must focus on topics that develop a student's understanding of mathematics and mathematical problem-solving skills beyond the level the student attained in secondary school. These topics should illustrate different aspects of mathematical reasoning (for example, quantitative, symbolic, geometric) and the interplay between them.
- In this course, students must be involved in solving problems that require them to use creativity and insight.
- The course must provide practice reading mathematics and explaining mathematics.
- The course must place the topics studies within some broader context, for example, the origins and historical development of the topics or applications of the topics to other disciplines.
Comments: (Numbers correlate to numbered guidelines)
1. Three to four years of high school mathematics are recommended for admission to St. Olaf; this usually includes elementary and intermediate algebra, geometry and precalculus. A course in mathematical reasoning should not simply duplicate the content of these courses. It may go beyond previous experience by assuming the mathematical maturity developed in earlier courses or by building on the content of earlier courses, by either extension or application.
Courses whose primary focus is not mathematics should comprise mathematics as a significant component of the course.
2. While drill on techniques is necessary, students should solve problems that require more than applying formulas or executing clearly-defined algorithms. Such problems could involve making extensions or generalizations of known results, developing mathematical models, or exploring examples to make conjectures.
3. Explaining mathematical ideas and arguments, either verbally or in writing, serves two purposes: it helps clarify students' thinking about problems and concepts and it improves their facility with mathematical language. For example, students could be asked to describe their approach to problems, to justify their answers to questions, or to give examples to illustrate concepts and theorems. Practice in reading mathematical resources enhances students' ability to learn more mathematics on their own.