Volume IV: What works, what matters, what lasts
MAA Partner Disciplines
Taking the opinions of "partner disciplines" through a series of eleven workshops across the country and a final conference, an MAA study group established a collective vision presented in MAA's Curriculum Foundations Project. It offers a series of recommendations that can serve as resources for multi-disciplinary discussions at individual institutions.
Promoting and supporting informed interdepartmental discussions about the undergraduate curriculum might ultimately be the most important outcome of the Curriculum Foundations Project.
Summary Recommendations: A Collective Vision
Understanding, Skills, and Problem Solving
- Emphasize conceptual understanding.
- Focus on understanding broad concepts and ideas in all mathematics courses during the first two years.
- Emphasize development of precise, logical think. Require students to reason deductively from a set of assumptions to a valid conclusions.
- Present formal proofs only when they enhance understanding. Use informal arguments and well-chosen examples to illustrate mathematical structure.
Emphasize problem solving skills.
- Develop the fundamental computational skills the partner disciplines require, but emphasize integrative skills: the ability to apply a vareity of approaches to single problems, to apply familiar techniques in novel settings, and to devise multi-stage approaches in complex situations.
Emphasize mathematical modeling.
- Expect students to create, solve, and interpret mathematical models.
- Provide opportunities for students to describe their results in several ways: analytically, graphically, numerically and verbally.
- Use models from the partner disciplines: students need to see mathematics in context.
Emphasize communication skills.
- Incorporate development of reading, writing, speaking, and listening skills into courses.
- Require students to explain mathematical concepts and logical arguments in worlds. Require them to explain the meaning– the hows and why– of their results.
Emphasize balance between perspectives.
- Continuous and discrete
- Linear and nonlinear
- Deterministic and stochastic
- Deductive and inductive
- Exact and approximate
- Pure and applied
- Local and global
- Quantitative and qualitative