Volume IV: What works, what matters, what lasts

MAA Partner Disciplines

http://www.maa.org/cupm/crafty/

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