Abstract and Quantitative Reasoning (AQR)

[Currently Mathematical Reasoning (MAR)]

Revised requirement

Adopted March 2006; anticipated effective date September 2008

Description:

Abstract and Quantitative Reasoning: A course that develops analytic thinking skills through systematic focus on abstract and quantitative reasoning.

Guidelines for courses:

  1. Abstract reasoning is the study of structures and patterns that arise in quantitative or computational settings. Quantitative reasoning is the use of formal structures and methods to model and analyze phenomena in the natural and human-made worlds. An AQR course should include elements of both of these reasoning activities.

  2. An AQR course should develop students' problem-solving proficiency through analytic thinking, not merely routine calculation. An AQR course should develop skills and ideas beyond what is typically attained in secondary school.

  3. An AQR course should incorporate multiple elements of abstract or quantitative reasoning (e.g., symbolic, geometric, and numerical perspectives; data analysis and statistical inference; visualization; algorithms and formal models).

Intended learning outcomes for students:

Students will demonstrate:

  1. An ability to recognize and employ patterns, structures, and models appropriate to particular theoretical or applied problems, as well as derive and understand properties of patterns, structures, and models themselves;

  2. An ability to apply abstract and quantitative reasoning to solve problems in novel contexts.

  3. An ability to approach problems from multiple perspectives, employing a variety of strategies.

Abstract and Quantitative Reasoning requirement complete description - includes committee comments on course guidelines to assist instructors in preparing proposals for GE accreditation

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Current requirement

Description:

Mathematical Reasoning: A course that develops a student's understanding of mathematics and mathematical problem-solving.

Guidelines for courses:

  1. 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.

  2. In this course, students must be involved in solving problems that require them to use creativity and insight.

  3. The course must provide practice reading mathematics and explaining mathematics.

  4. The course must place the topics studied within some broader context, for example, the origins and historical development of the topics or applications of the topics to other disciplines.

Intended learning outcomes for students:

The current version of this requirement does not include a statement of intended learning outcomes.

Mathematical Reasoning requirement complete description - includes committee comments on course guidelines to assist instructors in preparing proposals for GE accreditation