# Quantitative Reasoning

## Rationale

The ability to reason quantitatively is essential for citizenship in the 21st Century world. An understanding of data and quantity, and how they are presented and interpreted by the press and on the Internet, is invaluable. Mathematics and logic are used throughout the world as essential tools in many fields, including natural science, engineering, medicine, and the social sciences. In the words of John Allen Paulos,

“…. There are three reasons or, more accurately, three broad classes of reasons to study mathematics. Only the first and most basic class is practical. It pertains to job skills and the needs of science and technology. The second concerns the understandings that are essential to an informed and effective citizenry. The last class or reasons involves considerations of curiosity, beauty, playfulness, and perhaps even transcendence and wisdom.”

In a Q course, the student will be exposed to the methods employed in the mathematical sciences. This will include the application of mathematical or statistical models to complex problems which can then lead to potential solutions of these problems.

There are two types of Q courses: foundation and terminal. The type of course taken is dependent on a student's program of study.

## Criteria

- A foundation Q course (e.g. calculus or introductory statistics) provides the mathematical foundation prerequisite for successful completion of courses contained in a student's program of study. Thus, a core goal of the foundation course is to provide the quantitative and logical tools required in subsequent courses that demand a high level of mathematical sophistication and preparedness.
- A terminal Q course stresses mathematical and related foundational methods and concepts over a broad array of topics, and, in particular, mathematical and statistical foundational methods. Mathematical-foundation methods include the understanding of numerical or foundational concepts and the proper expression, proof, and refutation of arguments in the language of mathematics. Statistical-foundation methods include the understanding of quantitative and statistical concepts, the analysis of data, and the critical interpretation of statistical information.
- Mathematical and statistical foundational concepts include properties of numbers (integers, fractions, real numbers, complex numbers,...), problems in higher dimensions, shapes (classical geometric, topological equivalence,...), measures (distance, angles, area, volume, data-based statistics), random variables (distributions, expectations,...), functions of these concepts and their interplay, as well as methods of formal proof in the language of mathematics.
- Q courses enable students to develop those skills that lead to an understanding of quantitatively-based problems related to contemporary society. They provide practical applications that relate to their current daily and future professional lives as consumers of quantitative information. Ultimately, after having developed certain Q skills, they can apply them to make informed decisions in their personal and professional lives.

## Student Learning Outcomes

Students completing a Core 2.0 Quantitative Reasoning (Q) course should demonstrate an ability to:

- Interpret and draw inferences from mathematical models such as formulas, graphs, diagrams or tables.
- Represent mathematical information numerically, symbolically and visually.
- Employ quantitative methods in symbolic systems such as, arithmetic, algebra, or geometry to solve problems.