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Quantitative/Symbolic Reasoning: General Outcome

Use mathematics to understand and model the natural world.


Overall Guidelines

Courses for which a Q designation is sought must engage students in learning and applying a number of the learning outcomes (1) through (4) below. That engagement must be substantial and pervasive. Development of quantitative facility must be a true objective of the course and not incidental to it. In judging whether a course is a “Q Course”, one needs to consider course content, methods of assessment, and percentage of instructional time dedicated to quantitative ideas.

Student Learning Outcomes

  1. Work comfortably in standard quantitative modalities: Students should be able to read and interpret information about the world presented in the following ways. They should be able to translate between these modes:
    • Graphs
    • Data tables and charts
    • Equations, expressions or other symbolic forms
    • Verbal descriptions using ordinary language.
  2. Identify and utilize an appropriate mathematical model: Students should recognize what it means to model a situation using quantitative methods, including:
    • Evaluating formulas at specific points to answer practical questions.
    • Recognizing appropriate limitations on a model and identifying model breakdown, e.g. understanding the limitations on extrapolation.
    • Examining the hypotheses of a model or theory and evaluating their validity.
    • Learning to think inductively, e.g. striving to recognize patterns and to move from the specific to the general.
  3. Understand axiomatic systems : Students should be able to:
    • Identify the axioms or the underlying principles in a field of study, and distinguish these from the conclusions logically deduced.
    • Be able to make logical inferences from a given set of assumptions.
  4. Develop a quantitative "Toolkit" Students should master a variety of tools or skills used by "experts" and develop the judgment required to apply them meaningfully. Toolkit elements include:
    • Algebraic skills: Ability to manipulate symbolic expressions, solve equations, and express ideas symbolically.
    • Geometric skills: Ability to recognize basic geometric shapes and be familiar with their properties.
    • Statistical skills: Understand basic statistical terms and processes sufficient to critically read a newspaper story or evaluate a statistical study.
    • Estimation skills and number sense: Ability to roughly estimate the numbers encountered in everyday life (without use of technology). Understand order of magnitude particularly as it relates to the very large and very small quantities encountered in topics like astronomy and biology.
    • Technology Skills: Ability to utilize available technology tools to answer meaningful questions, e.g. Calculators, Spreadsheets, Computer Algebra Systems, and Statistical Programs.
    • Reasoning Skills: Ability to determine reasonableness of answers; ability to distinguish between a statement and its converse.



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