The Office of Institutional Assessment and Studies coordinated the 2013-2014 quantitative reasoning competency assessment. A faculty committee composed of representatives of the undergraduate schools wrote the definition, goal, learning outcomes and standards for the assessment.

## Definition

Quantitative reasoning is correctly using numbers and symbols, studying measurement, properties, and the relationships of quantities, or formally reasoning within abstract systems of thought to make decisions, judgments, and predictions.

## Student Learning Outcomes

A graduating fourth-year undergraduate at the University of Virginia will be able to:

- Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
- Communicate mathematical information symbolically, visually, numerically, and verbally.
- Use arithmetical, algebraic, geometric, and analytic methods to solve problems.
- Estimate and check answers to mathematical problems in order to determine reasonableness.
- Solve word problems using quantitative techniques and interpret the results.
- Apply mathematical/statistical techniques and logical reasoning to produce predictions, identify optima, and make inferences based on a given set of data or quantitative information.
- Judge the soundness and accuracy of conclusions derived from quantitative information, recognizing that mathematical and statistical methods have limits and discriminating between association and causation.
- Solve multi-step problems.
- Apply statistics to evaluate claims and current literature.
- Demonstrate an understanding of the fundamental issues of statistical inference, including measurement and sampling.

## Standards

The following standards have been established for graduating fourth-years:

- 25% of undergraduates are expected to be highly competent;
- 75% competent or above;
- 90% minimally competent or above.

The criterion that will indicate competence for fourth-years is the overall score on the quantitative reasoning test. A score of 11-15 indicates minimal competence, a score of 16-22 indicates competence, and a score of 23-30 indicates high competence.

## Methods

### Instrument

A faculty committee representing major disciplines and each undergraduate school developed an “in-house” instrument to assess quantitative reasoning. Questions address quantitative reasoning skills in three areas: General Mathematics, Statistics/Statistical Reasoning, and Calculus/Trigonometry. The format includes a mix of 30 multiple-choice questions and was administered at scheduled one hour test sessions.

### Sampling

Two hundred and forty-four (244) fourth-year students, representing five undergraduate schools at the University (Commerce, Engineering, Nursing, Architecture, and the College of Arts and Sciences. No students from the BIS program of the School of Continuing and Professional Studies (SCPS) participated. Students had been invited using a disproportionate stratified sampling method with over-sampling in the smaller schools to allow the results to be analyzed by school In order to report on the competency of a representative sample of fourth-years, 29 fourth-years were randomly removed from the overrepresented schools of Engineering, Commerce, and Nursing. The resulting representative sample contained 215 fourth year students. In addition, a representative sample of 208 first-year students was created out of a total of 300 first-years who took the test.

### Confidentiality and Compensation

Only students who consented to participate voluntarily were assessed. Confidentiality was ensured. Students who consented to participate were given a $20 gift certificate to Amazon.com to complete the test.