The Office of Institutional Assessment and Studies coordinated the 2007-2008 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. Please direct all questions about the assessment to Sarah Schultz Robinson (982-2321).

## 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.

## Goal

The central purpose of the University of Virginia is to enrich the mind by stimulating and sustaining a spirit of free inquiry directed to understanding the nature of the universe and the role of humans in it. A specific, articulated goal associated with this purpose is “fostering in students the habits of mind and character required to develop…an ability to test hypotheses and re-interpret human experience.” These habits of mind and character advance good citizenship in a democratic society, enrich the lives of individuals, and improve communities. The University expects graduating students to effectively use quantitative reasoning to evaluate information and argument, solve problems, and make decisions to these ends.

## 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.

Standards for gain between first-years and fourth-years will be considered after this first administration of the assessment to both first and fourth years. The criterion that will indicate competence for fourth-years is the overall score on UVa’s 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.

## Methodology

### Instrument

A faculty committee representing major disciplines and each undergraduate school developed an “in-house” instrument to assess quantitative reasoning. The format includes a mix of 30 multiple-choice questions and was administered at scheduled one hour test sessions of 60 students each. Results will be reported and evaluated for the six undergraduate schools as well as aggregated for the University as a whole.

In addition, individual schools within the University were encouraged to add a small number of questions or measures that would allow them to assess quantitative reasoning abilities that are of particular importance to their students. The Nursing School used this opportunity to assess the quantitative reasoning skills of their students using a brief additional assessment.

### Sampling

Approximately 350 4th-year students were sampled from five undergraduate schools at the University (Commerce, Engineering, Nursing, Architecture, and the College of Arts and Sciences) using a disproportionate stratified sampling method. Over-sampling in the smaller schools will allow the results to be analyzed by school. Because each undergraduate school is responsible for designing its own curriculum, this method will allow schools to make the best use of the results. Approximately 200 1st-year students also were randomly sampled to add a value-added perspective. The first year cohort’s results will be compared with the fourth years, and at a future point in time the cohort will be tested again to provide further perspective on value-added.. First-year students were not over sampled by school. All school results for fourth-years were aggregated to form an overall result for the University, but first-year results will be used exclusively as a point of comparison.

### 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 the UVa bookstore to complete the test.

## List of 2007-08 Committee Members

- Michele Claibourn, Politics
- Emily Drake, Nursing
- Jim Freeman, Psychology
- Tom Guterbock, Sociology
- Jeff Holt, Statistics
- Tom Kriete, Math
- David Phillips, Architecture
- Bill Roberts, Engineering
- Mark Thomas, History
- Bob Webb, Commerce