2007-08 Quantitative Reasoning Competency Assessment Plan

The development of the University of Virginia’s quantitative reasoning competency assessment plan is being coordinated by the Office of Institutional Assessment and Studies. A faculty committee composed of representatives of the undergraduate schools wrote the definition, goal, learning outcomes and standards. If you have questions about the process, please contact coordinator Sarah Schultz Robinson, 982-2321, sas6tb@virginia.edu.

Definition of Quantitative Reasoning
Goal for Undergraduates
Student Learning Outcomes
Standards/Level of Performance Expected
Description of the Methodology Used to Gather Evidence
Reports of Results for Quantitative Reasoning
List of 2007-08 committee members

Plan in PDF Format

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:

1. Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
2. Communicate mathematical information symbolically, visually, numerically, and verbally.
3. Use arithmetical, algebraic, geometric, and analytic methods to solve problems.
4. Estimate and check answers to mathematical problems in order to determine reasonableness.
5. Solve word problems using quantitative techniques and interpret the results.
6. 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.
7. 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.
8. Solve multi-step problems.
9. Apply statistics to evaluate claims and current literature.
10. Demonstrate an understanding of the fundamental issues of statistical inference, including measurement and sampling.

Standards/Level of Performance Expected
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.

Description of the Methodology Used to Gather Evidence

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.

Reports of Results for 2007-2008 Quantitative Reasoning Competency Assessment:

The report of results is available on the Quantitative Reasoning worksite at UVa Collab. Click "UVa Login" and then sign into UVa Collab through Netbadge using your UVa ID and Eservices password. In "My Workspace" click "Membership" then click "Joinable Sites." Search for "Quant Reasoning" and then join the site. The worksite contains all supporting documentation of this year's quantitative reasoning assessment. If you have any questions about the worksite, please contact the site's adminstrator, Sarah Schultz Robinson at 982-2321 or sas6tb@virginia.edu.

List of 2007-08 Committee Members

2003-04 Quantitative Reasoning Competency Assessment Plan and Report of Results

Plan Submitted to SCHEV

Reports of Results

Standards/Definition of Quantitative Reasoning Competency

Plans Submitted to SCHEV (PDF files)

• College of Arts & Sciences, Schools of  Architecture, Commerce, and Education
• School of Engineering and Applied Science
• School of Nursing

Reports of Results

Standards/Definition of Quantitative Reasoning Competence

College, Architecture, Commerce, Nursing and Education

Engineering

Nursing

Standards/Definition of Mathematics/Quantitative Literacy Competency: College of Arts & Sciences, Schools of Architecture, Commerce, and Education

The University of Virginia expects graduates of its College of Arts and Sciences and its Schools of Architecture, Commerce, and Education to have and to understand basic knowledge and skills about mathematics and/or quantitative literacy in order to use it effectively and productively for their own purposes. Specifically, we expect these graduates to be able to apply simple mathematical methods to the solution of real-world problems. We believe a quantitatively literate graduate should be able to:

1. Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
2. Represent mathematical information symbolically, visually, numerically, and verbally.
3. Use arithmetical, algebraic, geometric, and statistical methods to solve problems.
4. Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results.
5. Recognize that mathematical and statistical methods have limits.

Standards/Definition of Mathematics/Quantitative Competency:
Engineering

All students graduating from the University of Virginia's School of Engineering and Applied Science (SEAS) should be able to demonstrate the ability to:

1. Use proper mathematical notation and terminology.
2. Express mathematical arguments clearly, demonstrating an understanding of what is necessary and sufficient support.
3. Solve multi-step problems.
4. Graph basic functions without a calculator. These functions include linear, factored polynomial, trigonometric, exponential, and logarithmic.
5. Compute, without a calculator, derivatives and integrals of single variable and multivariable functions.
6. Set up and solve problems involving the application of the derivative and integral in both single variable and multivariable context. Such applications must include optimization, rates of change, area, volume, arc length.
7. Set up and solve simple problems in polar and spherical coordinate systems.
8. Calculate and use the dot product and cross product.
9. Solve the differential equations and .
10. Define the concepts of linear independence; superposition.
11. Solve nth order, homogeneous constant coefficient ODEs.
12. Solve nth order, inhomogeneous constant coefficient ODEs.

Standards/Definition of Scientific Reasoning and Quantitative Literacy Competency: Nursing

The University of Virginia's School of Nursing proposes to assess its students' knowledge and skills in the areas of scientific and quantitative reasoning together because both are very closely related in the curriculum of the School. The School of Nursing expects its graduates to have mastered essential fundamental knowledge in scientific and quantitative reasoning in preparatory coursework and in clinical application of professional nursing practice. Specifically, the School of Nursing expects its graduates to know and be able to accomplish the following:

1. Apply statistics to evaluate current literature.
2. Apply quantitative reasoning to evaluate epidemiologic and genetic risk analysis.
3. Apply scientific and quantitative reasoning to the analysis of graphs (example dissociation curves, risk curves).
4. Use complex mathematical formulas (ex. fluid and electrolyte and acid base problems, arterial blood gas interpretation).
5. Interpret tables of physiologic and pathophysiologic data.
6. Use scientific reasoning to interpret complex pathophysiologic processes and deduce how these processes will be manifested clinically.
7. Use practical mathematics to calculate and verify medication dosages.
8. Use practical mathematics for weight based protocols for children.
9. Use practical mathematics to determine IV titration and administration pump programming.
10. Use practical mathematics to implement and verify anticoagulant and insulin protocols.
11. Use practical mathematics to determine Vasopressor drips.
12. Use practical mathematics on drug calculations prior to administering them in the clinical area.

Quick Links:
Origins and purpose of competency assessments at UVa

2003-04 Quantitative Reasoning Competency Assessment Plan and Report of Results