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Quantitative Reasoning Competency 2003-2004

The Schools at UVa were divided into three groups for the 2003-2004 quantitative reasoning competency assessment.

Assessment Plans:

College, Architecture, Commerce, and Education

Summary Reports:

College, Architecture, Commerce, and Education

Standards and Definitions

College, 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.


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.
  10. Define the concepts of linear independence; superposition.
  11. Solve nth order, homogeneous constant coefficient ODEs.
  12. Solve nth order, inhomogeneous constant coefficient ODEs.


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.