## Quantitative Reasoning

Definition and Learning Outcomes

Quantitative reasoning competency at Norfolk State University refers to the ability to use critical thinking to solve problems of a numerical nature arising in life and work. It includes those mathematical skills and concepts that an educated citizen needs to function in contemporary society. At a minimum, it involves elements of arithmetic, informal geometry, algebraic symbolization, data representation and analysis, probability, mathematical modeling, and informal logic. Individuals proficient in quantitative reasoning possess a basic understanding of the role that numbers play in society, and they possess the ability to make reasoned judgments using mathematical tools to solve real world problems.

NSU graduates demonstrating competent quantitative reasoning skills will be able to solve problems that involve:

1. Numeric or arithmetic contexts: Estimation and approximation, percent, ratio and proportion, simple and compound interest, simple formulas, etc.
2. Conceptual contexts: Pattern recognition, symbolizing data, graphing analysis, algebraic expressions, equations, models, etc.
3. Geometric contexts: Measurement, conversion of units, shapes and sizes, basic relationships among lines, angles, triangles, polygons, etc.
4. Data representation and chance element contexts: Counting techniques, data distribution, basic statistical measures, elementary probability, etc.

Assessment Methodology

NSU employs both direct (NSU QRT) and indirect assessment measures (NSSE and GSES).

1)       NSU has adopted a course-embedded direct approach to assess the competency of NSU students on the four quantitative reasoning dimensions. To gather evidence of quantitative reasoning competency, the faculty developed NSU Quantitative Reasoning Test (QRT) will be administered to all students enrolled in the required mathematics general education courses (MTH 103, 105, 132, or 153). The QRT is a 20-item multiple-choice test. The QRT’s table of specifications demonstrates that all four dimensions of quantitative reasoning are appropriately and sufficiently reflected in the test items. External test development and evaluation consultants have validated the table of specifications and the QRT items.

2)       The National Survey of Student Engagement (NSSE) is administered annually, with at least 300 seniors completing the survey. The NSSE data for seniors on item 11F (as used on the 2010 NSSE) will be reported.

3)       The NSU Graduating Student Exit Survey (GSES) is administered to all NSU graduating students every semester. Annually, at least 600 students complete the survey. Data on the following GSES items will be reported to triangulate QRT and NSSE data:

• My major/program developed or enhanced my quantitative (mathematical) reasoning skills.
• In general, my education at Norfolk State developed or enhanced my ability to apply mathematical concepts to solve technological and other problems.
• In general, my education at Norfolk State developed or enhanced my ability to use a computer to calculate and manipulate quantitative information.

Standards

1)       Competency in quantitative reasoning is defined as an overall score of 70% correct or higher on the NSU Quantitative Reasoning Test (QRT). It is expected that at least 70% of students successfully completing courses meeting the University’s general education mathematics requirement will earn an overall score of 70% or higher on the NSU QRT.

2)       Seniors will report levels of engagement/ perceived growth at the national average on item 11f on the National Survey of Student Engagement (NSSE).

3)       At least two-thirds of NSU graduates will report, on the Graduating Student Exit Survey (GSES), that their education at Norfolk State significantly developed or enhanced their quantitative (mathematical) reasoning skills; developed or enhanced their ability to apply mathematical concepts to solve technological and other problems; and developed or enhanced their ability to use a computer to calculate and manipulate quantitative information (% 4+5 on a scale of 1-not at all to 5-a great deal).

Resource Box

Articles of Interest

Grawe, N.D. (2011). Beyond math skills: Measuring quantitative reasoning in context. New Directions for Institutional Research, 149, 41-52. doi:10.1002/ir.379

Lutsky, N. (2006). Quirks of rhetoric: A quantitative analysis of quantitative reasoning in student writing. Proceedings of the Joint Statistical Meetings, 2006. Alexandria, VA; American Statistical Association.

Rutz, C., & Grawe, N.D. (2009). Pairing WAC and quantitative reasoning through portfolio assessment and faculty development. Across the Disciplines, 6, 15.

Shavelson, R.J. (2008). Reflections on quantitative reasoning: An assessment perspective. In B.L. Madison & L.A. Steen (Eds.), Calculation vs. context: Quantitative literacy and its implications for teacher education (pp.27-44). Washington, DC: Mathematical Association of America.

Thelk, A.D., & Hoole, E.R. (2006). What are you thinking?: Postsecondary student think-alouds of scientific and quantitative reasoning items. The Journal of General Education, 55(1), 17-39.

Websites of Interest

Quantitative Reasoning and Literacy Assessment - The Association of American Colleges and Universities (AAC&U) provides links to assessment plans, rubrics, and peer reviewed articles to assist colleges and universities with assessment of their general education learning outcomes.

Teaching Quantitative Reasoning with the News - Pedadogy in Action, a portal for educators, provides teaching tips, assessment activities, and various reference resources that can be used to engage students in quantitative reasoning and critical thinking.

Supporting Assessment in Undergraduate Mathematics - the Mathematical Association of America promotes pedagogical and assessment methods that enhance teaching and learning in mathematics at the collegiate level.

Assessment Resource Tools for Improving Statistical Thinking (ARTIST) project  - The ARTIST website provides resources for evaluating students' statistical literacy (e.g. understanding words and symbols, being able to read and interpret graphs and terms), reasoning (e.g. reasoning with statistical information) and thinking (e.g. asking questions and making decisions involving statistical information). These resources were designed to assist faculty who teach statistics, across various disciplines (e.g. mathematics, statistics and psychology), to assess student learning of statistics, to evaluate individual student achievement, to evaluate and improve their courses, and to assess the impact of reform-based instructional methods on important learning outcomes.

Numeracy: Advancing Education in Quantitative Literacy - Numeracy, an open-access, peer-reviewed journal, aims to support education at all levels that integrates quantitative skills across disciplines. The journal seeks evidence-based articles on teaching strategies and resources, education research, curriculum design, assessment strategies, and faculty development, as well as perspectives, reviews of educational resources, and commentaries/replies.