Examples of QR Assessment Instruments
There are a variety of Quantitative Reasoning (QR) assessment instruments that have been developed by researchers interesting in gathering information on and improving students' QR skills (as well as their attitudes towards QR). A sampling is included below broken down into four categories:
- Generalized Critical Thinking Assessment Instruments that Include Quantitative Reasoning Skills.
- Generalized Quantitative Reasoning Assessment Instruments.
- Health Literacy Assessment Instruments.
- Other Focused Assessment Instruments.
For assessment instruments developed at the course/instructor level, please see our page on resources developed as a result of this project.
(1) Generalized Critical Thinking Assessment Instruments that Include Quantitative Reasoning Skills
CLA "presents realistic problems that require students to analyze complex materials and determine the relevance to the task and credibility. Students' written responses to the tasks are evaluated to assess their abilities to think critically, reason analytically, solve problems and communicate clearly and cogently."Critical Thinking Assessment Test (CAT)
The CAT is a faculty-scored short-answer test and most of the questions are open-ended, including a number that focus on QR skills. In particular, the CAT questions assess how well students can: (1) summarize the pattern of results in a graph without making inappropriate inferences, (2) evaluate how strongly correlational data support hypotheses, (3) provide alternative explanations for a pattern of results that has many possible causes, (4) identify additional information needed to evaluate a hypothesis/interpretation, (5) evaluate whether spurious relationships strongly support a claim, (6) provide alternative explanations for spurious relationships, (7) identify additional information needed to evaluate a hypothesis/interpretation, (8) determine whether an invited inference in an advertisement is supported by information, (9) provide relevant alternative interpretations of information, (10) separate relevant from irrelevant information, (11) analyze and integrate information from multiple sources to solve a real-world problem, (12) use basic math skills to solve a real-world problem, (13) identify suitable solutions for a real-world problem using relevant information (14) identify and explain the best solution for a real-world problem using relevant information, and (15) explain how changes in a real-world problem might affect the solution.
(2) Generalized Quantitative Reasoning Assessment Instruments
Association of American Colleges and Universities (AAC&U) Quantitative Literacy Valid Assessment of Learning in Undergraduate Education (VALUE) rubric
Carleton College's Quantitative Inquiry, Reasoning and Knowledge Initiative (QuIRK) Rubric for Assessing Quantitative Reasoning in Papers
See Quantitative Literacy Value Rubric (Acrobat (PDF) 123kB Feb17 12)
See also Madison et al. modified AAC&U rubric (Acrobat (PDF) 111kB Jan19 13) also known as the Quantitative Literacy Assessment Rubric (QLAR).
This rubric is designed for use at the institutional level and is designed to assess four QR goals including whether students (1) think quantitatively, (2) implement QR competently, (c) interpret and evaluate QR thoughtfully, and (4) communicate effectively.
See: Carleton QuIRK Rubric (Microsoft Word 71kB May27 12)
In addition to their coursework, students must obtain a satisfactory score on a Quantitative Reasoning (QR) assessment. Information about the assessment is available online as well as practice problems.
This initiative resulted in a survey that assesses students' attitudes towards QR and mathematics. See pages 29-30.
The GRE "is a standardized exam that is administered as part of the graduate school admissions process." The exam includes three sections including (1) verbal reasoning, (2) quantitative reasoning, and (3) analytical writing.
Hollins University QR Assessment Instrument
Human Resources and Skills Development Canada
Hollins has a Quantitative Reasoning assessment instrument for which students must obtain a satisfactory score on (or enroll in a course entitled, "Introduction to Quantitative Reasoning").
See the study guide here.
James Madison University Quantitative Reasoning Assessment Instrument
Human Resources and Skills Development Canada has a numeracy self-assessment which focuses on individuals' attitudes and self-described ability to undertake a variety of quantitative tasks.
This instrument is "a computerized, multiple-choice test developed by the JMU Center for Assessment and Research Studies (CARS) and faculty from science and mathematical domains. It is designed to assess quantitative reasoning of students who have completed their general education requirements, and measures the following learning objectives: (1) use graphical, symbolic, and numerical methods to analyze, organize, and interpret natural phenomena; and (2) discriminate between association and causation, and identify the types of evidence used to establish causation." This test is recommended for use with general education program assessment and evaluation.
A generalized QR instrument that focuses on both QR attitudes and skills, developed by Esther Wilder. See: QR Assessment at Lehman (Microsoft Word 247kB May27 12)
Milo Schield's Statistical Literacy Tests
Milo Schield (Augsburg College) has a statistical literacy assessment instrument that focuses on readings graphs as well as a test on describing and comparing percentages.
This numeracy quiz is part of a project designed to "improve quantitative awareness, critical analysis, and evidence-based perspectives among journalism students and journalism instructors." This initiative is led by Michael Ranney at the University of California/Berkeley.
Quantitative Reasoning is defined to encompass four skills for purposes of assessment including: "(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., and (4) Data representation and chance element contexts: Counting techniques, data distribution, basic statistical measures, elementary probability, etc." 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 the NSU Quantitative Reasoning Test (QRT) and they also rely on some indirect measures of assessment (e.g., the National Survey of Student Engagement).
Quantitative Literacy and Reasoning Assessment (QLRA) Instrument
At Northern Essex, "the institutional co-chairs created a uniform assignment that would tap into into the abilities described in two outcomes developed by the Core Academic Skills Assessment Committee, named Global Awareness and Quantitative Reasoning. The assignment created was a scenario which presented a real-world problem faced by the United States; a graphical display of information relevant to solving the problem; and brief descriptions of situations in six fictional countries including information on political, economic and cultural factors." The results are available online.
This is a non-proprietary QLRA instrument and is a compilation of the Bowdoin, Wellesley and Colby Sawyer exams. As described by Eric Gaze at Bowdoin College, PI on an NSF-funded QLRA grant, this instrument is "is being piloted at schools across the country, including community colleges, public universities and liberal arts schools." Over 1600 students have taken the test, with mean scores at schools ranging from 39% to 79%.
As noted on U-Akron's web site, "During the 2010 – 2011 academic year, faculty coordinating College Algebra and Statistics for Everyday Life (SEL) performed an assessment of students' ability in quantitative reasoning and mathematical reasoning." The results of the assessment are available online.
University of Arkansas (Shannon Dingman and Bernard Madison's) QR Assessment Instrument
This is a multiple choice QR assessment instrument used in a foundational QR course at the University of Arkansas.
See the appendices here
A subjective test to measure numeracy (Fagerlin et al. 2007).
A faculty committee representing major disciplines and each undergraduate school developed an "in-house" instrument to assess quantitative reasoning. The reports are available at the above web site.
Wellesley College QR Assessment Instrument
Wellesley College has a Quantitative Reasoning assessment instrument for which students must obtain a satisfactory score on (or enroll in a course entitled, "Introduction to Quantitative Reasoning"). As described in their student study guide, "The QR Assessment tests your quantitative skills, including your ability to read and understand information presented in formulas, tables, and graphs; to interpret information and draw appropriate inferences; and to solve real world problems that deal with numbers or data. The mathematical skills you will apply on this test span arithmetic, algebra, graph reading, geometry, and linear and exponential modeling. Logical and statistical skills are core 'QR skills.'"
WizIQ Quantitative Reasoning Tests
See the study guide here.
WizIQ includes a number of resources for online education, including a unique platform. Some of the tests for quantitative reasoning are particularly useful.
(3) Health Numeracy Assessment Instruments
Diabetes Numeracy Test
A four-item asthma numeracy questionnaire (Apter et al. 2006).
The Diabetes Numeracy Test is "an assessment test designed to investigate the numeracy skills in patients with diabetes." For more information about the test, see Huizinga and associates (2008).
Medical Data Interpretation Test
A general health numeracy test (Osborn et al. 2013).
The medical data interpretation test is "a reliable and valid measure of the ability to interpret medical statistics" (Schwartz et al. 2005).
The Newest Vital Sign
A variety of numeracy instruments including a 3-item (chance, proportions and percentages) (Schwartz et al. 1997), an 11-item (risk and fractions as well as chance, proportions and percentages) (Lipkus et al. 2011), and a 15-item test (base rates and complex likelihood calculations as well as risk, fractions, chance, proportions, and percentages) (Peters et al. 2007).
The Newest Vital Sign assesses general literacy and numeracy skills as applied to health information, yielding an overall estimate of health literacy. Developed by Pfizer.
The Test of Functional Health Literacy in Adults (TOFHLA) -- Numeracy Component
An instrument that measures perceived ability to understand and interpret medical statistics (Woloshin et al. 2005).
The TOFHLA consists of a 50-item reading comprehension and a 17-item numerical ability test, taking up to 22 minutes to administer.
The TOFHLiD is an instrument designed to measure functional oral health literacy (Gong et al. 2007).
(4) Other Focused QR Assessment Instruments
Lehman College Sociology Program
As part of an initiative to infuse data analysis into the sociology curriculum at Lehman College (NSF DUE 0411401], 3 versions of a QR assessment instrument were developed (PI Esther Wilder) to assess a wide range of basic mathematical and QR skills including measures of central tendency, percentages, ratios, and reading tables and graphs.
Apter, Andrea J., Jing Cheng, Dylan Small, Ian M. Bennett, Claire Albert, Daniel G. Fein, Maureen George, and Simone Van Home. 2006. "Asthma Numeracy Skill and Health Illiteracy." J Asthma 43(9): 705-710.
Fagerlin, A., Zikmund-Fisher, B.J., Ubel, P.A., Jankovic, A., Derry, H.A., & Smith, D.M. 2007. "Measuring Numeracy without a Math Test: Development of the Subjective Numeracy Scale (SNS)." Medical Decision Making 27(5): 672-680.
Gong, D.A. J.Y. Lee, R.G. Rozier, B.T. Pahel, J.A. Richman, and W.F. Vann, Jr. 2007. "Development and Testing of the Test of Functional Health Literacy in Dentistry (TOFHLiD)." Journal of Public Health Dentistry 67(2): 105-112.
Huizinga, Mary M., Tom A. Elasy, Kenneth A. Wallston, Kerri Cavanaugh, Dianne Davis, Rebecca P. Gregory, Lynn S. Fuchs, Robert Malone, Andrea Cherrington, Darren A. DeWalt, John Buse, Michael Pignone, and Russell L. Rothman. 2008. "Development and Validation of the Diabetes Numeracy Test (DNT)." BMC Health Services Research 8: 96.
Lipkus, Isaac, Greg Samsa, and Barbara K. Rimer. 2001. "General Performance on a Numeracy Scale among Highly Education Samples." Medical Decision Making 21(1): 37-44.
Osborn, C.Y., K.A. Wallston, A. Shpigel, K. Cavanaugh, S. Kripalani, and R.L. Rothman. 2013. "Development and Validation of the General Health Numeracy Test (GHNT)." Patient Education and Counseling. [Epub ahead of print]
Peters, Ellen, Nathan Dieckmann, Anna Dixon, Judith H. Hibbard, and C.K. Mertz. 2007. "Less is More in Presenting Quality Information to Consumers." Medical Care Research and Review 64(2): 169-190.
Schwartz, Lisa M., Steve Woloshin, William C. Black, and H. Gilbert Welch.1997. "The Role of Numeracy in Understanding the Benefit of Screening Mammography." Annals of Internal Medicine 127(11): 966-972.
Schwartz, Lisa M., Steve Woloshin, and H. Gilbert Welch. 2005. "Can Patients Interpret Health Information? An Assessment of the Medical Data Interpretation Test." Medical Decision Making 25(3): 290-300.
Woloshin, Steve, Lisa M. Schwartz, and H.Gilbert Welch. 2005. "Patients and Medical Statistics. Interest, Confidence, and Ability." Journal of General Internal Medicine 20(11): 996-1000.