Developing Quantitative Reasoning

Compiled by Nathan Grawe, Carleton College
This resource references and draws upon materials developed for Pedagogy in Action and Teach the Earth.

"The world of the twenty-first century is a world awash in numbers....Unfortunately, despite years of study and life experience in an environment immersed in data, many educated adults remain functionally innumerate." Lynn Arthur Steen in Mathematics and Democracy: The Case for Quantitative Literacy

What is Quantitative Reasoning?

Quantitative reasoning (QR), defined as the habit of mind to apply data and quantitative tools to a wide range of problems in personal, professional, and public contexts, stands among key learning outcomes for 21st century students. For example, in its LEAP initiative the Association of American Colleges and Universities names QR among 6 "Intellectual and Practical Skills" necessary to "prepare for twenty-first-century challenges."

In the United States we have good reason to doubt that we are preparing our students for this world. For example, the Organization for Economic Co-operation and Development's Programme for International Student Assessment (PISA) finds US high schoolers in the middle of the pack - ranked 31st out of 65 countries in QR's cousin, mathematical literacy.

This site provides teaching tips and materials for those who aim to address this critical QR learning gap, and points to national organizations which share the mission of supporting teachers who wish to take on the challenge.

What's in a name?

While the terms Quantitative Reasoning, Quantitative Literacy, and Numeracy are generally used interchangeably, each suggests subtly different facets of students' work with quantitative evidence. In many contexts, "literacy" is associated with basic skill comprehension while "reasoning" suggests the synthesis of quantitative concepts into a larger whole. Because this collection intends to move students toward high-order applications, we prefer "Quantitative Reasoning," but mean no distinction when quoting others who refer to literacy or numeracy.

QR, Mathematics, and Other Disciplines: Complementary Partners

What is the relationship between QR, mathematics, and other disciplines? While mathematics and quantitative literacy deal with related skill sets, their approaches differ substantially. Much of the power of the former stems from abstraction while the latter delves into context. As a result, QR is often found in disciplines outside mathematics. Recognizing these complementary differences, the Mathematical Association of America has argued that both disciplines are critical for student education. This section discusses the connections between QR, mathematics, and other disciplines and provides links to organizations supporting this work and discipline-specific approaches to QR.

Learn more about QR across disciplines »

Principles for Teaching

Before getting bogged down in the details of revising specific assignments, it may be helpful to step back and think about more general principles for teaching QR. This page provides five pedagogical fundamentals to keep in mind when working out the specifics of course or assignment revision.

Principles for teaching »

Designing Assignments

When you are ready to dig into the specifics of revising or creating an assignment to enhance student QR experience, this page provides a list of useful assignment-writing principles. The page also provides links to useful tips for using real data, pedagogic methods for teaching QR and a large collection of QR assignments you might borrow or adapt.

Start designing assignments »

Assessment Tools

Several national examples have been developed to assess QR using multiple-choice exams and rubrics for evaluating papers and short essays. Because most faculty are interested in assessing QR in the context of other course objectives rather than as a stand alone learning outcome, this section also includes information on how to create grading rubrics for assignments that include QR and provide several example grading rubrics.

QR assessment tools »

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