Quantitative Reasoning, Mathematics, and Other Disciplines
Differences between Mathematics and Quantitative Reasoning (QR)
The differences between mathematics and QR create a strong complementarity between the two disciplines. For example, QR emphasizes specific context while mathematics wrestles with generalizable abstractions. QR includes finding, interpreting, and using "dirty," real-world data--data which may include missing values, may not match theoretical constructs, may be dominated by outliers, or may be of questionable reliability. From these imperfect data, quantitatively literate students often use inductive reasoning (sometimes through formal statistics) to better understand the problem of interest. By contrast, mathematics generally begins with "clean" postulates and then uses deductive reasoning to generate conclusions.
A student who masters both of these disciplines will likely be better in applying both mathematics and QR than has she who has mastered one alone. For instance, we would surely like QR-equipped students to be able to pair their data exploration with formal modeling which may in turn involve significant mathematical abstraction. As we revise courses to support student QR, we would expect students to exercise their mathematical skills at the same time. Ultimately, the best quantitative thinking flows from a cycle between the abstract approach of mathematics and the context-rich skills of QR.
QR across the Curriculum
The contextual nature of QR does, however, suggest that QR needs to be taken up across the curriculum and not just in mathematics courses.
In Achieving Quantitative Literacy (an excellent introduction to QR and its interaction with mathematics), Lynn Steen writes,
"If quantitative literacy remains the responsibility solely of mathematics departments--especially if it is caged into a single course such as 'Math for Liberal Arts'--students will continue to see it as something that happens only in the mathematics classroom" (2004 p. 18).
And that outcome would fundamentally undermine the entire point of the QR movement. If we want to train students in the tricky work of transference, teaching them to apply their quantitative understanding to varied and distinct contexts, then we need to teach them in an equally wide range of fields.
While the most explored applications of QR may be found in the social and natural sciences, recent work in the digital humanities highlights the relevance of QR to these disciplines as well. Even in the arts, QR has a role. For one example, see Chris Jordan's collection Running the Numbers, which uses digital tools to represent our society through quantities. In all of these applications, the key point is that QR is authentically relevant to the discipline--not tacked on as a contrived exercise.
Support for Integrating QR in the Curriculum
The complementarity between math and applied disciplines in teaching QR is reflected in the coordinated work by three supporting organizations which seek to advance QR instruction:
- The Mathematical Association of America (MAA)'s special interest group for quantitative literacy (SIGMAA-QL ), provides support specific to mathematics.
- Project Kaleidoscope (PKAL ), provides support specific to science.
- and the National Numeracy Network (NNN), provides support for faculty from all disciplines including the arts, literature, and the humanities.
Resources for Teaching QR
A number disciplines have taken up this challenge of weaving QR in a natural way into their subject matter. Below are links to these disciplinary (and interdisciplinary) assignment collections. If your discipline is not represented, take heart. Most users of the collections revise assignments to the particulars of their own course context even when they find an assignment originally designed for their discipline. So, go ahead and browse a collection from a neighboring field and look for assignments can can be altered to meet your own needs.
- Numeracy Infusion Course for Higher Education: NICHE is a project of the City University of New York (CUNY) Quantitative Reasoning (QR) Alliance to foster the infusion of QR instruction and assessment into undergraduate courses in a broad range of disciplines. The NICHE site includes many tips, videos, and online resources to support curriculum revision.
- The Math You Need, When You Need It: Math You Need is designed to give students the quantitative knowledge that they need, just before they need to use it in their concurrent geoscience course. This program includes pre- and post-testing and self-paced modules.
- Teaching Quantitative Skills in the Geosciences: This site provides resources for faculty that include pedagogic methods, teaching resources, supporting materials for students and a discussion of the issues.
- Kéyah Math: The Kéyah Math Project has developed a series of versatile online activities in mathematical geoscience, using the natural and cultural landscapes of the Southwest United States as context and setting.
- Using Data in the Classroom: This site provides information and resources mainly for science faculty to incorporate collecting, manipulating, and aggregating data in their classes.
- DataCounts! : DataCounts! is an interactive website designed to help integrate social statistics into the classroom setting and provides access to an archive of datasets and teaching modules created for SSDAN's Census in the Classroom project.
- Starting Point: Teaching and Learning about Economics: This project provides teaching resources for two-year college economics faculty and also runs workshops and webinars to help two-year college faculty connect with each other and stay current on important topics in economics and teaching.