The Case for Assessing Quantitative Reasoning in Student Writing

"As in book literacy, evidence of students' ability to play the messy game of the [quantitative reasoning] discipline depends on seeing whether they can handle tasks without specific cues, prompts, or simplifying scaffolds from the teacher-coach or test designer."
-Grant Wiggins, "'Get Real!': Assessing for Quantitative Literacy" in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges

The very nature of QR presents challenges for traditional curricular reform and assessment strategies. The literature identifies four facets of QR.

  1. First, effective implementation of QR requires a basic skill set. Without a nuanced understanding of basic mathematical concepts like ratios, percentages, and averages it is impossible to apply that quantitative knowledge with a high degree of sophistication. This understanding includes an appreciation for both the power and pitfalls of various QR tools.
  2. Second, unlike traditional mathematics, which is intentionally abstract, QR explicitly requires that these skills be implemented in context(De Lange 2003 p. 80, Richardson and McCallum 2003 p. 100-102, Steen 2004 p. 9-10, Bok 2006 p. 129). As Steen writes, "The test of numeracy, as of any literacy, is whether a person naturally uses appropriate skills in many different contexts" (2001 p. 6). Contextualized problem-solving requires students to engage in intellectual transference, applying lessons learned in one setting to a newly discovered problem. To teach QR in context, effective programs must "permeate the curriculum, not only in the sciences but also in the social sciences and, in appropriate cases, in the humanities" (Bok 2006 p. 134).
  3. Third, students must learn to communicate contextualized applications of QR (De Lange 2003 p. 77, Brakke 2003 p. 168). This includes visual presentation through tables and figures in addition to writing with numbers.
  4. Finally, even students with the ability to communicate quantitative evidence in context must acquire the habit of mind to approach questions with a quantitative lens (Steen 2001 p. 5, Hughes-Hallett 2003 p. 91, Steen 2004 p. 16-17). Steen argues that students "need a predisposition to look at the work through mathematical eyes" (2001 p. 2).

The multi-disciplinary, contextual character of QR often confounds efforts to create effective QR programs. As Steen (2004) points out, "Curricular talk tends to be dominated by disciplines....With no discipline naturally exercising leadership, there is neither an insistent nor a consistent call to make [QR] a priority of education at the college level" (p. 13-15). Even when a group of faculty members drawn from across the disciplines overcome institutional barriers and agree to prioritize QR instruction, it can be very difficult to devise a program which truly infuses the curriculum.

The same contextual elements of QR also challenge effective assessment. According to quantitative-literacy assessment expert Grant Wiggins, traditional standardized tests ably assess student skill sets, but are inherently ill-suited to QR assessment because "standardized conditions are decontextualized by design" (2003 p. 125). Steen concurs: "[QR] requires creativity in assessment, since neither course grades nor test scores provide a reliable surrogate" (2004 p. 16).

Some educators have responded to this challenge by rethinking the nature of standardized testing, creating context-rich test questions. Through short-answer essays, such tests may detect fluency in writing with numbers but do not permit students the time, space, or capacity to demonstrate the ability to choose wisely between graphical, tabular, and textual presentation.

What is much more important, QR problems in the real world are inherently ill-structured-ill-defined in some cases. In Wiggins' words, "As in book literacy, evidence of students' ability to play the messy game of the [QR] discipline depends on seeing whether they can handle tasks without specific cues, prompts, or simplifying scaffolds from the teacher-coach or test designer" (2003 p. 134 emphasis added). Because standardized QR tests clearly prompt students to apply a quantitative lens, such tests are inherently unable to assess students' propensity to consider voluntarily the quantitative facets of problems.

QuIRK's novel, writing-based assessment strategy reflects all four facets of quantitative literacy.

  1. Given the cross-disciplinary nature of QR, only an equally cross-disciplinary assessment strategy can fully measure our effectiveness. As Steen (2004 p. 18) writes, "The interdisciplinary and contextual nature of [QR] cries out for a cross cutting approach." With student work drawn from courses taught by 197 different professors (Carleton has 170 FTE), Carleton's writing portfolio truly represents student thinking across the curriculum.
  2. Moreover, the application of QR skills in student papers provides an inherently context-rich environment in which to assess proficiency.
  3. Writing sample assessment also allows detailed evaluation of student sophistication in communication with numbers.
  4. Of particular value, writing assessment reveals as much about students' abilities to create tables and charts as to read them. While students may capably interpret charts and tables made by others, highly effective presentation skills only develop with practice (Miller 2004 p. 5). Most importantly, portfolio assessment provides insight into students' habits of mind concerning the power of quantitative evidence: because papers often do not explicitly require quantitative evidence we are able to determine whether students reflexively consider numerical facets of problems they face.

Moreover, by emphasizing the rhetorical aspects of QR our program models how a curriculum-wide QR reform initiative can be implemented quickly by leveraging existing writing programs. This approach has three distinct advantages. First, writing programs have amassed a wealth of knowledge concerning the development of across-the-curriculum programming. Second, existent writing programs already reflect the unique campus culture allowing nascent QR programs faster integration into the curriculum. Finally, the rhetorical slant on the mathematical tools of QR appeals to a broader audience ensuring greater buy-in from fields which traditionally eschew STEM topics.

References

Bok, Derek 2006. Our Underachieving Colleges: A Candid Look at How Much Students Learn and Why They Should Be Learning More. Princeton, NJ: Princeton University Press.

Brakke, David F. 2003. "Addressing Societal and Workforce Needs," in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

De Lange, Jan. 2003. "Mathematics for Literacy," in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

Hughes-Hallett, Deborah. 2003. "The Role of Mathematics Courses in the Development of Quantitative Literacy" in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

Miller, Jane E. 2004. The Chicago Guide to Writing about Numbers. Chicago: University of Chicago Press.

Richardson, Randall M. and William G. McCallum. 2003. "The Third R in Literacy" ," in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

Steen, Lynn Arthur. 2001. Mathematics and Democracy: The Case for Quantitative Literacy. Washington DC: Mathematical Association of America.

Steen, Lynn Arthur. 2004. Achieving Quantitative Literacy: An Urgent Challenge for Higher Education. Washington, DC: Mathematical Association of America.

Wiggins, Grant. 2003. "'Get Real!': Assessing for Quantitative Literacy" in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.