Quantitative writing assignments can play an important role in an institution's general education curriculum. Moreover, QW assignments can increase the level of critical thinking in disciplines that are already math-intensive. Because QW assignments focus on outcome goals connected to writing, mathematics, inquiry, critical thinking, problem-solving, and even information literacy, they are potentially powerful assessment tools. This page shows how some institutions are using QW assignments to assess outcome goals in both general education and in math-based major fields.

The Role of QW Assignments in Assessing General Education

Almost every institution has a requirement for quantitative reasoning in its gen-ed program. In many cases, students are required to take one or two mathematics and/or statistics courses. In other cases, the requirement can be fulfilled by courses in other disciplines, where quantitative reasoning is applied. But what is the curricular purpose of this requirement? What should graduating seniors be able to do as a result of completing the required courses? One answer to this question is that students should be able to confront ill-structured problems infused with quantitative data requiring analysis and argument-in other words, to do the kind of critical thinking required by QW assignments. If an institution is not satisfied with the quantitative literacy of its students, perhaps the best approach is infusion of QW assignments across the curriculum rather than additional required math courses. This approach is recommended by the Mathematics Association of America in its proposals for "mathematics-across-the-curriculum" such as the papers in Why (Quantitative) Literacy Matters .

Two examples of institutions taking this approach are Carleton College and Macalester College.

• Carleton College. Using funds from a FIPSE grant, Carleton College has established an innovative curricular initiative known as QUIRK (Quantitative Inquiry, Reason, and Knowledge), which focuses on "how quantitative reasoning is used in the development, evaluation, and presentation of principled argument." Carleton faculty are using their institution's end-of-sophomore-year portfolio assessment of student writing to investigate the extent to which students are asked to address quantitative problems during their first two years at Carleton. Faculty are tracking the percentage of portfolios that include quantitative writing, analyzing the characteristic strengths and weaknesses of student work, and developing curricular strategies to improve students' ability to analyze quantitative data in real-world settings. Simultaneously, through a series of faculty workshops and other initiatives, Carleton faculty are developing QW assignments for a wide variety of courses and majors. Most of the examples of QW assignments on this site are the result of this FIPSE-funded initiative. For further details about the Carleton QUIRK project see the QUIRK website .
• Macalester College. To improve the mathematical skills of its students, Macalester College has made quantitative literacy an important outcome goal. As part of its general education requirements, Macalester has established the QM4PP program (Quantitative Methods for Public Policy) with funding from FIPSE and NSF. This program focuses "on quantitative literacy in the context of case studies that illustrate how its tools can be used to illuminate debate over real policy issues." The goals of the program are highlighted in this striking statement from its website.
  Quantitative Literacy (QL) is not mathematics. It has almost nothing to do with mathematics as taught at the college level. It is about gaining the ability and habit to seek out quantitative information, to be able to analyze and critique it, and to use it in our public, personal, and professional lives. By its nature, QL is interdisciplinary. It appears in political debate and polling, in issues of health care, in understanding the choices we face with regard to the environment, in grappling with the complexities of poverty, education, and social action. QL recognizes the fact that quantitative information in the real world is messy, complex, often incomplete, sometimes overwhelming, and not infrequently appears to be contradictory. At a basic level, the methods needed to think critically about this information use nothing beyond high school mathematics: ratios, percentages, rates, simple probabilities. But basic does not mean easy. There is still a lot to learn about how to choose and think about quantitative information when it is outside the idealized world of the mathematics classroom.
  Macalester College is able to assess students' quantitative literacy by examining select pieces of writing produced in the program.

QW Assignments and the Assessment of Critical Thinking in Math-Intensive Disciplines

Many institutions are also discovering the value of QW assignments in disciplines that are already math-intensive such as economics, finance, physics, chemistry, or engineering. Typically, the homework in these disciplines consists of "problem sets" composed of well-structured problems with right answers. Such problem sets help students master what cognitive psychologists call "declarative" and "procedural knowledge--the ability to understand a formula or algorithm and use it to perform accurate calculations. However, these problems sets are less effective at promoting "schematic" or "strategic" knowledge-the critical thinking kind of knowledge needed to know when and why to use certain algorithms in an ambiguous, ill-structured setting. QW assignments can add a rigorous critical thinking dimension to students' engagement with quantitative data in these disciplines.

Here are two examples:

• At Seattle University, a research team consisting of a finance professor, economist, mathematician, and English professor has created a program in "rhetorical mathematics." In a guidebook they are developing for finance majors, they explain this program as follows:
  Finance students tend to think of mathematics as algorithmic calculations-often quite complex ones--aimed at finding right answers to problem sets at the back of the textbook. The purpose of this [guidebook] is to urge you to think of mathematics in a somewhat different way, what we call "rhetorical mathematics." To finance professionals, mathematics is a way of thinking. The analytical tools learned in finance courses help the professional investigate quantitative problems in many different ways. Clearly, finance professionals must be able to use these tools, but even more, they must use them in ill-structured situations to analyze a complex scenario, arrive at judgments, and support these judgments with clear and logical reasoning, often using mathematical data as evidence. Frequently the final step of the problem-solving process is to make recommendations that they must then explain and justify to a client or supervisor.
  Finance faculty are developing QW assignments for upper level finance courses aimed at teaching high level critical thinking in the discipline.
• At Cornell University, organic chemistry professor Barry Carpenter has developed QW assignments in which he hopes to move students beyond what he calls "the myth of certainty." As Carpenter explains in his syllabus, "You will be given a set of facts that you can imagine might have been acquired in your own laboratory. You will be requested to formulate some theory about these facts and to communicate both the facts and your ideas about their significance to the editor of a scientific journal in a brief article." According to the book chapter reporting Carpenter's assignments, these "problem sets simulated many aspects of scientific research and writing: real laboratory research problems, enigmatic results, irregular data tables [and situations where] one frequently doesn't know which of the many pieces of data that can be gathered are really relevant to the problem at hand (Hjortshoj, 2003, pp. 50-51)."

In both the Seattle University and the Cornell examples, assessment of students' difficulties in producing effective responses to these assignments provides guidance for improving teaching methods.

A Simple Assessment Process

Quantitative assignments can be used to assess student learning through the following simple process.

1. An instructor or faculty group designs a QW assignment intended to generate the kind of critical thinking, writing skill, and quantitative literacy the individual faculty member or group hopes for.
2. This assignment is embedded in a course within the curriculum.
3. The instructor or faculty group scores the student papers using a rubric created for the assignment and notes typical patterns of student strengths and weaknesses.
4. Results are reported at a meeting devoted to discussing how changes in the curriculum or instruction might address patterns of weakness.
5. Faculty initiate the changes in curriculum or instruction and reiterate the process at a later date.

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