THE DEPTH, RANGE AND VARIED NATURE OF QR COURSES

Program Development

Beginning in the fall semester of 2003, I chaired a committee to create a new “Quantitative Reasoning” (QR) math course at the Borough of Manhattan Community College (BMCC) of the City University of New York. Since we did not offer this type of course, some of my colleagues felt that our department needed such a course. Because I had prior experience teaching QR at another university, I volunteered to chair a committee to design the course. Thirteen faculty members from the mathematics department volunteered to join the committee to assist me in this process. Some committee members were senior faculty with prior experience creating courses. Others were junior faculty members who were eager to learn about QR and course design. The course was developed and unanimously approved by the BMCC faculty council at the end of the fall 2004 semester.

Several mathematical organizations including the American Mathematical Association of Two Year Colleges (AMATYC) and the Mathematical Association of America (MAA), have stated the need for all college graduates to be quantitatively literate. Consequently, we felt that such a course would be of great value to our students. Some of the committee members were unfamiliar with this type of course, while others had differing viewpoints about QR courses.

With some research, I discovered, and reported to the committee, that there are significant variations among such courses. I discovered variation in the course title; for example, Quantitative Reasoning (QR), Quantitative Literacy (QL), Mathematics Literacy (ML), Numeracy, Mathematical Thinking, or simply Mathematics. To some, these terms are synonymous but to others there is a difference in how these terms are defined.

The National Adult Literacy Survey defines quantitative literacy as: “The knowledge and skills required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed material (e.g, balancing a checkbook, completing an order form).” (Steen, 2001, p.7). Others cast quantitative literacy as a specific collection of skills – basic mathematical skills, statistical reasoning skills, critical thinking skills, and problem solving skills (QL_SIAM). “Like literacy itself, these are survival skills, needed by any person who wants to understand and make decisions in a complex world flooded with data.” (QL_SIAM, p. 1). QL is also defined as the “level of mathematical knowledge and skills required of all citizens. It includes the ability to apply aspects of mathematics (including measurement, data representation, number sense, variables geometric shapes, spatial visualization, and chance) to understand, predict, and control routine events in people’s lives.” (QL, p. 1).

Quantitative literacy is regarded by some as a combination of skills, comfort and confidence when dealing with fundamental quantitative problems. (QL_ SIAM). Others view QL from a cultural or historical perspective. “It provides students with an idea of the power and utility of mathematics, and makes them aware of how it has shaped the society in which we now live.” (QL_SIAM, p. 1)

Some differentiate between Quantitative Literacy and Quantitative Reasoning. Quantitative Reasoning is viewed by some “as an interpretive activity that takes place within a deductively structured framework. It involves tapestry of meaning provided by a warp of abstract patterns and a weft of context and story line. In quantitative reasoning, context provides meaning.” (QR/QL, p.3).

Mathematics literacy is defined by the Programme for International Assessment as “an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgments and to engage in mathematics in ways that meet the needs of that individual’s current and future life as a constructive, concerned and reflective citizen.” (Steen, 2001, p.7)

Some distinguish between “literacy” type courses (QL, QR, Mathematics literacy, Numeracy) and mathematics.

“Whereas mathematics tends to be hierarchical and abstract, quantitative literacy is broad, outreaching, and practical because of its interfaces with other disciplines.” (QL_SIAM, p.1). “Quantitative literacy is mathematics in context, it is mathematics as it arises in diverse real situations.” (QL_SIAM, p. 1).

“Numeracy is not the same as mathematics. It is an aggregation of skills, knowledge, beliefs, dispositions, habits of mind, communication capabilities, and problem solving skills that people need in order to engage effectively and autonomously in quantitative situations arising in life and work.” (QL, p.1)

These definitions suggest substantial variation among QR courses. The emphasis of some courses is critical thinking skills, others basic arithmetic skills. Still some focus on math appreciation by applying concepts taught to real world problems, and others emphasize problem solving (Steen, 2001). While I was a graduate student at NYU, I was exposed to this variation since the QR courses offered at NYU are:

a) Mathematical Patterns in Nature – emphasizes the application of mathematics to the physical sciences,

b) Mathematical Patterns in Society – emphasizes the application of mathematics to the social sciences,

c) Mathematics and the Computer – emphasizes the application of Boolean algebra and logic to digital electronics,

d) Probability, Statistics, and Decision Making – emphasizes probability from the viewpoint of gambling and games and

e) Elementary Statistics – emphasizes the use of statistical methods (MAP, 2003-2004).

Each of these courses has weekly workshops (called recitation) where graduate assistants review material covered in lecture and work on lab projects.

The task that our QR committee faced was to determine which approach to QR was best suitable for our student population.

Program Goals and Learning Objectives

Our students are required to demonstrate skills associated with academic literacy upon graduation. These skills include “the ability to understand and think critically about ideas and information presented in print and the ability to write clearly, logically, and correctly.” (CPE, 2003-2004, p.1). All students are required to pass an exit exam, called the CPE (CUNY Proficiency Examination). This exam is divided into two parts, Task 1: Analytical Reading and Writing; and Task 2: Analyzing and Integrating Materials from Graphs and Text (CPE, 2003-2004). The committee agreed that one of the course objectives should be to assist students in developing these necessary skills. The committee also felt that writing should be an integral part of the course since it would better prepare students for the Proficiency exam.

The committee unanimously agreed that the learning objectives for this course should satisfy the general education learning outcome goals of the college. At the time this course was being developed, the general education objectives for the college were being revised. The following general education learning outcome goal was under consideration by the college: Students will use quantitative skills and the concepts and methods of mathematics to solve problems across all disciplines. The objectives under consideration were:

Students will

Understand and apply basic methods of arithmetic, algebra, geometry and statistics for computational problems in a variety of theoretical and real world situations.
Interpret, make appropriate judgments, and draw logical conclusions based on quantitative information.
Critically evaluate quantitative material, identifying deceptive or erroneous reasoning.

The committee compared these general education objectives to the Mathematical Association of America guidelines for QR courses. According to the MAA, a quantitatively literate student should be able to:

Interpret graphs, tables, and schematics, and draw inferences from them.
Represent mathematical information symbolically, visually, numerically, and verbally.
Use arithmetical, algebraic, geometric and statistical methods to solve problems.
Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results. (MAA, p.2).

The committee reflected on the general education and MAA guidelines to determine which of the various forms of quantitative literacy (discussed previously) is best suitable for our student population. After carefully studying and discussing these guidelines, we agreed that this course should contain applications from various disciplines. An interdisciplinary course of this nature is recommended by the American Mathematical Association of Two –Year Colleges (AMATYC).

According to AMATYC, “Because liberal arts students will encounter mathematics in a variety of settings, the approach taken should involve applications from several disciplines” (AMATYC, p. 20). Further, “just as the “writing across the curriculum movement” addresses the need for students to write frequently in order to improve as verbal thinkers, a “mathematics across the curriculum movement” is needed so that students develop as mathematical thinkers.” (AMATYC, p. 20).

Based on our program goals, learning objectives, and student population, our form of QL will emphasize certain skills (e.g critical thinking, statistical reasoning, etc) and provide opportunities for students to master these skills and be comfortable and confident when applying them to their everyday lives.

CROSS - DISCIPLINARY PARTICIPATION CONCLUSION

BMCC is committed to improving the performance of Quantitative Reasoning will be offered at BMCC for

students on Task 2 of the CPE exam by integrating the first time in Fall 2005. I believe this course will

quantitative reasoning skills more fully in the serve the needs of our students. It will enable them

curriculum. The college has implemented a to develop the quantitative reasoning skills

“Coordinated Undergraduate Education” (CUE) necessary to be productive citizens.

Initiative in an effort to infuse quantitative reasoning

skills into course and programs across the curriculum.

Faculty members will collaborate with their colleagues

in other disciplines to find opportunities to relate

quantitative reasoning skills to students’ general education

goals and to include authentic applications with real data,

charts and graphs, and problem solving skills in their

courses.

This course, which is independent of the CUE

Initiative, is consistent with it’s goals. QR is

an elective course for Liberal Arts majors to

fulfill their mathematics graduation

requirement. However, this course is open to

students across all disciplines. Any student who

lacks adequate quantitative literacy skills to

succeed on the CPE exam can take this

course to improve these skills.

REFERENCES

AMATYC (1995). Crossroads in Mathematics Interpreting the Standards. Retrieved April, 2004 from the World Wide Web: http:// www.imacc.org/standards/interpreting.html

Bennett, J.O., & Briggs, W.L. (2003). Using and Understanding Mathematics. A Quantitative Reasoning Approach. Addison Wesley.

BMCC(2000-2002). 2000-2002 Bulletin.

CPE (2003-2004). A Description of the CUNY Proficiency Examination. Information for Students. http:// www.cuny.edu/cpe, Office of Assessment, The City University of New York.

Factbook (2001-2002). BMCC Factbook 2001-2002. The Office of Institutional Research Academic Affairs.

MAA (1998). Quantitative Literacy: Goals. Retrieved September, 2003 from the World Wide Web: http:// www.maa.org/past/ql/ql_part2.html

MAP (2003-2004). The Morse Academic Plan. The General Education Program of New York University. Prepared by the Morse Academic, New York, NY.

QL. Different Views on Quantitative Literacy. Retrieved April, 2004 from the World Wide Web: http:// www. stolaf.edu/other/extend/Numeracy/defns.html

QL_SIAM. Quantitative Literacy and SIAM. Retrieved April 2004 from the World Wide Web: http:// www-math.cudenver.edu/~wbriggs/qr/siam_news.html

QR/QL. What is QL/QR? Retrieved September, 2003 from the World Wide Web: http:// www-math.cudenver.edu/~wbriggs/qr/whatisit.html

Steen, L.A. (2001). Mathematics and Democracy. The Case for Quantitative Literacy, prepared by the National Council on Education and the Disciplines, Washington, D.C.