DEVELOPING QUANTITATIVE REASONING AT A TWO – YEAR COLLEGE.
During the Fall 2003 semester, I chaired a committee to create a new math course at the Borough of Manhattan Community College (BMCC) of the City University of New York. The course I proposed to create is typically called “Quantitative Reasoning” (QR). 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, I felt that such a course would be of great value to our students.
Some of the committee members were unfamiliar with this course and others had differing viewpoints about QR courses. Consequently, I carefully researched QR courses and discovered that there are significant variations among such courses.
The first thing I discovered was variation in the course title, for example, quantitative reasoning (QR), quantitative literacy (QL), mathematics literacy (ML), numeracy, mathematical thinking, or simply mathematics (Steen, 2001). 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). Some view quantitative reasoning “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)
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). I was exposed to this variation among QR courses as a graduate assistant at NYU where I taught some sections of QR. The QR courses offered there 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 the QR committee faced was to determine which approach to QR is best suitable for our student population.
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 also reviewed the Mathematical Association of America guidelines for QR courses. Based on these guidelines the QR committee unanimously agreed that a quantitatively literate student should be able to:
(MAA, 1998, p.2)
Committee members also agreed that the course context should be interdisciplinary and the topics chosen should relate to students’ everyday lives. I felt that many of the topics covered in the textbook “Using and Understanding Mathematics. A Quantitative Reasoning Approach” by Jeffery O. Bennett and Willam L. Briggs reflected our course goals. Several committee members shared this opinion. Topics that reflect our course objectives include “Numbers in the real world”; “Financial management”; and “Statistical Reasoning” (Bennett & Briggs, 2003).
I believe that many of these topics will adequately serve the needs of our students. This course will enable students to develop quantitative literacy skills necessary to make them productive citizens. Quantitative literacy skills which requires students to read and write critically about graphs (Task 2 of the CPE exam) were highly recommended at a recent (November 7 – 9, 2003) Project Kaleidoscope (PKAL) workshop focusing on scientific and quantitative literacy. This course is still a work in progress, however I believe it will soon have all the essentials to make it a success.
REFERENCES
Quantitative Reasoning Approach. Addison Wesley.