Abstracts from the Quantitative Learning Session in San Antonio, Texas, January 1999


Kate G. McGivney, Deborah Hughes Hallett: Precalculus: Labs and Literacy

Christopher Tisdale III, Danny W. Turner, Gary T. Brooks: Precollege Preparation for College Mathematics: A Survey of South Carolina Faculty

Barry Schiller: Incorporating QL Widely into the Curriculum

Jerry A. Johnson: Quantitative Literacy through "Math Across the Curriculum"

Shandy Hauk: Motivating Quantitative Literacy

William L. Briggs, Jeffrey O. Bennett: A Precalculus Quantitative Reasoning Course for Liberal Arts Students

Harris S. Shultz: Web-based Intermediate Algebra Minicourse

Janet L. Andersen: Connecting Science and Mathematics General Education Courses - One Approach to Quantitative Literacy

William E. Haver: An Appropriate Culminating Mathematics Course

Mark L. Klespis, Peter A. Cooper: An Integrated Introductory Mathematics and Computer Science Course

Todd M. Swanson: Helping Students Take Responsibility for Their Learning

Todd M. Swanson, Arnold R. Silverman: Learning Communities and Computer Based Assignments for Improving Quantitative Literacy Among College Freshmen

Paul R. Coe: Introducing Quantitative Literacy at Dominican University

Judith F. Moran, Gove W. Effinger: Moving Beyond the First Stage: Developing Links to Other QL Programs and Other Academic Disciplines

Judith F. Moran, Helen S. Lang: Moving Beyond the First Stage: Developing Links to Other Academic Disciplines

James R. Smith, Holly Peters Hirst: An Award-Winning Quantitative Literacy Course

Janet E. Teeguarden: The Quantitative Reasoning Program at DePauw University: Nearly Twenty Years of Experience

Thomas G. Wangler: Piloting a Quantitative Literacy Course at a Liberal Arts Institution: Pedagogical Issues, Interesting Projects, and Assessment Criteria


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Precalculus: Labs and Literacy

Kate G. McGivney(mcgivney@math.arizona.edu). Department of Mathematics, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721, and
Deborah Hughes Hallett(dhh@math.arizona.edu), Department of Mathematics, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721. Preliminary Report.

Precalculus courses often serve two distinct purposes: preparing students for calculus and improving the quantitative literacy of students going into a wide variety of fields. Nationally, a large number of students who take precalculus do not go on to take calculus so it is important for us to think about the experiences we should provide for such students. Of the students who do not go into calculus, many will go into fields or take courses which involve gathering, organizing, and interpreting data. We propose to talk about a version of precalculus in which data interpretation is introduced in the classes and homework, and practical experience with gathering and interpreting data is provided by a series of labs. We expect to demonstrate as many of the materials as time allows. (Received Sept. 19, 1998)

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Precollege Preparation for College Mathematics: A Survey of South Carolina Faculty

J. Christopher Tisdale III, Winthrop University, Mathematics Department, Rock Hill, SC 29733
Danny W. Turner
(turnerd@winthrop.edu), Winthrop University, Mathematics Department Rock Hill, SC 29733, and
Gary T. Brooks, Winthrop University, Mathematics Department, Winthrop University, Mathematics Department Rock Hill, SC 29733.

This survey addresses whether or not students enter South Carolina (SC) higher education institutions with the appropriate background to be successful in college mathematics. Recent releases of SC performance from National Assessment of Educational Progress, the College Board, and so forth give parents and the general public some indication of student preparation. We decided to access a source different from these formal evaluations. We asked the people who know best--the college faculty (from all state-supported schools) who provide instruction in the initial college mathematics course. This report presents their answer to whether or not our students are prepared. The survey contains interesting information about a number of important issues: trends in precollege preparation; calculus in high school; preparation in arithmetic, geometry, albegra, trig, probability/statistics; study skills; problem solving; student attitudes; calculators and more. We feel that what we discovered about quantitative literacy in our state will be of general interest. (Received September 23, 1998)

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Incorporating QL Widely into the Curriculum

Barry Schiller(bschiller@ric.edu), Mathematics/Computer Science Department, Rhode Island, Providence, RI 02908.

Rhode Island College has no official "quantitative literacy" course and is unlikely to be able to establish one. However, this talk will describe how some QL elements (such as citizenship education, recognizing plausibility, making inferences from quantitative information, working with large numbers, detecting fallacies) are being incorporated into a variety of lower division courses, including algebra, "technical" math, QBA, and basic statistics. An emphasis on multistep problems, or those with multiple methods of solution, which this contributor feels are too often underemphsized, will be described. (Received September 23, 1998)

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Quantitative Literacy through "Math Across the Curriculum"

Jerry A. Johnson,(jerryj@unr.edu), Department of Mathematics, University of Nevada, Reno, Reno, NV 89557. Preliminary Report.

Mathematics Across the Curriculum is an NSF-funded program (DUE 9354652) whose aim is to improve the quantitative ltieracy of students and promote their appreciation of mathematics by integrating quantitative components into a variety of courses in the university curriculum. It was conceived at the University of Nevada-Reno, along the lines of a successful Writing Across the Curriculum model. Our goal is to enhance the quantitative content of courses where it exists and introduce it where it does not, thereby increasing students' exposure to applications of mathematics in a variety of courses and making quantitative learning a "shared responsibility" across campus. In this talk we will describe some of the features of the project that affect quantitative literacy. In particular we have implemented math components in political science, humanities, anthropology, psychology, and art, among others. A Math Across the Curriculum web site has been established that allows users to get detailed information and to download documents and resources. The URL is http://www.math.unr.edu/MAC (Received September 23, 1998)

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Motivating Quantitative Literacy

Shandy Hauk,(hauk@chapman.edu). Preliminary Report.

A discussion of approaches to stimulating student interest and willingness to invest time in understanding mathematics. Fifteen class sections of a one-semester quantitative literacy mathematics course are evaluated. Clear among the various results is that student participation in a seminar-type project presentation outside of the classroom very early in the semester increases student dedication to the course and course work. The programming and use of calculators (an aplication of the symbolic logic taught in the course), to simplify tedium without eliminating conceptual mastery, are also investigated.

Additionally, the effect of investigating with students the accepted meanings of "teacher" and "classroom" in mathematics are examined. Early analysis indicates the method is motivational for those students for whom the ritualized rigor of mathematics is anathema (about 50% of most class sections). The results, including comparisons of student self-perception with the same/different instructor and same course material, are discussed. (Received September 24, 1998)

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A Precalculus Quantitative Reasoning Course for Liberal Arts Students

William L. Briggs,(wbriggs@math.cudenver.edu), Mathematics Department, Box 170, University of Colorado at Denver, P.O.173364, Denver, CO 80217, and
Jeffrey O. Bennett

Survival in the 21st century will require fundamental quantitative skills that all college and university students should possess. In this talk, we will begin by briefly surveying the rationale for developing a quantitative reasoning (QR) course for liberal arts students and discussing the issues that arise in teaching such a course. This discussion will draw on the presenters' experience in developing such a course at the University of Colorado and writing a textbook (Addison-Wesley) to support the course. The remainder of the talk will consist of classroom activities and presentations that are used in the course. The topics that will be surveyed in these activities include (as time permits): an in-class simulation with dice of the spread of a disease (among workshop participants!) and its modeling; supply and depletion problems as they arise in finance, engineering, drug use, and environmental sciences; mathematics and music; the uses and abuses of percentages; mathematics in the news; the mathematics of voting. The talk is designed for instructors at two-year and four-year colleges who are contemplating teaching QR courses, as well as for instructors who are already teaching QR courses. (Received September 24, 1998)

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Web-based Intermediate Algebra Minicourse

Harris S. Shultz,(hshultz@fullerton.edu), Department of Mathematics, California State University-Fullerton, Fullerton, CA 92834-6850

This Web-based Intermediate Algebra MInicourse is desinged for entering freshmen who have failed the California State University Entry Level Mathematics (ELM) Examination with a score that falls within the upper quartile of all students who failed the test. Typyically, students who fail the ELM must take a course in Intermediate Algebra The assumption in developing this minicourse is that students who come close to passing a placement examination need less insturctional time than do others who fail the same examination. Because the target audience consists of students still in high school, there is a strong rationale for a course that requires minimal time on campus. The creation of a Web-based remedial mathematics course helps the University meet two of its major objectives: (1) Decrease the amount of remediation on campus and (2) develop strategies that allow and encourage incoming freshmen to resolve their deficiences while still in high school. (Received September 24, 1998)

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Connecting Science and Mathematics General Education Courses - One Approach to Quantitative Literacy

Janet L. Andersen,(andersen@math.hope.edu), Dept. of Mathematics, Hope College, Holland, MI 49422-9000. Preliminary Report.

At Hope College, with the partial support of the National Science Foundation, a team consisting of two mathematicians, a geologist, and a biologist, is developing three new general education courses. The mathematics course (Mathematics in Public Discourse) is a co- or pre-requisite for the science course (The Atmoshpere and Environmental Change and Populations in Changing Environments). The science courses will use and build on the mathematics the students have learned. The courses connected by common content themes (the use of functions, graphs, and statistical analysis of data to interpret the physical world); common pedagogy (exploratory labs, investigative worksheets, cooperative learning); and common technology (the IT-83 and DBL). These courses were piloted Spring 98 with approximately 20 students. During Fall 98, there are 150 students enrolled in the mathematics course and 40 students enrolled in the biology course (the atmospheric science course will be taught Spring semester). The assessment done during the pilot study indicated that both attitudes and mathematical ability improved. (Received September 27, 1998)

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An Appropriate Culminating Mathematics Course

William E. Haver,(wehaver@vcu.edu), VCEPT, Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA 23284-2014.

VCU offers a course "Contemporary Applications of Mathematics: that is required of all non-science majors. Its goal is to improve students' ability: to study quantitative situations; to use quantitative skills in actual siatuions; to learn through reading and communication with others; and to explain mathematics in writing and orally. Topics include optimal routing; fair division; election theory; linear and exponential growth; interpreting and explaining data. As well as taking tests, each student in each section makes weekly entries in a log; studies mathematics as a member of a team and orally describes this mathematics to others; writes two three-page typed papers; studies topics independently to prepare for a "poster-session". The course was developed and piloted with Gwen Turbeville of J. Sargeant Reynolds Community College. The challenge has been to devleop materials and approaches to make it possible to teach this course to large numbers of students. Wtih support from the NSF-supported Virginia Collaborative for Excellence in the Preparations of Teachers (VCEPT), currently 25 different instructors (faculty, part-time instructors and GTAs) annually enjoy teaching this course to 2,000 students. Its features are being adopted by other VCEPT institutions.
(Received September 28, 1998)

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An Integrated Introductory Mathematics and Computer Science Course

Mark L. Klespis,(mth_mlk@shsu.edu), Dept. of Mathematical & Informational Sciences, Sam Houston State University, Huntsville, TX 77341-2206, and
Peter A. Cooper,(csc_pac@shsu.edu), Dept. of Mathematical & Informational Science, Sam Houston State University, Huntsville, TX 77341-2206.

The presentation will report on an NSF-funded project for implementing a 6-hour quantitative literacy core course at Sam Houston State University. The quantitative literacy course integrates mathematics and computer science content to extend student skills in interpreting and analyzing problems, applying problem solving strategies, identifying appropriate quantitative tools, and applying those tools in the construction and communication of solutions. Students are expected to exhibit teamwork and a sense of scientific inquiry through student projects and lab activities. Freshman students from mathematically weak and technologically disadvantaged backgrounds have been encouraged to take the course, giving them a jump-start in their collegiate experience. Curriculum materials have been customized and extended from exemplary materials in mathematics and computer science. Topics include: internet services, word processing, presentation and graphics software, spreadsheets, functions, trigonometry, descriptive statistics, finance, and linear programming. Effects on student retention, attitudes, and comparisons with current general education classes in mathematics and computer science will be presented. Samples of student work will be included.
(Received September 28, 1998)

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Helping Students Take Responsibility for Their Learning

Todd M. Swanson, (swansont@hope.edu), Mathematics Department, Hope College, Holland, MI 49424-9000. Preliminary Report.

The use of investigations, prljects, reading questions, and web sites can be used to help students take responsibility for their learning in a precalculus course. This has resulted in a course that is more in-depth and one that is quite different from a traditional course. The inviestigations and projects allow students to be actively engaged in the matieral they are studying. The investigations are more elaborate and more in-depth than exercises. They usually involved discussion questions and are completed by studnets working in groups. The projects are longer and more involved than the investigations. Students are also encouraged to be creative when writing up their projects. To allow enough class time to work on investigations and projects, it is expected that studentslearn much of the basic material on their own. To help them with this, a number of things are done. The text is written for students to read and they are expected to read it. To guide them in this, reading questions are interspersed throughout the reading. Using these questions helps students pick out the important concepts and checks them on their understanding of these concepts. Also, the instructor's class notes, assignments, and solutions to assignments are placed on the web for student access.
(Received September 30, 1998)

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Learning Communities and Computer Based Assignments for Improving Quantitative Literacy Among College Freshmen


Lyle Hallowell, (hallowl@sunynassau.edu), Department of Sociology, Long Island Consortium & Nassau Community College, Carden City, New York 11530, and
Arnold R. Silverman, (YeniHoja@Aol.Com), Department of Sociology & Long Island Consortium, Nassau Community College, Garden City, New York 11530.

Our approach combines computer-based assignments with learning communities. The core course is "Introduction to Sociology". Students learn and apply statistical concepts to sociological questions using the STATA analysis package and social survey data. There are three sections per term, one is a learning community section. This section has a joint enrollment with either freshman composition or intro to statistics. Faculty cooperate, but do not team-teach. Among our findings are: (1) students in the English/Sociology Community perform at a higher level; (2) students in the Statistics/Sociology Learning Community performed poorly; this may be a result of problems in integrating the two courses; (3) when the classes involved qualitative ways of conceptualizing of statistical concepts there was accelerated learning; (4)when students indentify with each other, they teach each other, and transform initial anxiety into confidence; (5) the focus on the logic of writing improves problem solving abilities. We note that this computer-based approach requires additional time for students and faculty and that a Learning Community approach requires active faculty management. This effort was funded by the Long Island Consortium for Interconnected Learning.
(Received October 2, 1998)

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Introducing Quantitative Literacy at Dominican University


Paul R. Coe, (coepaul@email.dom.edu), Dept. of Mathematics and Computer Sciences, Dominican University, 7900 W. Division Street, River Forest, Illinois 60305.

In the fall of 1997 Domincan University faculty completely revised the general education requirements for the College of Arts and Sciences. Part of that revision was the addition of another math course beyond the previous requirement of Intermediate Algebra. Courses already offered that would satsify the requirement included College Algebra (and several others). One of the selling points of the proposal, drafted by our department, was the creation of a new general math course that would satisfy the requirement. The intent was to create a course more relevant to students who did not plan to take any additional mathematics. In my presentation I will discuss the contents of the course. In it I try to focus on developing consumers more than creators of mathematical content. I will also talk about the difficulties involved in getting such a course embraced by the university. Not only did we struggle to get the additional mathematics requirement in the new curriculum, but now that we have it we are still struggling to get advisors to place students into the new course. Most of the enrollments las spring were still for College Algebra, even though many of the students in that course would have been much better served by the new course.
(Received 2, 1998)

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Moving Beyond the First Stage: Developing Links to Other QL Programs and Other Academic Disciplines


Judith F. Moran, (judith.moran@mail.trincoll.edu), Department of Mathematics, Trinity College, Hartford, CT 06106, and
Gove W. Effinger, (effinger@scott.skidmore.edu), Department of Mathematics, Skidmore College, Saratoga Springs, NY 12866.

Representatives of a dozen colleges in the northeast have been meeting for the last two years to pursue a common interest in implementing quantitative reasoning courses and quantitative support on their several campuses. Members of the Math Departments of two of the schools, Trinity and Skidmore, will report on their efforts to move beyond the first tier of foundation courses to develop second-tier quantitative courses and modules for non-math courses. Judith Moran, Director of the Math Center at Trinity, will describe QL courses incorprating Hartford data which were created under Trinity's Urban Curricular Initiative, as well as quantitative modules and laboratories designed for science and social science courses. Gove Effinger, Director of Skidmore's QL program, will describe several second-tier courses created at Skidmore, including Statistical Controversies, Mathematics and the Art of M.C. Escher, and The Theory of Epidemics. Materials from both schools, as well as information about programs at the other colleges in the Northeast QL group, will be available.
(Received October 2, 1998)

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Moving Beyond the First Stage: Developing Links to Other Academic Disciplines


Judith F. Moran, (judith.moran@mail.trincoll.edu), Department of Mathematics, Trinity College, Hartford, CT 06106, and
Helen S. Lang, (helen.lang@mail.trincoll.edu), Department of Philosophy, Trinity College, Hartford, CT 06106.

Under a major NSF grant: The Integration of Science and Mathematics into a Humanities Curriculum, science and mathematics faculty at Trinity College have created laboratories for a variety of humanities and social science courses. Helen Lang, Chair of Trinity's Philosophy Department, and PI of the grant, will report on the overall project and the range of courses affected and laboratories created. Judith Moran, Director of the Math Center at Trinity and a consultant on the grant, will describe in more detail two of the laboraties: on Mayan mathematics and Mayan astronomy, that she has created for a Latin American history course.
(Received October 2, 1998)

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An Award-Winning Quantitative Literacy Course


James R. Smith, (smithjr@appstate.edu), Mathematical scineces, Appalachian State University, Boone, NC 28608, and
Holly Peters Hirst, (hirstp@appstate.edu), Mathematical Sciences, Applachian State University, Boone, NC 28608.

The presentation will describe our quantitative literacy course at Appalachian State University which we believe catches the spirit of the "Crossroads" report. It includes a computer lab and lots of hands-on work in areas of mathematics that sutdents see as useful - Finance, Statistics, Trigonometry, and Linear Programming. Students solve problems using the computer and write reports on their solutions. Our course won the award given by the Annenberg Foundation for quantitative literacy courses that use technology well. You can check out some of what we are doing at http://www.mathsci.appstate.edu
(Received October 5, 1998)

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The Quantitative Reasoning Program at DePauw University: Nearly Twenty Years of Experience


Janet E. Teeguarden, (JTEEGUARDEN@DEPAUW.EDU), Depauw University, Harrison Hall 211C, 7 E. Larabee St., Greencastle, IN 46135.

The Quantitative Reasoning Program at DePauw University was developed in the early 1980's as part of a three-part competency program for all students. Students may enter the program at either of two levels. Placement issues and descriptions of the evolution of the developmental course(s) will be discussed. In addition, a list of the second level "Q" courses, from many different departments, will be used to illustrate the broad base of this program.

One of the strongest features of the program is the faculty development component. Participation in an intensive faculty workshop is required in order for faculty members andone or more of their courses to be part of the quantitative reasoning program. A description of the workshop will be included in this presentation.

The Quantitative Reasoning Center, part of the Academic Resource Center, is the supporting arm of the program for students. Peer consultants are recruited, trained, and supervised by the Center Director. A look at how all this works will be included if time permits.
(Received October 7, 1998)

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Piloting a Quantitative Literacy Course at a Liberal Arts Institution: Pedagogical Issues, Interesting Projects, and Assessment Criteria

Thomas G. Wangler, (twangler@ben.edu), Dept. of Mathematics, Bendictine University, 5700 College Road, Lisle, IL 60532-0900.

In this paper I will talk about some pedagogical issues related to piloting a quantitative literacy course at a liberal arts institution and some projects I've had my students work on. These projects tend to be intersting and useful (to the student) and hence are generally well received.
Some of the issues that will be addressed are:
Which majors are better served by a quantitative literacy course?
What is the underlying philosophy of instruction (e.g. skills versus appreciation)?
What should the prerequisite be?
What are the goals and objectives of the course? How do they affect the course content?
What assessment criteria would be appropriate for such a course?
What is a working definition of a quantitatively literate person?Why would anybody want to pilot a course in quantitative literacy?
On the lighter side, I will also share some of the humorous responses I got from students who forgot to "determine the reasonableness" of their answers.
(Received October 14, 1998)

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