A Progress Report on an Exploratory Mathematics Course: Incorporating a Programming Component
Goldberg, Robert, Waxman, Jerry, Mathematics and Computer Education
This paper reports on an ongoing effort to incorporate a programming component into exploratory mathematics courses and analyzes some of the many practical considerations required for successfully managing such a course in large lecture hall classes. Two pedagogical paradigms (top-down and bottom-up) are compared and contrasted for teaching Visual Basic, the macro language for Excel. It is suggested that both of these paradigms are essential to presenting the material and directly complement each other. The top-down approach fits the lecture component of the course while the bottom-up approach broadens the laboratory experience. In addition we outline the use of the Insight system to facilitate group interaction for problem discussion, program construction and solution and code debugging.
At Queens College we have completed two years of a three-year DOE-FIPSE funded project to implement a new approach for curing "quantiphobia". Quantiphobia is the fear of, and consequent inability of many to understand and utilize quantitative information and reasoning. Our approach is an outgrowth of an earlier course developed for teaching non-specialists high-level computing skills (Waxman, 1996). A marked decrease in students' fear of thinking quantitatively was noticed after just a short (5 week) exposure to quantitative reasoning using Excel. In addition there was an increase in the students' willingness to take additional "mathematically oriented courses." As a result, we are currently developing a new course, "Exploring Quantitative Relationships (EQR)", to be offered as one of the alternatives to the college-wide first level general mathematics requirement (we expect about 80 % of the EQR classes to be non-science, non-computing majors). This course will be exploratory in nature and will directly address the issue of teaching students how to "read" and understand statements involving quantitative relationships; teach them how to formulate "mathematical" and quantitative relationships on their own; and teach them how one might go about solving problems that are formulated in a mathematical way.
This will be done within the context of Excel, which allows students to formulate quantitative problems and solve them even if they have poor mathematical manipulation skills. Excel allows experimentation and has a very powerful graphing capability. Moreover, Excel has very powerful macro facilities (VBA, the macro language provided by Excel spreadsheet applications, and Visual Basic) and thus would allow the students to develop computational and algorithmic perspectives.
The design and philosophy of this course has been described elsewhere (Goldberg and Waxman, 2002). In this paper we focus on managing the component of the course that teaches the Visual Basic programming paradigm. This paper addresses two issues. First, how do we reconcile the need to teach both top-down and the bottom-up perspectives on function construction? How do we effectively teach both "programming in the large" and "programming in the small" within the very limited time allotted to this component in the course? Second, program construction often is a solitary endeavor. How do we facilitate group interaction so that students can learn from each other's strengths and missteps? Such interaction is important because it exposes students to many more situations and ideas than when working independently.
Our approach is based on our experiences in teaching large-format introductory programming and non-major "software tools" courses over the past fifteen years. We have experimented with different methodologies and present them in section 2. Section 3 presents two representative examples from the course materials: leap year calculations and primality testing. section 4 introduces the use of specialized classroom technology to encourage student interaction in the laboratory components of the course. Conclusions are drawn (section 5) and the dual focus of this course is suggested to be applicable to other courses as well. …