Dr. Therese Shelton

ABSTRACT

Therese Shelton (shelton@southwestern.edu), Southwestern University Mathematics and Computer Science Dept., will develop technological modules for use in Calculus. Technological supports will primarily be the Calculator Based Laboratory System (CBL), through which students will collect data directly from experiments they perform, and the TI-85 Graphing Calculator. Students will also use the computer algebra system Mathematica, Excel spreadsheets, and other technological elements to help internalize course content and produce technical reports. Project results will be disseminated to other ACS institutions through three means: the ACS "Technology and Calculus Pedagogy" Workshops, a web page (http://www.southwestern.edu/~shelton), and through professional meetings. Although some aspects of the resulting materials will be course specific, adaptations can be made to customize segments for use in other courses, even in other departments. The low cost and portability of the CBL equipment and graphing calculators make their use feasible at any institution. The goal is to use technology as a teaching/learning tool, rather than an end in and of itself, in a manner appropriate for a liberal arts education. The goals are consistent with the ideals of the National Calculus Reform Movement, an ongoing effort to better prepare students in mathematics.

Purpose and Goals
During the proposed Fellowship period, Fall 1998, my full load will consist of teaching our newly revised Calculus I. Dr. K. Richards and Dr. E. Brooks of my department upgraded the course last year to have five contact hours a week for four hours credit, a vast improvement over the previous three hours. The increased contact allowed a heavier emphasis on graphical approaches, aided by the CBL, TI-85, and Graph Link. The latter is communication software between a computer and the graphing calculators, enabling screens to be printed and files to be saved. The newer pedagogy increases motivation and focuses on concepts rather than rote mathematical techniques. This means a better balance between interpretation of visual information, numerical values, and equations. Although I have experience teaching with technology, I have not yet fully embraced the new pedagogy, nor do I feel proficient in graphing calculators. I have increasingly used visual and graphical techniques, but only in segments of several courses. I am most anxious to further improve my teaching through a more thoughtful and comprehensive use of technology and associated pedagogy. I plan to supplement the work of my colleagues at Southwestern University and at other ACS institutions with additional teaching modules.

Preparation
My preparation during Summer 1998 will revolve around several conferences offering exciting opportunities for faculty enhancement. The first focuses on national efforts to reform undergraduate education; "Shaping the Future of Undergraduate Science, Mathematics, Engineering and Technology Education" is sponsored in part by the National Science Foundation. Assessment issues, pedagogy, and the role of technology are primary elements in this conference and in the two workshops. The Mathematical Association of America short course "Enhancing Calculus Using the TI-92 and the CBL" directly deals with the Calculus course and technology. I will thus already have new ideas to discuss at the ACS Workshop "Technology and Calculus Pedagogy" in its first session this summer. Links to these workshops may be accessed through my new web page. Other related projects are also briefly described there. Undoubtedly I will continue revising my approach to the course as I teach it.

Technical Experience
I have used technology as a teaching tool and for student projects in numerous courses, most notably Calculus II and III, Differential Equations I and II, Introduction to Computing, and Mathematical Modeling, the latter of which I designed. I have extensively used several technological supports of interest to this Fellowship: the computer algebra system Mathematica; graphing, spreadsheet, and database capabilities of EXCEL; and word processing for generating technical reports. My programming experience may prove useful in preparing course materials. I have used the TI-85 Graphing Calculator, the Calculator Based Laboratory System (CBL), and Graph Link enough in class to present a short paper at the Texas Section Meeting of the Mathematical Association of America. The summer workshops will provide me with increased proficiency to ensure success in this project. I will also learn to use Graphical Analysis, a software package to ease regressions and plotting. I will learn how to save and access files, such as Mathematica documents, through web pages. This will facilitate student use of the files. I will seek help from other faculty and from our Information Technology Staff.

Plan
My work on this Project will produce an environment conducive to creating opportunities for student projects as an alternative to using a plethora of small, separate homework problems. Certainly homework problems will still be required. It is important to note that I will be using technology to support the teaching/learning environment, rather than be the focus of the course. Students will have a variety of opportunities to present their understanding of the concepts, with and without technology. Thus, students cannot use the technology as a "crutch", producing results that might look impressive superficially even when the student does not sufficiently understand the concepts.

Technology is useful when it fosters an atmosphere of student independence, allowing greater opportunity for a student to build his or her skills outside of a class lecture. The portability of the TI-85 and the Calculator Based Laboratory equipment allows for out-of-class, independent experiences. This empowers the student to make conjectures and investigate them on his/her own.

The low cost of the equipment is a bonus for many departments. Student may purchase a TI-85 for $120. Departments may purchase the basic CBL system for $179; the CBR motion detector for $95; and Graph Link for $55.

Initially, I will use carefully outlined problems to ensure students are sufficiently comfortable with the technology. The mix of technological support and traditional methods I plan to use allows for a wider variety of teaching and learning methods, enhancing my teaching as well as student learning. In fact, graphing calculators have served to level the playing field across gender and mathematical background.

Although I will be well prepared by the time the semester commences, I will be flexible and open to improvements during the course of the semester. I will seek more ideas during the Fellowship period through participation in the International Conference on Technology in Collegiate Mathematics (ICTCM) in Nov. 1998.

Assessment
Currently, I plan to evaluate the technical level of the students at the beginning and at the end of Calculus I in Fall 1998. Students will be required to keep an Academic Journal to periodically analyze their learning of mathematics and the impact of technology on that learning. I will also administer a student self-assessment of the usefulness of technology at the end of the course. I will learn more about assessment tools this summer in each of the workshops.

Dissemination
The two-year ACS workshop will provide the primary opportunity for dissemination of results to ACS members, particularly the second session in Summer 1999. My web page will be available to all members. There are also other opportunities for dissemination, beginning with the ICTCM previously mentioned. In Jan. 1999, I plan to attend the Joint National Meetings of the American Mathematical Society, the Mathematical Association of America, and Women and Mathematics. Other possibilities for paper presentations include the International Conference on Mathematics/Science Education and Technology in March 1999. I hope to see other faculty from the various ACS institutions at these professional meetings. I will present preliminary results of this project during at least one.

Institutional Support
The proofs of support are multiple and diverse. The institution already has the physical support needed for the aforementioned technology. The new Calculus course has been taught for a year. My colleagues in the department are supportive of my endeavors. The Department encourages students to participate in nearby professional meetings by subsidizing expenses. I will receive financial support through the Provost's office of Southwestern University to participate in the NSF workshop this summer.

General Enhancement of Student Learning and of My Teaching
The use of technology in mathematics allows for discovery based learning, writing across the curriculum, data based problems, student independence, increased use of projects, greater opportunity for interdisciplinary study, student presentations at professional meetings, and student/faculty collaboration. All of these are goals of the Calculus Reform Movement. This Fellowship will allow me to include state-of-the-art methodologies in my teaching. Technology allows for greater realism in and applicability of problems. The use of carefully constructed exercises with mathematically tractable answers invariably requires oversimplifying the situation modeled. Without technology, performing complicated problems is overly burdensome. Students lose sight of the true focus of the problem, get lost in the detail, and fail to see the point and beauty of the mathematics. A discovery based approach allows students to build intuition by experiencing concepts concretely, facilitating generalizations. With the Calculator Based Laboratory and related technology, students perform their own experiments and collect and analyze real data. Students will learn a great deal and derive a sense of satisfaction and pride from creating a cohesive report of project findings. Graphical approaches, fostered by the use of technology, enhance the learning of mathematics. The CBL equipment is ideal for interdisciplinary study. Various probes allow experiments in electricity, motion, temperature, dissolved oxygen levels, etc. Thus students more clearly see the applicability of mathematics as well as its connection to other disciplines. In addition, the use of such equipment provides a structure for conversation, conjecture, and active learning.

Some students will be able to extend projects in an Independent Study, allowing for more individualized and more collaborative faculty/student interaction as well as greater choice and creativity by students. Students will be encouraged to present the projects at professional meetings. For our students in particular, opportunities are available through the Texas Section Meeting of the Mathematical Association of America. The Spring 1999 meeting will be held in San Marcos, TX, an easy trip for our students. Internal funding (The Mundy Fellowship and The Science Initiative) might be available for intense student/faculty collaboration with a few students. The use of technology will prepare students for participation in the international COMAP (Consortium for Mathematics and its Applications) Modeling Contest held each Spring. The contest is open to any institution. The technological complement to their education will also make students more competitive with those from larger, more research oriented institutions in a way consistent with the goals of a liberal arts institution.

By targeting Calculus I, I hope to better prepare students for subsequent courses. Some students who might have thought Calculus I would be their only math course might find they wish to study more. I have great plans for several other courses, knowing that the pool of students will be ready for more. It is reasonable to expect the benefits of this project to be reaped for many years.