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Session 1265 .

Technology-Based Problems in Calculus From Science and Engineering (1) Aaron D. Klebanoff and (2) Brian J. Winkel

(1) Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute IN 47803 USA Aaron. Klebanof@Rose-Hulman. edu and (2) Department of Mathematical Sciences. United States Military Academy, West Point NY 10996 USA ab3646@usma2.usma. edu. ‘

student curiosity and fails to develop required problem for- ABSTRACT mulation skills. Moreover, error-fraught handwork stops We report on the development of a site 1 for complex, students from going into depth or playing ‘iWhat if?” technology-based problems in calculus, from science and games with problem formulation, solution, or parameters. engineering. Five college faculty from mathematics and en- We believe one remedy for the these weaknesses is to de- gineering and seven high school teachers from mathematics velop complex, technology-based problems in calculus from and science developed a collection of complex problems in science and engineering. We have done that! We present mathematics which demand the use of technology. Specifi- situations in which students formulate strategies to reach a cally, the underlying technology is a computer algebra sys- solution, work towards a solution using technology (in our tem (in our case, Mathematical). The intent of the project is case Mathematical), and then evaluate the reasonableness to provide faculty with a source of such problems. Accord- of their solutions in the context of a science or engineering ingly the problems, in the form of Mathematical notebooks, setting in most cases. We refer to these as technology-based ASCII files, and .html files, are on the World Wide Web problems. and can be accessed at These problems were developed during the summers of http: //www.rose-hulman. edu/Class/CalculusProbs 1994, 1995, and 1996. A team of faculty and associate high We would welcome further contributions of problems, cri- school mathematics teachers developed problems, polished tiques of in place problems, descriptions of use of the prob- established problems, prepared standard formats for prob- lems, and problem improvements and suggestions. lem presentation, produced Mathematical resources to ac- company problems, and wrote up guidelines for using prob- INTRODUCTION lems in high school and college calculus settings. Dr. Kle- banoff prepared the World Wide Web site and uploaded the We believe there are a number of weaknesses in current materials for electronic access through site facilities at Rose- curricula. Huhnan. During the academic years 1994-95 and 1995-96, faculty at Rose-Hulman at USMA located resources, devel- 1. There is an overemphasis on rote manipulation, hence oped significant problems, tested them in courses, summa- lack of focus on the bigger picture and deeper problems. rized student reactions and solution strategies, and modified Students become lost in the vast amount of numeric and extended problems. One high school student developer and symbolic manipulations which they are asked to assisted (summer 1995) in evaluating solutions, assessed perform by hand. prerequisite knowledge needed for attempting these prob- 2. Few opportunities exist to fully utilize current software lems, and determined the level of effort and time needed for (Mathematical, Maple, MathSoft, DERIVE, etc.) success. 3. Compartmentalization exists in which students see lit- tle substantive relationships between mathematics, sci- ence, and engineering. PHILOSOPHY AND IMPLEMENTATION OF THE PROJECT Further, without technology students are reduced to mem- orizing collections of special techniques. Overemphasis on We believe students can grow when challenged and moti- manipulative skills at the expense of concepts suppresses vated. Moreover, students are motivated to learn math- 1 Preparation of the materials described in this paper is supported ematics when they see a reason for, most often an appli- by the National Science Foundation under Division of Undergraduate cation of, the mathematics at hand. One can increase the Education grant DUE-9352849 and the Arvin Foundation of Columbus complexity of the problem beyond the traditional text book IN. . - . . _ problem through a number of ways: ‘..~.&, :4 Conference Proceedings ‘.,*,131yR:i ’9 9 6 ‘ S E E ‘“”””

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Winkel, B. J., & Klebanoff, A. D. (1996, June), Technology Based Problems In Calculus Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6346