Jungck Et Al Manipulatives CBE 2010

Essay Mathematical Manipulative Models: In Defense of “Beanbag Biology” John R. Jungck,* Holly Gaff, † and Anton E. Weisstein ‡ *BioQ UEST Curriculu m Conso rtium, Beloit College, Beloi t, WI 53511; † Community and Environmental Health, College of Health Sciences, Virginia Modeling, Analysis and Simulation Center, Old Dominion University, Norfolk, VA 23529; and ‡ Truman State University; Kirksville, MO 63501 Submitted March 16, 2010; Revised June 22, 2010; Accepted June 23, 2010 Monitoring Editor: Pat Marsteller Mathematical manipulative models have had a long history of influence in biologic al research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core pr in ci pl es , and 4) an al ys is of re al data se ts —we demonstrate a pr oc es s that we ha ve shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consor- tiu m ov er the past 24 yr. We bu ilt this app roach base d up on a bro ad sur vey of lit er ature in ma the ma tical educational research tha t has co nvi nci ngl y demons tra ted the uti lit y of mu lti pl e model s that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Under- grad uate Math emat ical Bio logy Edu cati on (NU MB3R 5 COUN T; http ://b ioq uest .org /numbers - count). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epi dem io lo gy. Ma the ma tic al ma nip ul ative mo del s hel p lea rne rs bre ak thr ou gh pr io r fea rs to dev el op an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. INTRODUCTION Numerous national commissions have emphasized mathematical fluency as a crucial component of educational reform in biol ogy. None thel ess, biol ogy cur ricu la at most institutions remain resolutely free of meaningful quantitative reasoning and analysis. To break this impasse, we propose a pedagogical approach that approaches mathematics from four complemen- tary perspectives: 1) physical manipulatives, 2) computer simulation s, 3) derivation of mathem atical relationshi ps from core principles, and 4) analysis of real data sets. We demonstrate this appro ach with spec ific examp les tak en from the Bio- QUEST Curriculum Consortium’s 24-yr experience of holding faculty development workshops for biology and mathematics educators. In these workshops, we have frequently found that manipulatives help learners break through prior fears to develop an app rec iat ion for howmat hem ati cal rea son ing info rms pro ble m solvin g, infere nce, and preci se comm unication in biolog y. Unfortunately, two main concerns have hindered the adop- tio n of man ipu lati ves in unde rgra dua te science educ ati on. Some faculty worry that college students are already skilled in abstract thinking and will therefore view use of manipulatives as condescending. Furthermore, students’ experience with so- phistica ted and interac tive visualizations from comput er gam- ing may make physical manipulatives seem hopelessly out- dated. What, then, do manipulatives have to offer? First, many studies provide evidence that appropriate class- room use of manipulatives both broadens and deepens students’ learning of mathematical concepts. For example, group DOI: 10.1 187/ cbe.1 0 –03– 0040 Address correspondence to: John R. Jungck ([email protected]). © 2010 J. R. Jungck et al. CBE—Life Sciences Education © 2010 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the aut hor (s) . It is ava ila ble to the public under an Att ributi on– Noncommercia l–Sha re Alike 3.0 Unpor ted Creativ e Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0). CBE—Life Sciences Education Vol. 9, 201–211, Fall 2010 201

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Jungck Et Al Manipulatives CBE 2010