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Mathematical Manipulative Models: In Defense of “Beanbag Biology”

Mathematical manipulative models have had a long history of influence in biological 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...

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Detalles Bibliográficos
Autores principales: Jungck, John R., Gaff, Holly, Weisstein, Anton E.
Formato: Texto
Lenguaje:English
Publicado: American Society for Cell Biology 2010
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2931667/
https://www.ncbi.nlm.nih.gov/pubmed/20810952
http://dx.doi.org/10.1187/cbe.10-03-0040
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author Jungck, John R.
Gaff, Holly
Weisstein, Anton E.
author_facet Jungck, John R.
Gaff, Holly
Weisstein, Anton E.
author_sort Jungck, John R.
collection PubMed
description Mathematical manipulative models have had a long history of influence in biological 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 principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models 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 Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
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spelling pubmed-29316672010-09-02 Mathematical Manipulative Models: In Defense of “Beanbag Biology” Jungck, John R. Gaff, Holly Weisstein, Anton E. CBE Life Sci Educ Essays Mathematical manipulative models have had a long history of influence in biological 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 principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models 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 Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. American Society for Cell Biology 2010 /pmc/articles/PMC2931667/ /pubmed/20810952 http://dx.doi.org/10.1187/cbe.10-03-0040 Text en © 2010 J. R. Jungck et al. CBE-Life Sciences Education © 2010 The American Society for Cell Biology under license from the author(s). It is available to the public under Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
spellingShingle Essays
Jungck, John R.
Gaff, Holly
Weisstein, Anton E.
Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title_full Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title_fullStr Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title_full_unstemmed Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title_short Mathematical Manipulative Models: In Defense of “Beanbag Biology”
title_sort mathematical manipulative models: in defense of “beanbag biology”
topic Essays
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2931667/
https://www.ncbi.nlm.nih.gov/pubmed/20810952
http://dx.doi.org/10.1187/cbe.10-03-0040
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