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) 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.
Jungck
John R
JR
BioQUEST Curriculum Consortium, Beloit College, Beloit, WI 53511, USA. jungck@beloit.edu
Gaff
Holly
H
Weisstein
Anton E
AE
D000818:Animals; D001695:Biology / Q000193:education*; D003198:Computer Simulation; D005589:Foxes; D040961:Genetic Drift; D006801:Humans; D008433:Mathematics / Q000193:education*; D017145:Models, Educational; D011156:Population Density; D011817:Rabbits; D012984:Software; D013334:Students
Math Biosci Eng. 2009 Jul;6(3):469-92
19566121
Perspect Biol Med. 1964;7:343-59
14161266
Judgm Decis Mak. 2009 Jun 1;4(4):256-272
24179560
Prev Vet Med. 1998 Jun 1;35(3):181-93
9658444
Genetics. 1943 Nov;28(6):491-511
17247100
PLoS Biol. 2004 Dec;2(12):e439
15597117
Int J Epidemiol. 2008 Jun;37(3):451-4
18522986
Int J Epidemiol. 2008 Jun;37(3):435-42
18522982
Math Biosci. 1999 Nov-Dec;162(1-2):1-32
10616278
Proc Natl Acad Sci U S A. 1989 Dec;86(23):9441-5
2687881
Epidemiology. 2009 Jul;20(4):508-11
19525687