Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T19:13:02.711Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Biology Education: Modeling Makes Meaning

Published online by Cambridge University Press:  05 October 2011

J. R. Jungck
J. R. Jungck*
Affiliation:
Department of Biology, Beloit College, Beloit, WI 53511, USA
Get access

Abstract

This special issue of Mathematical Modelling of Natural Phenomena on biomathematics education shares the work of fifteen groups at as many different institutions that have developed beautiful biological applications of mathematics that are different in three ways from much of what is currently available. First, many of these selections utilize current research in biomathematics rather than the well-known textbook examples that are at least a half-century old. Second, the selections focus on modules that are intended for instant classroom adoption, adaptation, and implementation. Instead of focusing on how to overcome the challenges of implementing mathematics into biology or biology into mathematics or on educational research on the effectiveness of some small implementation, the authors develop individual biological models sufficiently well such that they can be easily adopted and adapted for use in both mathematics and biology classrooms. A third difference in this collection is the substantive inclusion of discrete mathematics and innovative pedagogies. Because calculus-based models have received the majority of the biomathematics modeling attention until very recently, the focus on discrete models may seem surprising. The examples range from DNA nanostructures through viral capsids to neuronal processes and ecosystem problems. Furthermore, a taxonomy of quantitative reasoning and the role of modeling per se as a different practice are contextualized in contemporary biomathematics education.

Keywords

biomathematics educationdiscrete mathematicsmodeling
Type
Introduction
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 6: Biomathematics Education , 2011 , pp. 1 - 21
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cohen, J.. Mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better. PLOS Biology, 2, (2004), 439. CrossRefGoogle ScholarPubMed
J. Jungck, P. Marsteller, editors. Bio 2010: Mutualism of biology and mathematics. A special issue of CBE Life Science Education, 9, (2010) No. 3. Available from: (http://www.lifescied.org/content/vol9/issue3/index.dtl).
Jungck, J.. Ten equations that changed biology. Bioscene, 23 (1997), No. 1, 11–36. Google Scholar
Board on Life Sciences. National Research Council. BIO2010: Transforming undergraduate education for future research Bbologists. National Academies Press: Washington, D.C., 2003.
Weisstein, A.. Building mathematical models and biological insight in an introductory biology course. Math. Model. Nat. Phenom., 6 (2011), No. 6, 198–214. CrossRefGoogle Scholar
Gaff, H., Lyons, M., Watson, G.. Classroom manipulative to engage students in mathematical modeling of disease spread: 1+1 = Achoo!. Math. Model. Nat. Phenom., 6 (2011), No. 6, 215–226. CrossRefGoogle Scholar
Neuhauser, C., Stanley, E.. The p and the peas: An intuitive modeling approach to hypothesis testing. Math. Model. Nat. Phenom., 6 (2011), No. 6, 76–95. CrossRefGoogle Scholar
Koch, G.. Drugs in the classroom: Using pharmacokinetics to introduce biomathematical modeling. Math. Model. Nat. Phenom., 6 (2011), No. 6, 227–244. CrossRefGoogle Scholar
AAAS Vision and Change in Undergraduate biology education: A call To action. American Association for the Advancement of Science, Washington, D.C., 2011.
National Research Council. A New Biology for the 21st Century: Ensuring that the United States Leads the Coming Biology Revolution. National Academies Press, Washington, D.C., 2009.
S. Emmott, S. Rison, Editors. Towards 2020 science. Microsoft Corporation, Cambridge, 2006, http://research.microsoft.com/en-us/um/cambridge/projects/towards2020science/\downloads/t2020s_report.pdf
L. Steen, Editor. Math and Bio 2010: Linking Undergraduate Disciplines. Mathematics Association of America, Washington, D.C., 2005.
T. Hey, St. Tansley, K. Tolle, Editors. The fourth paradigm: Data-intensive scientific discovery. Microsoft: Redmond, Washington, 2009. (http://research.microsoft.com/en-us/collaboration/fourthparadigm/4th_paradigm_book_complete_lr.pdf).
Scientific Foundations for Future Physicians: Report of the AAMC-HHMI Committee. Association of American Medical Colleges, Washington, D.C., 2009. (http://www.hhmi.org/grants/pdf/08–209_AAMC-HHMI_report.pdf).
J. Woodger. Biological principles : a critical study. Harcourt, Brace, London, 1929.
C. Anderson. The end of theory: The data deluge makes the scientific method obsolete. Wired, 16 (2008) 7.
Pigliucci, M.. The end of theory in science? EMBO Reports, 10 (2009), 534. CrossRefGoogle Scholar
An, G.. Closing the scientific loop: bridging correlation and causality in the petaflop age. Sci Transl Med., 2 (2010), No. 41, 34. CrossRefGoogle ScholarPubMed
An, G., Christley, S.. Agent-based modeling and biomedical ontologies: a roadmap. Computational Statistics, 3 (2011) No. 4, 343-356. CrossRefGoogle Scholar
Levins, R.. The strategy of model building in population biology. American Scientist, 54 (1966) 421–431. Google Scholar
A. Clark, E. Wiebe. Scientific visualization for secondary and post-secondary schools. Journal of Technology Studies, 26 (2000), No. 1.
Goldstein, H.. The future of statistics within the curriculum. Teaching statistics, 29 (2006), No. 1, 8–9. CrossRefGoogle Scholar
C. Konold, T. Higgins. Reasoning about data. In J. Kilpatrick, W. Martin, D. Schifter (Eds.), A research companion to principles and standards for school mathematics, Reston, VA, National Council of Teachers of Mathematics, (2003), 193–215.
Haak, D., Hille, J., Lambers, R., Pitre, E., Freeman, S.. Increased structure and active learning reduce the achievement gap in introductory biology. Science, 332 (2011), 1213–1216. CrossRefGoogle Scholar
S. Ziliak, D. McCloskey. The cult of statistical significance. The University of Michigan Press, Ann Arbor, 2008.
Zadeh, L.. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1 (1978), 3–28. CrossRefGoogle Scholar
Friedman, N., Halpern, J.. Plausibility measures and default reasoning. Journal of ACM, 48 (2001), No. 4, 648-685. CrossRefGoogle Scholar
Qi, G.. A semantic approach for iterated revision in possibilistic logic. AAAI, (2008), 523–528. Google Scholar
Schwarz, C., Reiser, B., Davis, E., Kenyon, L., Acher, A., Fortus, D., Shwartz, Y., Hug, B., Krajcik, J.. Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. Journal of Research in Science Teaching. 46 (2009), No. 6, 632–654. CrossRefGoogle Scholar
Ost, D.. Models, modeling and the teaching of science and mathematics. School Science and Mathematics, 87 (1987), No. 5, 363–370. CrossRefGoogle Scholar
Odenbaugh, J.. The strategy of model building in population biology. Biology and Philosophy, 21 (2006), 607–621. CrossRefGoogle Scholar
G. Box. Robustness in the strategy of scientific model building. (May 1979) in R. Launer, G. Wilkinson, Editors, Robustness in Statistics: Proceedings of a Workshop, 1979.
W. Wimsatt. False models as means to truer theories. In M. Nitecki, editor, Neutral models in biology; Oxford University Press, Oxford, (1987), 23–55.
Bhadeshia, H.. Mathematical models in materials science. Materials Science Technology, 24 (2008), 128–136. CrossRefGoogle Scholar
J. Stewart, C.Passmore, Cartier, J.. Project MUSE: Involving high school students in evolutionary biology through realistic problems and causal models. Biology International, 47 (2010), 78–90. Google Scholar
J. Jungck. Genetic codes as codes: Towards a theoretical basis for Bioinformatics. In R. Mondaini (Universidade Federal do Rio de Janeiro, Brazil), Editor. BIOMAT 2008. World Scientific, Singapore, (2009), 300–331.
A. Caldeira. Mathematical modeling and environmental education. Proceedings of the 11th International Congress on Mathematics Education, Monterrey, Mexico, July 6 - 13, 2008, (20009), (http://tsg.icme11.org/document/get/493).
L. Steen. Data, shapes, symbols: Achieving balance in school mathematics. In B. Madison, L. Steen, Editors, Quantitative literacy: Why numeracy matters for schools and colleges. Mathematics Association of America, Washington, DC., (2003), 53–74.
G. Wiggins. Get real! assessing for quantitative literacy. In B. Madison, L. Steen, Editors, Quantitative literacy: Why numeracy matters for schools and colleges. Princeton, NJ, National Council on Education and the Disciplines, (2003), 121–143.
R. Richardson, W. Mccallum. The third R in literacy. In B. Madison, L. Steen, Editors, Quantitative literacy: Why numeracy matters for schools and colleges. Mathematics Association of America, Washington, DC., (2003), 99–106.
Krathwohl, D.. A revision of Bloom’s Taxonomy: An overview. Theory Into Practice, 41 (2002), No. 4, 212–218. CrossRefGoogle Scholar
H. Freudenthal. Weeding and sowing: Preface to a science of mathematics education. Dordrecht, Netherlands, 1980.
Gravemeijer, K., Terwel, J.. Hans Freudenthal: a mathematician on didactics and curriculum theory. J. Curriculum Studies, 32 (2000), No. 6, 777–796. CrossRefGoogle Scholar
R. Khattar, C. Wien. Review of complexity and education: Inquiries into learning, teaching, and research by B. Davis, D. Sumara, 2006. New York and London: Lawrence Erlbaum Associates. Complicity, 7 (2010), No. 2, 122–125.
M. Andresen. Teaching to reinforce the bonds between modelling and reflecting. In M. Blomhoj, S. Carreira, Editors, Mathematical applications and modelling in the teaching and learning of mathematics. Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematical Education in Monterrey, Mexico, July 6-13, 2008, (2009), 73–83. (Available at http://diggy.ruc.dk:8080/retrieve/14388#page=77).
Andresen, M.. Modeling with the software ‘Derive’ to support a constructivist approach to teaching. International Electronic Journal of Mathematics Education, 2 (2007), No. 1, 1–15. Google Scholar
Gadanidis, G., Geiger, V.. A social perspective on technology-enhanced mathematical learning: from collaboration to performance. ZDM, 42 (2010), No. 1, 91–104. CrossRefGoogle Scholar
Doorman, L., Gravemeijer, K.. Emergent modeling: discrete graphs to support the understanding of change and velocity. ZDM, 41 (2009), No. 1/2. CrossRefGoogle Scholar
Gravemeijer, K., Doorman, M.. Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39 (1999), 111–129. CrossRefGoogle Scholar
K. Gravemeijer, M. Stephan. Emergent models as an instructional design heuristic. In Gravemeijer et al., (2002), 145–169.
K. Gravemeijer, R. Lehrer, L. Verschaffel, B. Van Oers (Eds.). Symbolizing, modeling, and tool use in mathematics education. Dordrecht, Netherlands, Kluwer, 2002.
Kondrashov, D.. Using normal modes analysis in teaching mathematical modeling to biology students. Math. Model. Nat. Phenom., 6 (2011), No. 6, 278–294. CrossRefGoogle Scholar
Ellis-Monaghan, J., Pangborn, G.. Using DNA self-assembly design strategies to motivate graph theory concepts. Math. Model. Nat. Phenom., 6 (2011), No. 6, 96–107. CrossRefGoogle Scholar
Robic, S., Jungck, J.. Unraveling the tangled complexity of DNA: Combining mathematical modeling and experimental biology to understand replication, recombination and repair. Math. Model. Nat. Phenom., 6 (2011), No. 6, 108–135. CrossRefGoogle Scholar
Kerner, R.. Self-assembly of icosahedral viral capsids: the combinatorial analysis approach. Math. Model. Nat. Phenom., 6 (2011), No. 6, 136–158. CrossRefGoogle Scholar
Robeva, R., Kirkwood, B., Davies, R.. Boolean biology: Introducing boolean networks and finite dynamical systems models to biology and mathematics courses. Math. Model. Nat. Phenom., 6 (2011), No. 6, 39–60. CrossRefGoogle Scholar
Gill, J., Shaw, K., Rountree, B., Kehl, Ca., Chiel, H.. Simulating kinetic processes in time and space on a lattice. Math. Model. Nat. Phenom., 6 (2011), No. 6, 159–197. CrossRefGoogle Scholar
Milton, J., Radunskaya, A., Ou, W., Ohira, T.. A team approach to undergraduate research in biomathematics: Balance control. Math. Model. Nat. Phenom., 6 (2011), No. 6, 260–277. CrossRefGoogle Scholar
Cozzens, M.. Food webs, competition graphs, and habitat formation. Math. Model. Nat. Phenom., 6 (2011), No. 6, 22–38. CrossRefGoogle Scholar
Hartvigsen, G.. Using R to build and assess network models in biology. Math. Model. Nat. Phenom., 6 (2011), No. 6, 61–75. CrossRefGoogle Scholar
Knisley, J.. Compartmental models of migratory dynamics. Math. Model. Nat. Phenom., 6 (2011), No. 6, 245–259. CrossRefGoogle Scholar
Grossman, Y., Berdanier, A., Custic, M., Feeley, L., Peake, S., Saenz, A., Sitton, K.. Integrating photosynthesis, respiration, biomass partitioning, and plant growth: Developing a Microsoft Excelő-based simulation model of Wisconsin Fast Plants (Brassica rapa, Brassicaceae) growth with students. Math. Model. Nat. Phenom., 6 (2011), No. 6, 295–313. CrossRefGoogle Scholar