Mathematical Biology Education: Modeling Makes Meaning

J. R. Jungck

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 6, page 1-21
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Jungck, J. R.. "Mathematical Biology Education: Modeling Makes Meaning." Mathematical Modelling of Natural Phenomena 6.6 (2011): 1-21. <http://eudml.org/doc/222240>.

@article{Jungck2011,
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. },
author = {Jungck, J. R.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {biomathematics education; discrete mathematics; modeling},
language = {eng},
month = {10},
number = {6},
pages = {1-21},
publisher = {EDP Sciences},
title = {Mathematical Biology Education: Modeling Makes Meaning},
url = {http://eudml.org/doc/222240},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Jungck, J. R.
TI - Mathematical Biology Education: Modeling Makes Meaning
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 1
EP - 21
AB - 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.
LA - eng
KW - biomathematics education; discrete mathematics; modeling
UR - http://eudml.org/doc/222240
ER -

References

top
  1. J. Cohen. Mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better. PLOS Biology, 2, (2004), 439.  
  2. 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: ().  URIhttp://www.lifescied.org/content/vol9/issue3/index.dtl
  3. J. Jungck. Ten equations that changed biology. Bioscene, 23 (1997), No. 1, 11–36.  
  4. Board on Life Sciences. National Research Council. BIO2010: Transforming undergraduate education for future research Bbologists. National Academies Press: Washington, D.C., 2003.  
  5. A. Weisstein. Building mathematical models and biological insight in an introductory biology course. Math. Model. Nat. Phenom., 6 (2011), No. 6, 198–214.  Zbl1241.92002
  6. H. Gaff, M. Lyons, G. Watson. Classroom manipulative to engage students in mathematical modeling of disease spread: 1+1 = Achoo!. Math. Model. Nat. Phenom., 6 (2011), No. 6, 215–226.  Zbl06050987
  7. C. Neuhauser, E. Stanley. The p and the peas: An intuitive modeling approach to hypothesis testing. Math. Model. Nat. Phenom., 6 (2011), No. 6, 76–95.  Zbl1274.97048
  8. G. Koch. Drugs in the classroom: Using pharmacokinetics to introduce biomathematical modeling. Math. Model. Nat. Phenom., 6 (2011), No. 6, 227–244.  Zbl1241.92030
  9. AAAS Vision and Change in Undergraduate biology education: A call To action. American Association for the Advancement of Science, Washington, D.C., 2011.  
  10. 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.  
  11. S. Emmott, S. Rison, Editors. Towards 2020 science. Microsoft Corporation, Cambridge, 2006,  URIhttp://research.microsoft.com/en-us/um/cambridge/projects/towards2020science//t2020sreport.pdf
  12. L. Steen, Editor. Math and Bio 2010: Linking Undergraduate Disciplines. Mathematics Association of America, Washington, D.C., 2005.  Zbl1141.92303
  13. T. Hey, St. Tansley, K. Tolle, Editors. The fourth paradigm: Data-intensive scientific discovery. Microsoft: Redmond, Washington, 2009. ().  URIhttp://research.microsoft.com/en-us/collaboration/fourthparadigm/4th_paradigm_book_complete_lr.pdf
  14. Scientific Foundations for Future Physicians: Report of the AAMC-HHMI Committee. Association of American Medical Colleges, Washington, D.C., 2009. ().  URIhttp://www.hhmi.org/grants/pdf/08–209_AAMC-HHMI_report.pdf
  15. J. Woodger. Biological principles : a critical study. Harcourt, Brace, London, 1929.  
  16. C. Anderson. The end of theory: The data deluge makes the scientific method obsolete. Wired, 16 (2008) 7.  
  17. M. Pigliucci. The end of theory in science?EMBO Reports, 10 (2009), 534.  
  18. G. An. Closing the scientific loop: bridging correlation and causality in the petaflop age. Sci Transl Med., 2 (2010), No. 41, 34.  
  19. G. An, S. Christley. Agent-based modeling and biomedical ontologies: a roadmap. Computational Statistics, 3 (2011) No. 4, 343-356.  
  20. R. Levins. The strategy of model building in population biology. American Scientist, 54 (1966) 421–431.  
  21. A. Clark, E. Wiebe. Scientific visualization for secondary and post-secondary schools. Journal of Technology Studies, 26 (2000), No. 1.  
  22. H. Goldstein. The future of statistics within the curriculum. Teaching statistics, 29 (2006), No. 1, 8–9.  
  23. 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.  
  24. D. Haak, J. Hille, R. Lambers, E. Pitre, S. Freeman. Increased structure and active learning reduce the achievement gap in introductory biology. Science, 332 (2011), 1213–1216.  
  25. S. Ziliak, D. McCloskey. The cult of statistical significance. The University of Michigan Press, Ann Arbor, 2008.  Zbl1274.62025
  26. L. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1 (1978), 3–28.  Zbl0377.04002
  27. N. Friedman, J. Halpern. Plausibility measures and default reasoning. Journal of ACM, 48 (2001), No. 4, 648-685.  Zbl1127.68438
  28. G. Qi. A semantic approach for iterated revision in possibilistic logic. AAAI, (2008), 523–528.  
  29. C. Schwarz, B. Reiser, E. Davis, L. Kenyon, A. Acher, D. Fortus, Y. Shwartz, B. Hug, J. Krajcik. 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.  
  30. D. Ost. Models, modeling and the teaching of science and mathematics. School Science and Mathematics, 87 (1987), No. 5, 363–370.  
  31. J. Odenbaugh. The strategy of model building in population biology. Biology and Philosophy, 21 (2006), 607–621.  
  32. 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.  
  33. W. Wimsatt. False models as means to truer theories. In M. Nitecki, editor, Neutral models in biology; Oxford University Press, Oxford, (1987), 23–55.  
  34. H. Bhadeshia. Mathematical models in materials science. Materials Science Technology, 24 (2008), 128–136.  
  35. J. Stewart, C.Passmore, J. Cartier. Project MUSE: Involving high school students in evolutionary biology through realistic problems and causal models. Biology International, 47 (2010), 78–90.  
  36. 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.  
  37. A. Caldeira. Mathematical modeling and environmental education. Proceedings of the 11th International Congress on Mathematics Education, Monterrey, Mexico, July 6 - 13, 2008, (20009), ().  URIhttp://tsg.icme11.org/document/get/493
  38. 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.  
  39. 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.  
  40. 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.  
  41. D. Krathwohl. A revision of Bloom’s Taxonomy: An overview. Theory Into Practice, 41 (2002), No. 4, 212–218.  
  42. H. Freudenthal. Weeding and sowing: Preface to a science of mathematics education. Dordrecht, Netherlands, 1980.  
  43. K. Gravemeijer, J. Terwel. Hans Freudenthal: a mathematician on didactics and curriculum theory. J. Curriculum Studies, 32 (2000), No. 6, 777–796.  
  44. 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.  
  45. 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 ).  URIhttp://diggy.ruc.dk:8080/retrieve/14388#page=77
  46. M. Andresen. Modeling with the software ‘Derive’ to support a constructivist approach to teaching. International Electronic Journal of Mathematics Education, 2 (2007), No. 1, 1–15.  
  47. G. Gadanidis, V. Geiger. A social perspective on technology-enhanced mathematical learning: from collaboration to performance. ZDM, 42 (2010), No. 1, 91–104.  
  48. L. Doorman, K. Gravemeijer. Emergent modeling: discrete graphs to support the understanding of change and velocity. ZDM, 41 (2009), No. 1/2.  
  49. K. Gravemeijer, M. Doorman. Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39 (1999), 111–129.  
  50. K. Gravemeijer, M. Stephan. Emergent models as an instructional design heuristic. In Gravemeijer et al., (2002), 145–169.  
  51. K. Gravemeijer, R. Lehrer, L. Verschaffel, B. Van Oers (Eds.). Symbolizing, modeling, and tool use in mathematics education. Dordrecht, Netherlands, Kluwer, 2002.  
  52. D. Kondrashov. Using normal modes analysis in teaching mathematical modeling to biology students. Math. Model. Nat. Phenom., 6 (2011), No. 6, 278–294.  Zbl1241.92001
  53. J. Ellis-Monaghan, G. Pangborn. Using DNA self-assembly design strategies to motivate graph theory concepts. Math. Model. Nat. Phenom., 6 (2011), No. 6, 96–107.  
  54. S. Robic, J. Jungck. 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.  Zbl1241.92025
  55. R. Kerner. Self-assembly of icosahedral viral capsids: the combinatorial analysis approach. Math. Model. Nat. Phenom., 6 (2011), No. 6, 136–158.  Zbl1241.92024
  56. R. Robeva, B. Kirkwood, R. Davies. 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.  Zbl06050979
  57. J. Gill, K. Shaw, B. Rountree, Ca. Kehl, H. Chiel. Simulating kinetic processes in time and space on a lattice. Math. Model. Nat. Phenom., 6 (2011), No. 6, 159–197.  Zbl1244.82048
  58. J. Milton, A. Radunskaya, W. Ou, T. Ohira. A team approach to undergraduate research in biomathematics: Balance control. Math. Model. Nat. Phenom., 6 (2011), No. 6, 260–277.  Zbl1244.97009
  59. M. Cozzens. Food webs, competition graphs, and habitat formation. Math. Model. Nat. Phenom., 6 (2011), No. 6, 22–38.  Zbl1241.92071
  60. G. Hartvigsen. Using R to build and assess network models in biology. Math. Model. Nat. Phenom., 6 (2011), No. 6, 61–75.  Zbl1241.92027
  61. J. Knisley. Compartmental models of migratory dynamics. Math. Model. Nat. Phenom., 6 (2011), No. 6, 245–259.  Zbl1241.92005
  62. Y. Grossman, A. Berdanier, M. Custic, L. Feeley, S. Peake, A. Saenz, K. Sitton. 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.  Zbl1241.92052

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