Biology is becoming more quantitative. If we are to support the future of quantitative biology, then the next generation of biologists must be prepared to consistently integrate quantitative reasoning into subject matter that has traditionally been considered through a qualitative lens. We introduce a quantitative reasoning framework and discuss the importance of quantitative modeling in biology. The framework includes the Quantitative Act as a support for Quantitative Modeling and Quantitative Interpretation. The QM BUGS diagnostic instrument was developed to assesses undergraduate biology students’ abilities to create and apply models employing pre-calculus mathematics. A brief discussion of our research findings based on implementation of the instrument include the lack of student ability to develop quantitative models. We present items from the instrument as examples of the Quantitative Act elements: variable quantification through identifying variable and attributes, measurement, variation, quantitative literacy, and context. We also provide items representing quantitative modeling and quantitative interpretation. We then view quantitative biology from K-12 and collegiate perspectives, including instructional practices for teaching quantitative biology, motivating problem contexts that afford quantification, instructional strategies of repetition, scaffolding, peer teaching and learning, direct instruction and teacher moves on the K-12 level, as well as identifying five competencies for the next generation of biologists which require QA abilities.
| Published in | Applied and Computational Mathematics (Volume 11, Issue 1) |
| DOI | 10.11648/j.acm.20221101.11 |
| Page(s) | 1-17 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Quantitative, Biology, Modeling, Interpretation
| [1] | Richards, R. J. (2002). The Romantic Conception of Life: Science and Philosophy in the Age of Goethe. University of Chicago Press. ISBN 978-0-226-71210-9. |
| [2] | Magner, L. N (2002). A History of the Life Sciences, Revised and Expanded. CRC Press. ISBN 978-0-203-91100-6. |
| [3] | Thompson, D. W. (1942). On Growth and Form. |
| [4] | Gregor, T. (2017). Beyond D'Arcy Thompson: Future challenges for quantitative biology. Mechanisms of development, 145, 10-12. |
| [5] | Greddes and Hoff (1971). The discovery of bioelectricity and current electricity The Galvani-Volta controversy. IEEE spectrum, 8 (12), 38-46. |
| [6] | Abbot, L, Hooper, S. Kepler, T., & Marder, E. (1990). Oscillating networks: Modeling the pyloric circuit of the stomatogastric ganglion. In 1990 IJCNN International Joint Conference on Neural Networks (pp. 175-180). IEEE. |
| [7] | Krotov, D., Dubuis, J. O., Gregor, T., & Bialek, W. (2014). Morphogenesis at criticality. Proceedings of the National Academy of Sciences, 111 (10), 3683-3688. |
| [8] | Hopfield, J. J., & Tank, D. W. (1986). Computing with neural circuits: A model. Science, 233 (4764), 625-633. |
| [9] | Attanasi, A., Cavagna, A., Del Castello, L., Giardina, I., Grigera, T. S., Jelić, A., & Viale, M. (2014). Information transfer and behavioural inertia in starling flocks. Nature physics, 10 (9), 691-696. |
| [10] | Bialek, W., & Ranganathan, R. (2007). Rediscovering the power of pairwise interactions. arXiv preprint arXiv: 0712.4397. |
| [11] | Bialek, W. (2012). Biophysics: searching for principles. Princeton University Press. |
| [12] | Mayes, R., Forrester, J., Christus, J., Peterson, F., & Walker, R. (2014). Quantitative reasoning learning progression: matrix. Numeracy, 7 (2). |
| [13] | AAAS (2011). Vision and Change In Undergraduate Biology Education: A Call to Action. Retrieved from http://visionandchange.org/finalreport/ |
| [14] | AAMC-HHMI (2014). Teaching quantitative biology: goals, assessments, and resources. Molecular Biology of the Cell, 25 (22), 3437-3716. |
| [15] | COMAP & SIAM Garfunkel, S. A. & Montgomery, M. (2016). GAIMME: Guidelines for Assessment & Instruction in Mathematics Modeling Education. New York: COMAP Inc. |
| [16] | National Research Council (2003). Bio 2010: Transforming Undergraduate Education for Future Research Biologists. Washington, D.C.: The National Academies Press. |
| [17] | NGSS Lead States (2013). Next Generation Science Standards: for States, by States. Washington, DC: The National Academies Press. |
| [18] | Magnani, L., & Casadio, C. (Eds.) (2012). Model-Based Reasoning in Science and Technology: Logical, Epistemological, and Cognitive Issues. Switzerland: Springer International Publishing. |
| [19] | Windschitl, M., Thompson, J., & Braaten, M. (2008). Beyond the scientific method: Model-based inquiry as a new paradigm of preference for school science investigators. Wiley InterScience. www.interscience.wiley.com. |
| [20] | Papaevripidou, M., Constantinos P. C., & Zacharias C. Z. (2007). Modeling complex marine ecosystems: An investigation of two teaching approaches with fifth graders. Journal of Computer Assisted Learning, 23 (2), 145–157. |
| [21] | Svoboda, J., & Passmore, C. (2013). The strategies of modeling in biology education. Science & Education, 22 (1), 119-142. |
| [22] | Papaevripidou, M., & Zacharias C. Z. (2015). Examining how students’ knowledge of the subject domain affects their process of modeling in a computer programming environment. Journal of Computers in Education, 2 (3), 251–82. doi: 10.1007/s40692-015-0034-1. |
| [23] | Schwarz, C. V., B. J. Reiser, E. A. Davis, L. Kenyon, A. Achér, D. Fortus, Y. Shwartz, B. Hug, & J. Krajcik. (2009). “Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. Journal of Research in Science Teaching 46 (6), 632–654. |
| [24] | Gilbert, S. W. (1991). Model building and a definition of science. Journal of research in science teaching, 28 (1), 73-79. |
| [25] | Koponen, I. T. (2007). Models and modelling in physics education: A critical re-analysis of philosophical underpinnings and suggestions for revisions. Science & Education, 16 (7-8), 751-773. |
| [26] | Sensevy, G., Tiberghien, A., Santini, J., Laubé, S., & Griggs, P. (2008). An epistemological approach to modeling: Cases studies and implications for science teaching. Science education, 92 (3), 424-446. |
| [27] | Fretz, E. B., Wu, H.-K., Zhang, B., Davis, E. A., Krajcik, J. S., & Soloway, E. (2002). An investigation of software scaffolds supporting modeling practices. Research in Science Education, 32 (4), 567–589. |
| [28] | Hestenes, D. (1992). Modeling games in the Newtonian world. American Journal of Physics, 60 (8), 732-748. |
| [29] | Sins, P. H. M., Savelsbergh, E. R., & van Joolingen, W. R. (2005). The Difficult Process of Scientific Modelling: An analysis of novices’ reasoning during computer-based modelling. International Journal of Science Education, 27 (14), 1695–1721. https://doi.org/10.1080/09500690500206408 |
| [30] | Halloun, I. A. (2007). Modeling theory in science education (Vol. 24). Springer Science & Business Media. |
| [31] | Louca, L. T., & Zacharia, Z. C. (2012). Modeling-based learning in science education: cognitive, metacognitive, social, material and epistemological contributions. Educational Review, 64 (4), 471-492. |
| [32] | Acher, A., Arcà, M., & Sanmartí, N. (2007). Modeling as a teaching learning process for understanding materials: A case study in primary education. Science Education, 91 (3), 398–418. https://doi.org/10.1002/sce.20196 |
| [33] | Penner, D. E. (2000). Explaining systems: Investigating middle school students’ understanding of emergent phenomena. Journal of Research in Science Teaching, 37 (8), 784–806. |
| [34] | Harrison, A. G., & Treagust, D. F. (2000). A typology of school science models. International Journal of Science Education, 22 (9), 1011–1026. |
| [35] | Tsui, C.-Y., & Treagust, D. F. (2013). Introduction to multiple representations: Their importance in Biology and Biological Education. In D. Treagust & C.-Y. Tsui (Eds.), Multiple Representations in Biological Education (Vol. 7). Springer. |
| [36] | Nersessian, N. J., & Patton, C. (2009). Model-based reasoning in interdisciplinary engineering. In Philosophy of technology and engineering sciences (pp. 727-757). North-Holland. |
| [37] | Rouwette, E. A., Vennix, J. A., & Thijssen, C. M. (2000). Group model building: A decision room approach. Simulation & Gaming, 31 (3), 359-379. |
| [38] | Jonassen, D., Strobel, J., & Gottdenker, J. (2005). Model building for conceptual change. Interactive Learning Environment, 13 (1–2), 15–37. |
| [39] | Bamberger, Y. M., & Davis, E. A. (2013). Middle-School Science Students’ Scientific Modelling Performances Across Content Areas and Within a Learning Progression. International Journal of Science Education, 35 (2), 213–238. https://doi.org/10.1080/09500693.2011.624133 |
| [40] | Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21 (1), 39-48. |
| [41] | Lesh, R. (2000). What Mathematical Abilities Are Most Needed for Success Beyond School in a Technology Based Age of Information? Proceedings of the International Conference on Technology in Mathematics Education (Auckland, NZ, December 11-14, 2000). |
| [42] | Metcalf, S. J., Krajcik, J., & Soloway, E. (2000). Model-It: A design retrospective. Innovations in science and mathematics education, 77-115. |
| [43] | Mayes, R., Peterson, F., & Bonilla, R. (2013). Quantitative reasoning learning progressions for environmental science: Developing a framework. Numeracy, 6 (1). |
| [44] | Eaton, C. D., Allen, D., Anderson, L. J., Bowser, G., Pauley, M. A., Williams, K. S., & Uno, G. E. (2016). Summit of the research coordination networks for undergraduate biology education. |
| [45] | Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33 (2), 131-152. |
| [46] | Stieff, M. (2017). Drawing for promoting learning and engagement with dynamic visualizations. In R. Lowe, & F. Ploetzner (Eds), Learning from Dynamic Visualization, (333–356). Switzerland, Cham: Springer. |
| [47] | Paivio, A. (1990). Mental representations A dual coding approach. Oxford University Press. doi: 10.1093/acprofoso/9780195066661.001.0001. |
| [48] | Robeva, R. S. (Ed.) (2015). Algebraic and Discrete Mathematical Methods for Modern Biology. Boston, MA: Elsevier. |
| [49] | Bialek, W., & Botstein, D. (2004). Introductory science and mathematics education for 21st-century biologists. Science, 303 (5659), 788-790. |
| [50] | Hastings, A., & Palmer, M. A. (2003). A bright future for biologists and mathematicians? Science, 299, 5615. |
| [51] | Van der Hoff, Q. (2017). Interdisciplinary education – a predator–prey model for developing a skill set in mathematics, biology and technology. International Journal of Mathematical Education in Science and Technology, 48 (6), 928-938. |
| [52] | Cros, D., Chastrette, M., & Fayol, M. (1988). Conceptions of second year university students of some fundamental notions in chemistry. International Journal of Science Education, 10 (3), 331-336. |
| [53] | Lin, J. W., & Chiu, M. H. (2007). Exploring the characteristics and diverse sources of students’ mental models of acids and bases. International Journal of Science Education, 29 (6), 771-803. |
| [54] | Mohan, L., Chen, J., & Anderson, C. W. (2009). Developing a multi-year learning progression for carbon cycling in socio-ecological systems. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 46 (6), 675-698. |
| [55] | BERAC. (2010). Grand Challenges for Biological and Environmental Research: A Long-Term Vision; A Report from the Biological and Environmental Research Advisory Committee March 2010 Workshop, DOE/SC-0135, BERAC Steering Committee on Grand Research Challenges for Biological and Environmental Research (www.science.doe.gov/ober/berac/BER_LTVreport.pdf). |
| [56] | Li, C., Donizelli, & M., Rodriguez, N. (2010). BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol 4 (92). doi: 10.1186/1752-0509-4-92. |
| [57] | Speth, E. B., Momsen, J. L., Moyerbrailean, G. A., Ebert-May, D., Long, T. M., Wyse, S., & Linton, D. (2010). 1, 2, 3, 4: infusing quantitative literacy into introductory biology. CBE—Life Sciences Education, 9 (3), 323-332. |
| [58] | Hoffman, K., Leupen, S., Dowell, K., Kephart, K., & Leips, J. (2016). Development and Assessment of Modules to Integrate Quantitative Skills in Introductory Biology Courses. CBE-Life Sciences Education, 15 (2), ar14. |
| [59] | Eager, E. A., Peirce, J., & Barlow, P. (2014). Math Bio or Biomath? Flipping the mathematical biology classroom. Letters in Biomathematics, 1 (2), 139-155. |
| [60] | Robeva, R., & Laubenbacher, R. (2009). Mathematical biology education: beyond calculus. Science, 325 (5940), 542-543. |
| [61] | Aikens & Dolan (2014). Teaching quantitative biology: Goals, assessments, and resources. Molecular Biology of the Cell, 3478-3481. DOI: 10.1091/mbc.E14-06-1045. |
| [62] | Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education. WISDOMe Mongraphs (Vol. 1, pp. 3357). Laramie, WY: University of Wyoming. |
| [63] | Shavelson, R. J. (2008). Reflections on quantitative reasoning: An assessment perspective. Calculation vs. context: Quantitative literacy and its implications for teacher education, 27-47. |
| [64] | Steen, L. A., & Madison, B. L. (2011). Reflections on the tenth Anniversary of Mathematics and Democracy. Numeracy, 4 (1), 1-6. |
| [65] | National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. |
| [66] | Hughes-Hallett, D. (2003). The Role of Mathematics Courses in the Development of Quantitative Literacy. In B. L. Madison & L. A. Steen, Quantitative Literacy: Why Numeracy Matters for Schools and Colleges (pp. 91–98). National Council on Education and the Disciplines. |
| [67] | Steen, L. A. (2004). Achieving quantitative literacy: An urgent challenge for higher education. Mathematical Association of America. |
| [68] | Johnson, Y., & Kaplan, J. (2014). Assessing the Quantitative Literacy of Students at a Large Public Research University. http://www.statlit.org/pdf/2008JohnsonKaplanCRUME.pdf |
| [69] | Stanhope, L., Ziegler, L., Haque, T., Le, L., Vinces, M., Davis, G. K., Zieffler, A., Brodfuehrer, P., Preest, M., M. Belitsky, J., Umbanhowar, C., Overvoorde, P. J., & Nehm, R. (2017). Development of a Biological Science Quantitative Reasoning Exam (BioSQuaRE). CBE—Life Sciences Education, 16 (4), ar66. https://doi.org/10.1187/cbe.16-10-0301 |
| [70] | Goldstein, J., & Flynn, D. F. B. (2011). Integrating Active Learning & Quantitative Skills into Undergraduate Introductory Biology Curricula. The American Biology Teacher, 73 (8), 454–461. https://doi.org/10.1525/abt. 2011.73.8.6 |
| [71] | National Research Council. (2013). Next Generation Science Standards: For States, By States. Washington, DC: The National Academies Press. https://doi.org/10.17226/18290. |
| [72] | Sadler, T. D. (2020). COVID-19 Curriculum Materials. Retrieved 7/28/20 from https://epiclearning.web.unc.edu/covid/ |
| [73] | Sampson, V., & Murphy, A. (2019). Argument-Driven Inquiry in Third-Grade Science: Three Dimensional Investigations. NSTA Press. 1840 Wilson Boulevard, Arlington, VA 22201. |
| [74] | Hardin, G. (1968). The tragedy of the commons. Science, 162 (3859), 1243-1248. |
| [75] | Elrod, S. (2014). Quantitative reasoning: The next “across the curriculum” movement. Peer Review, 16 (3), 4-8. |
| [76] | Moore, K. C., Silverman, J., Paoletti, T., & LaForest, K. (2014). Breaking conventions to support quantitative reasoning. Mathematics Teacher Educator, 2 (2), 141-157. |
| [77] | Weber, E., Ellis, A., Kulow, T., & Ozgur, Z. (2014). Six principles for quantitative reasoning and modeling. The Mathematics Teacher, 108 (1), 24-30. |
| [78] | Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. |
| [79] | White, K., Timmons, M., & Medders, P. (2011). ONE FISH TWO FISH REDFISH YOU FISH! The Science Teacher, 78 (2), 28. |
| [80] | Bozzone, D. M. (1997). Feeding Behaviors in Cellular Slime Molds: A Microbial System to Study Competition. The American Biology Teacher, 59 (9), 565-572. |
| [81] | Jessup, J., Ode, P. J., & Balgopal, M. M. (2016). Competition for Limiting Resources: Quantitative Reasoning in Evolutionary Ecology. The American Biology Teacher, 78 (4), 300-309. |
| [82] | Archer, E. K. (2014). American society of plant biologists: Position statement on the education of young children about plants. CBE—Life Sciences Education, 13 (4), 575-576. |
| [83] | Tan, T. W., Lim, S. J., Khan, A. M., & Ranganathan, S. (2009, December). A proposed minimum skill set for university graduates to meet the informatics needs and challenges of the"-omics" era. In BMC genomics (Vol. 10, No. 3, pp. 1-6). BioMed Central. |
| [84] | Koch, I., & Fuellen, G. (2008). A review of bioinformatics education in Germany. Briefings in bioinformatics, 9 (3), 232-242. |
| [85] | Magana, A. J., Clase, K. L., & Springer, J. (2015). A survey of scholarly literature describing the field of bioinformatics education and bioinformatics educational research. CBE – Life Sciences Education. 13, 1-17. |
| [86] | Rosenwald, A. G., Pauley, M. A., Welch, L., Elgin, S. C., Wright, R., & Blum, J. (2016). The CourseSource bioinformatics learning framework. CBE—Life Sciences Education, 15 (1), le2. |
| [87] | Rubinstein, A., & Chor, B. (2014). Computational thinking in life science education. PLoS computational biology, 10 (11), e1003897. |
| [88] | Eaton, C. D., LaMar, M. D., & McCarthy, M. L. (2020). 21st century reform efforts in undergraduate quantitative biology education: conversations, initiatives, and curriculum change in the United States of America. Letters in Biomathematics 7 (1), 55-66. |
| [89] | Donovan, S., Eaton, C. D., Gower, S. T., Jenkins, K. P., LaMar, M. D., Poli, D., Sheehy, R. & Wojdak, J. M. (2015). QUBES: a community focused on supporting teaching and learning in quantitative biology. Letters in Biomathematics, 2 (1), 46-55. |
| [90] | Waldrop, L. D., Adolph, S. C., Diniz Behn, C. G., Braley, E., Drew, J. A. Full, R. J., Gross, L. J., Jungck, J. A., Kohler, B., Prairie, J. C., Shtylla, B., & Miller, L. A. (2015). Using active learning to teach concepts and methods in quantitative biology. Integrative and Comparative Biology, 1-16. doi: 10.1093/icb/icv097. |
| [91] | Freeman, S., Eddy S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H. & Wenderoth, M. P. (2020). Active learning increases student performance in science, engineering, and mathematics. PNAS, 111 (23), 8410-8415. |
APA Style
Robert Mayes, David Owens, Joseph Dauer, Kent Rittschof. (2022). A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology. Applied and Computational Mathematics, 11(1), 1-17. https://doi.org/10.11648/j.acm.20221101.11
ACS Style
Robert Mayes; David Owens; Joseph Dauer; Kent Rittschof. A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology. Appl. Comput. Math. 2022, 11(1), 1-17. doi: 10.11648/j.acm.20221101.11
AMA Style
Robert Mayes, David Owens, Joseph Dauer, Kent Rittschof. A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology. Appl Comput Math. 2022;11(1):1-17. doi: 10.11648/j.acm.20221101.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20221101.11,
author = {Robert Mayes and David Owens and Joseph Dauer and Kent Rittschof},
title = {A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology},
journal = {Applied and Computational Mathematics},
volume = {11},
number = {1},
pages = {1-17},
doi = {10.11648/j.acm.20221101.11},
url = {https://doi.org/10.11648/j.acm.20221101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221101.11},
abstract = {Biology is becoming more quantitative. If we are to support the future of quantitative biology, then the next generation of biologists must be prepared to consistently integrate quantitative reasoning into subject matter that has traditionally been considered through a qualitative lens. We introduce a quantitative reasoning framework and discuss the importance of quantitative modeling in biology. The framework includes the Quantitative Act as a support for Quantitative Modeling and Quantitative Interpretation. The QM BUGS diagnostic instrument was developed to assesses undergraduate biology students’ abilities to create and apply models employing pre-calculus mathematics. A brief discussion of our research findings based on implementation of the instrument include the lack of student ability to develop quantitative models. We present items from the instrument as examples of the Quantitative Act elements: variable quantification through identifying variable and attributes, measurement, variation, quantitative literacy, and context. We also provide items representing quantitative modeling and quantitative interpretation. We then view quantitative biology from K-12 and collegiate perspectives, including instructional practices for teaching quantitative biology, motivating problem contexts that afford quantification, instructional strategies of repetition, scaffolding, peer teaching and learning, direct instruction and teacher moves on the K-12 level, as well as identifying five competencies for the next generation of biologists which require QA abilities.},
year = {2022}
}
TY - JOUR T1 - A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology AU - Robert Mayes AU - David Owens AU - Joseph Dauer AU - Kent Rittschof Y1 - 2022/01/18 PY - 2022 N1 - https://doi.org/10.11648/j.acm.20221101.11 DO - 10.11648/j.acm.20221101.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 17 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20221101.11 AB - Biology is becoming more quantitative. If we are to support the future of quantitative biology, then the next generation of biologists must be prepared to consistently integrate quantitative reasoning into subject matter that has traditionally been considered through a qualitative lens. We introduce a quantitative reasoning framework and discuss the importance of quantitative modeling in biology. The framework includes the Quantitative Act as a support for Quantitative Modeling and Quantitative Interpretation. The QM BUGS diagnostic instrument was developed to assesses undergraduate biology students’ abilities to create and apply models employing pre-calculus mathematics. A brief discussion of our research findings based on implementation of the instrument include the lack of student ability to develop quantitative models. We present items from the instrument as examples of the Quantitative Act elements: variable quantification through identifying variable and attributes, measurement, variation, quantitative literacy, and context. We also provide items representing quantitative modeling and quantitative interpretation. We then view quantitative biology from K-12 and collegiate perspectives, including instructional practices for teaching quantitative biology, motivating problem contexts that afford quantification, instructional strategies of repetition, scaffolding, peer teaching and learning, direct instruction and teacher moves on the K-12 level, as well as identifying five competencies for the next generation of biologists which require QA abilities. VL - 11 IS - 1 ER -
Email: