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Crossing boundaries in Undergraduate Biology Education: An Integrated Approach to Teaching and Learning Dirk Vanderklein - Department of Biology and Molecular Biology Mika Munakata – Department of Mathematical Sciences Rationale

The Set Up

The Plan

This project is a first attempt to systematically identify the mathematics that is crucial to biology students’ deep understanding of science and to develop, deliver, and assess the impact of modules that will engage students in interdisciplinary activities that promote critical thinking. Traditionally, mathematics is taught as a collateral course for biology majors generally using non-biology related examples. Consequently, mathematics is not considered part of biology, but separate and not relevant.

Dr. Vanderklein is slated to teach three sections of ecology in the fall of 2013 with a total of about 75 students. The ecology course is structured such that students registered for three separate sections attend the same lecture but receive their lab training at separate times. This structure allows us to divide the class into three semi-independent groups receiving different learning approaches.

Topics to be covered in Modules

Our goal is to develop a set of modules that will help biology majors identify and learn ecological and mathematical concepts in an integrated fashion enabling a deeper and interwoven understanding of mathematics and biology. The biology and mathematics integration in our modules will be informed by current literature which has shown that students learn best under contextualized instruction (Clay et al., 2008), and that ideally science/mathematics interdisciplinary instruction should promote an environment such that a visitor to the class would not be able to discern whether the course is a science or mathematics course (Huntley, 1999). Current science education research also shows the merits of problembased learning (e.g. Shore and Shore, 2003), team teaching (e.g. Tra and Evans, 2010), and interdisciplinary mathematics and biology instruction (e.g., Madlung et al., 2010). Our study will incorporate these principles, but will also address the need for activities designed to prepare students for interdisciplinary learning (Madlung et al., 2010).

Learning Approach #1: The first section will be taught using the current protocol, with mathematics interwoven into the curriculum, for the most part, when it appears in the textbook. This section will be our comparison group. Learning Approach #2: In the second section, Dr. Munakata and Dr. Vanderklein will co-teach, with Dr. Munakata giving standard mathematics lessons with mathematics taught in the context of ecology, where the instructor points out the connections. Learning Approach #3: For the third section, Dr. Munakata and Dr. Vanderklein will coteach integrated hands-on lessons whereby students explore the mathematics and are asked to make the connections to science on their own. We will meet regularly during the semester to reflect on the co-teaching and to refine our approach.

Hypothesis

Assessment

Our working hypothesis is that the students who receive the integrated hands-on lessons will show deeper learning in ecology and math as compared to the other two groups. We also hypothesize that the students who receive either form of enhanced teaching will show more deep learning than the students who don’t (the comparison group).

The qualitative data described below will help us identify successful elements of the modules and teaching so that they can inform further module development. At the beginning of the Fall 2013 semester, students who volunteer to participate in the study will be given a pretest of their content knowledge and beliefs and attitudes. The post-tests will be administered by a designated third party at two points: during the semester after students have been exposed to the modules and at the end of the semester. Though this hardly constitutes a longitudinal study, we hope that the separation in time between the two post-tests will allow us to determine the retention of skills and knowledge. Towards the end of the semester, a designated third party will also conduct focus group studies of each of the three sections to help triangulate the comparative data and to further elucidate students’ attitudes toward learning in an interdisciplinary environment. Students will be asked questions related to their understanding of the connections between biology and mathematics.

http://www.bio.davidson.edu/Courses/anphys/2000/CrawfordR/gigantothermy.htm

Proportional Reasoning: Rates, Percentages, Ratios, Proportions, Probabilities. E.g. Surface area to volume ratio, Hardy-Weinberg equilibrium Modeling: Graph Construction: Linear curves, logistic curves, exponential curves, limiting factors, rates, axis placement. E.g. population growth curves Graph/Data Interpretation: Probability, statistical significance, experimental design/sampling, data and interpretation bias. E.g. Gobal warming trends Ratios and probability will be presented with the HardyWeinberg test of evolution. The Hardy-Weinberg test asks whether the proportion (i.e. ratio) of traits in a population has changed over time. Since the ratios of traits in a population are always in flux, an important part of the test is whether the observed changes can be statistically verified. Through another module, students will explore how values and ratios of those values give us different information about how organisms respond to their environments. Students will, for example, explore the relationships between a) organism size and its surface area to volume ratio (SA/V); and b) plant size and its root mass to shoot mass ratio (R/S) as they consider the role of the environment and justify their conclusions from both the mathematical and biological perspectives. The modules will present the concepts in a way that encourages interpretation, analysis, and justification.

Background Reading Clay, T.W., Fox, J.B., Grünbaum, & D., Jumars, P.A. (2008). How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World. American Biology Teacher. 70(6). 363-370. Huntley, M. A. (1998). Design and implementation of a framework for defining integrated mathematics and science education. School Science and Mathematics, 98(6), 320-327. Madlung, A., Bremer, M., Himelblau, E., & Tullis, A. (2010). A Study Assessing the Potential of Negative Effects in Interdisciplinary Math-Biology Instruction. CBE Life Sciences Education, 10(1), 43-54. Munakata, M. and Vaidya, A. (in press). Undergraduate Research: Fostering Creativity through Personalized Education. Primus—Problems, Resources, and Issues in Mathematics Undergraduate Studies. Special issue. Munakata, M. and Vaidya, A. (2012). Encouraging Creativity in Mathematics and Science Through Photography. Teaching Mathematics and its Applications. 31(3). 121-132. Shore, M. A., & Shore, J. B. (2003). An integrative curriculum approach to developmental mathematics and the health professions using problem based learning. Mathematics and Computer Education, 37(1), 29-38. Tra, Y.V., & Evans, I.M. (2010). Enhancing Interdisciplinary Mathematics and Biology Education: A Microarray Data Analysis Course Bridging These Disciplines. CBE Life Sciences Education, 9(3), 216-226.