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.