We investigated using Mathematica to create an interactive exercise that allows
students to explore biological concepts. Exporting these active learning
experiences to the Wolfram Computable Document Format (CDF) lets students
enter data and modify parameters with only a browser plug-in and without
needing to know how to use Mathematica. This exercise enhances student
understanding by allowing them to focus on the biological concepts and
visualize the data and calculations without the tedium of hand computation. In
this article, we will highlight an interactive version of a biodiversity laboratory
that explores Simpson’s Diversity Index. Students are walked through sample
calculations with a small data set, and then analyze a larger data set, which is
presented as a set of interactive graphs and automatic calculations so that they
can explore the data to answer questions. For our non-major audience, this
laboratory leads to a more sophisticated discussion without getting stuck on the
calculations. We will present the exercise and assessment results.
Key Words: biodiversity; inquiry; technology; mathematical reasoning; ecology.
Teaching mathematics-based concepts in a biology classroom is
challenging. Particularly in classes for non-majors, students may
have weak mathematics skills. Those students need not only to learn
the new biology concepts, but also to address the relevant deficien-cies in their mathematics background. This increases their cognitive
load, making already difficult material vastly more so (Sweller,
1994). This activity aims to decrease students’ cognitive load by
designing a learning experience that helps first to focus students’
attention on the mechanics of the needed computation, and then
to relieve students of the need to attend to the mathematical content,
thereby facilitating their focus on the biology concepts. In addition,
students learn better when presented with active learning and interactive experiences (Prince, 2004).
One concept that students often struggle with in general bio-
logy and ecology courses is biodiversity and calculating biodiversity
indices. Biodiversity is a very important topic in most biology, ecol-
ogy, and environmental science classes because our current rate of
biodiversity loss may be high enough relative to background
extinction rates to be considered a sixth mass extinction event
(Ceballos et al., 2015; Hull et al., 2015; Waters et al., 2016). There
are many different types of biodiversity indices, and this exercise
could be modified to support various learning objectives (Bandeira
et al., 2013).
Quantitative reasoning is a core part of the AAAS report,
Vision and Change in Undergraduate Biology Education (AAAS,
2011). Undergraduates do not have strong mathematics skills,
and in fact, those skills are declining (Mulhern & Wylie, 2004).
To achieve the goals of incorporating additional quantitative reasoning elements in an undergraduate non-majors biology course,
bolstering student understanding of biodiversity and biodiversity
indices, and supporting students for whom the additional mathematics content presents an additional barrier to learning, we created an experience to help students visualize and understand
both the biology and mathematics behind Simpson’s Diversity
Index (Simpson, 1949). Students often struggle with understanding how indices and other mathematical equations relate to the
biology. This exercise aims to make the calculation easier to
understand and the effects of changing the environment on the
index visual and clear.
To create this lab, we examined other published diversity labs
(Boyce, 2005) and textbooks (Roach et al., 2010; Smith & Smith,
2012) to determine how others were teaching this material. We
wanted to create an activity that would complement the materials
in the books we were using in the course (Roach et al., 2010;
Smith & Smith, 2012). The lab’s interactive elements were created
in Mathematica and then exported to the Wolfram Computable
Document Format (CDF), which allows students to use and interact
with the lab using a free browser plug-in or stand-alone player
application ( https://www.wolfram.com/cdf-player/). Distributing the
lab as a CDF also has the benefit that students do not need to be
concerned with formal Mathematica code.
The American Biology Teacher, Vol. 80, No 5, pages. 372–378, ISSN 0002-7685, electronic ISSN 1938-4211. © 2018 National Association of Biology Teachers. All rights
reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Reprints and Permissions web page,
www.ucpress.edu/journals.php?p=reprints. DOI: https://doi.org/10.1525/abt.2018.80.5.372.
The Innovative Use of
Mathematica to Teach Biodiversity
• ELIZABETH C. DAVIS-BERG, DANIEL R.