The motivation for seeking funding for and ultimately undertaking this project came about as a result of a meeting between the faculty of Sacred Heart University’s Mathematics and Biology Departments to discuss concerns related to the level of student performance in mathematics courses required of Biology Majors and students’ inability to consistently perform mathematical and statistical calculations required in their biology courses.
On a broad scale, the project also constituted a partial response of the Mathematics and Biology Departments of Sacred Heart University to three statements in the “Recommendations for Urgent Action” in STEM education included in the Project Kaleidoscope (PKAL), Report on Reports II 2006:
- “give each undergraduate the opportunity for personal experience with inquiry-based learning that brings him or her to a deep understanding of the nature of science, the language of mathematics, the tools of technology”
- “respond to contemporary calls for interdisciplinarity by nurturing and rewarding faculty who make the kind of cross-discipline connections they hope their students will make.”
- “be adventurous in exploring opportunities to strengthen student learning in the STEM fields and in piloting new ideas, tools, and approaches to keep the work of transforming student learning at the cutting edge”
To accomplish our goals and address the issues summarized above we developed a strategy for improving current deficiencies in student achievement by adapting the Project INTERMATH Interdisciplinary Lively Application (ILAP) model to develop and implement “Interdisciplinary Laboratory Activity Projects” (iLabAPs). iLabAPs were developed by teams of faculty and accomplished at least one of the following objectives: development (or adaptation of existing) investigative biology laboratories employing substantial quantitative reasoning and integration of mathematics principles, creation of case studies for use in mathematics or biology courses that involved biological principles and analysis of biological data.
Five projects were ultimately completed and curricular materials describing their content are available for distribution to any interested faculty. It is not our intention that these materials be used “as is” for implementation (although they could be if so desired), instead, we offer these as a start point to encourage interaction between faculty of Departments of Biology and Mathematics at other colleges and universities and encourage their modification and adaptation to suite local desires, circumstances, resources and equipment.
The projects are summarized below and interested parties are encouraged to contact the principal investigator of the project, Kirk Bartholomew, via email (firstname.lastname@example.org) for access to copies of the relevant materials. Please include the acronym “iLabAP” in the subject line of the email request.
iLabAP I: Fermentation and Rate of Change
The investigative biology exercise resulting from iLabAP I is centered on the “rate” of enzymatic reactions or more generally rates of metabolic processes. It presents a background discussion of the relevant mathematical principles, a cellular model for understanding the metabolic processes governing the rate of fermentation in a simulated wine production and an investigative exercise where students investigate the effects of various additives on the rate of fermentation in wine production. The laboratory exercise as written is intended for implementation in majors-level introductory biology courses.
iLabAP II: Transpiration, Rate of Change, and Fick’s Law
The investigative biology exercise resulting from iLabAP II relates to the mathematical principles underlying transpiration (the loss of water from the shoots and leaves of plants). It presents a background discussion of the relevant mathematical principles, a model for understanding the loss of water from plant leaves based on Fick’s law of diffusion and an investigative exercise where students manipulate various environmental factors with the goal of elucidating their effect on transpiration rates. The laboratory exercise as written is intended for implementation in majors-level introductory biology courses although it could easily be adapted to upper level courses in plant biology or physiology.
iLabAP III: Mathematical Models of Population Growth
The investigative biology exercise resulting from iLabAP III relates to the mathematical principles underlying population growth including reference to general rate of change principles, as well as linear, exponential, and logistic growth. It presents a background discussion of the relevant mathematical principles an explanation of the various growth an investigative exercise where students compare the effects on population growth of two yeast strains under conditions typical of wine fermentation. The laboratory exercise as written is intended for implementation in majors-level introductory biology courses although it could easily be adapted to upper level courses in microbiology.
iLabAP IV: Evolution, Rate of Mutation, and the Poisson Distribution
The investigative biology exercise and related mathematics case studies resulting from iLabAP IV relate to the mathematical principles underlying the linked topics of evolution and mutation including the relation of exponential and logarithmic functions and probability distributions to the calculation of mutation rates. Background discussions of the relevant mathematical and biological principles are included appropriate for courses in both biology and mathematics. The associated investigative biology exercise involves discrimination between the acquired immunity and natural selection hypotheses as they relate to the evolution of antibiotic resistance in bacteria. The laboratory exercise as written is intended for implementation as a multi-week project in majors-level genetics course although it could easily be adapted to upper level courses in microbiology or majors level introductory biology courses.
We have written a case study on antibiotic resistance that can be used as an introduction to this lab exercise.
iLabAP V: Population Genetics, Inbreeding Depression, and Evolution
The investigative case study resulting from iLabAP V relates to the mathematical principles underlying the linked topics of population and transmission genetics as applied to conservation of endangered species including their relation to probability theory. Background discussions of the relevant mathematical and biological principles are included appropriate for courses in both biology and mathematics. While developed separately, this case study relates well to a semester long investigative biology exercise “Inbreeding Depression and the Evolutionary Advantage of Outbreeding” created by Christopher G. Eckert (Queen's University, Department of Biology, Ontario) that we currently use in the laboratory portion of our majors level course course in genetics and evolution Laboratory; this laboratory exercise is available in digital format through the Association for Biology Laboratory Education (http://www.ableweb.org/volumes/vol-15/12-eckert.pdf). The case study was developed for use in an introductory college-level probability and statistics course, but could also be used effectively in an introductory biology course (for non-majors or majors) or an advanced high school course in biology or probability. The case study is available through the National Center for Case Study Teaching in Science (http://sciencecases.lib.buffalo.edu/cs/).
This material is based upon work supported by the National Science Foundation under Grant Number 0632940: From ILAP to iLabAP—Linking Investigative Biology Laboratories to the Mathematics Curriculum.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors of the material and do not necessarily reflect the views of the National Science Foundation.