Excel
Simulations and
Tools for
Exploratory, Experiential
Mathematics

The Three E's of the Collection:

Excel    Microsoft's spreadsheet software Excel was chosen as a general development environment for the ESTEEM project because most biologists and mathematicians have it on their desktop computers, use it at least minimally for data collection, and find it fairly easy to operate. In addition, Excel is powerful enough to develop applications that involve matrix algebra, statistics, finite difference equations, and simple ordinary differential equations.

Exploratory    Since parameters are so easy to change in Excel and it is so easy to import data from diverse and heterogeneous resources, our modules are intended to be adoptable, adaptable, extensible, flexible, and utilitarian for students who are engaged in a variety of biology and mathematics courses. We often have built templates that are easily employed for major modification to modules or easy mimicry to include new data sets or additional complication to current models.

Experiential    A primary intention of the Biological ESTEEM project has been to sample elementary applications of mathematics across the spectrum of activity-based general biology curricula. Particular attention was paid to equations that have significantly transformed contemporary biological practice  and that are widely used in classroom, laboratory, and field activities in the context of measurement, analysis, modeling, and hypothesis testing. Through extensive use of simulations, tools, and databases, we believe that students will have an opportunity to develop an intuitive sense of the power, utility, and beauty of applying mathematics to biology.

Accessory materials for each module

In addition to a downloadable Excel (.xls) file, each module is supplemented with references to textbooks where the relevant biology and mathematics are introduced, the original sources of such models, current research articles that employ the models explicitly or derivatives of these models, and online related resources. In some instances, additional documentation, other software (particularly Java Applets and remotely run Web Mathematica applications), classroom-lab-field activities, science and mathematics education research references, and historical material are also provided.

The Biological ESTEEM Collection is an open collection

In addition to our continued development of modules, we invite biologists, mathematicians, computer scientists, and other interested parties to contribute new modules or to suggest major revisions to currently existing modules.

Support for this project was provided by three NSF grants: DUE-0232823 (National Dissemination BEDROCK), CFDA No. 47.076 (MAA NSDL), The SHODOR Education Foundation, and EPIC (Engaging People in Cyberinfrastructure), the HHMI Digital Scholars program, matching funds from Beloit College, and generous contributions from members of the BioQUEST Curriculum Consortium.

 

Biochemistry

Balancing Chemical Equations Using Matrix Algebra. This Excel workbook introduces using matrix algebra to balance chemical reactions.

Buffer Preparation. This workbook calculates the necessary components to create a buffer solution.

Bioinformatics

Protein Analysis. This workbook allows the analysis of sample or imported protein sequences.

Biometrics

BioBayes. This Excel workbook and documentation lead the user through several different methodologies for applying Bayesian probabilities to real life examples and problems.

Biostatistical Tools.  A collection of workbooks for linear regression, polynomial fit, and chi-square analysis to test whether a data set is in Hardy-Weinberg Equilibrium.

Database Construction and Sampling. The construction of three simple databases using a spreadsheet is described here and basic summary statistics are provided for each.

Fractal Fern Generator. This Excel workbook creates graphical images of a certain type of fractals that can be constructed by linear transformations.

PopTools. This downloadable Windows program allows the construction, analysis, and simulation of complex models in a simple spreadsheet format.

Botany

Three-D FractaL-Tree. This module allows scientists to collect data from specimens, insert the measurements into a spatially explicit L-system package, and visually compare to the computer generated 3D image with such specimens. The module consists of an Excel workbook and a Java applet.

Developmental Biology

Biological Cellular Automata Laboratory (BioCA Lab). This Excel workbook includes linear cellular automata and 2D cellular automata. Users can choose from a set of popular rules or define their own.

Developmental Allometry: Scaling in Growth. This Excel workbook illustrates a number of allometric equations in animal growth.

Ecology

Biodiversity.  This Excel workbook allows the diversity of a biological population to be estimated with both the Shannon and Simpson biodiversity indices.

Continuous Growth Models. This worksheet compares user-input growth data with predictions under linear, exponential, and logistic models of growth.

Island Biogeography. This Excel workbook demonstrates the principles of the MacArthur-Wilson theory of Island Biogeography.

Java Food Web. This Java applet is accompanied by 100 Excel worsheets that provide food web matrices for analysis by the applet.

Leslie Matrix for Age-structured Populations. This Excel workbook uses the Leslie Matrix Model for population projection of age-class or stage-class structured populations.

Two-Species Model. This worksheet simulates the population growth of two interacting species.

Epidemiology

SIR Model. This worksheet implements an SIR (Susceptible/ Infected/ Resistant) model of epidemiology for vector-borne diseases.

Evolution

DeFinetti 1.0. This workbook simulates evolution of a single gene with three alleles.

ESS: Evolutionary Stable Strategies Game Theory Module. This workbook illustrates a number of ESS examples. 

Luria-Delbrück. These two workbooks model the evolution of phage resistance in a bacterial population under two alternative hypotheses.

Genetics

ABO Blood Group Frequencies. The purpose of this workbook is to compare several methods for calculating allele frequencies for ABO blood groups.

Birthday Problem & Class Phenotypic Probabilities. This Excel workbook as two related applications, the Birthday Problem and Class Phenotypic Probabilities.

Deme 2.0. This worksheet simulates the population genetics of a single gene with two alleles.

Linkage Analysis. This workbook simulates a linkage analysis problem with up to four alleles.

ORF Finder. This workbook performs six-frame translation on a short user-input nucleotide sequence and highlights the position of stop codons.

Operon. This workbook models lac operon function in a partial diploid E. coli.

Phylogenetics

EvolSeq. This worksheet simulates the molecular evolution of DNA sequences.

GeoPhyl. This workbook allows students to explore evolution over space and time using published data on the invasive plant Tamarix (salt cedar).

Split Decomp. This worksheet performs split decomposition on a set of four DNA sequences and their associated amino acid sequences.

Sequence Alignment

Multiple Alignment. These two worksheets implement a dynamic programming algorithm for simultaneous alignment of multiple sequences.

Pairwise Alignment. These two worksheets implement a dynamic programming algorithm for pairwise sequence alignment.

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The Biological ESTEEM project is part of the BioQUEST Curriculum Consortium at 
http://www.bioquest.org/esteem

We hope to engage you in a process that is likely to lead to the development of high quality, adoptable, and adaptable curricular materials in biology and mathematics education. How can mathematics and biology education reformers use these five approaches to catalyze discussion, enhance learning, promote social action, and bridge a gap between us? How can we move beyond the separate and unequal educational practices of the past such that we can enable diverse learners to mutually and collaboratively learn both biology and mathematics in a seamlessly integrated learning environment? Can we do this in a way that maintains disciplinary strengths, builds on natural talents and interests of students in each distinct arena, and yet builds interdisciplinary communities? What metaphors will work? Border crossing? Hybridization? Cross-fertilization? Integration? Connectivity? Networking? Symbiosis? Synergisms? We do not yet know where these interactions will go, but we are driven by the recognition that problems don’t come in neat little packages, that future science will require students to learn how to deal with terabytes of data collected per day, and that multivariate, multidimensional, and multidisciplinary challenges will require far different approaches than are used in current practice. Furthermore, we recognize that already students know their careers will, with high probability, expect them to be able to be “versatilists” rather than specialists and flexible expertise is appropriate in such a dynamic landscape.

Sixty-one ESTEEM modules are in various stages of development. Currently, about thirty of these ESTEEM modules are available for trying out, commenting upon, and building upon. Eight primary authors: Anton Weisstein at Truman State University and seven of us at Beloit College: Rama Viswanathan; Vince Streif, Tia Johnson, Annelise Myers, Jennifer Spangenberg, DaYoung Chun, and John R. Jungck continue to work on the applications in the list above. Amanda Everse and Chiro Umezaki, in Burlington. Vermont, continue to work on the MySQL database driver and the ESTEEM website. International collaborators in Thailand, New Zealand, Germany, and Australia have already made major contributions and more are forthcoming. Obviously, some modules in which we have more expertise have received much more attention than others. Currently, eleven modules have extensive data sets that include: 114 foodwebs; numerous island biogeography datasets from archipelagos around the world; access to protein and nucleic acid sequence databanks; gravestone population life history data; morphology of over 600 Galapagos finches; a list of buffers for different pH ranges; ABO phenotypic frequencies of human populations spread around the earth; kinetic data; images; genomic data (orders); and simulation outputs (external). We feel that spreadsheet models are greatly enhanced when combined with heterogeneous data sets that can be used to test the models.

References

BIO2010: Transforming Undergraduate Education for Future Research Biologists.  Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st Century, Board on Life Sciences, National Research Council. The National Academy Press: Washington, DC 2002.

Math & Bio 2010: Linking Undergraduate Disciplines. Lynn Arthur Steen, Editor. Mathematics Association of America: Washington, DC 2005.

Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula. John R. Jungck. Bioscene: Journal of College Biology Teaching 23 (1): 11-36 (May 1997).

Editorial Board of the Biological ESTEEM Collection

Biology	Mathematics
Editor John R. Jungck Professor of Biology and Mead Chair of the Sciences Beloit College Beloit, WI 53511	Editor Raina Robeva Associate Professor of Mathematical Science Sweet Briar College Sweet Briar, VA 24595
Section Editors Evolutionary Biology and Bioinformatics Anton E. Weisstein Assistant Professor Division of Science Truman State University Kirksville, MO 63501 Genetics, Molecular Biology, and Microbiology Srebrenka Robic Beloit College Beloit, WI 53511 Population Biology and Developmental Biology Doug Green Professor of Biology Saint Michael's College Colchester, VT  05439 Physiology Tom Hoogendyck Instructional Technology Associate University of Massachusetts Amherst Amherst MA 01003 Botany Ethel D. Stanley Beloit College Beloit, WI 53511 Ecology Denny Fernández del Viso Department of Biology University of Puerto Rico at Humacao	Section Editors Eric Marland Assistant Professor of Mathematics Department of Mathematical Sciences Appalachian State University Boone, NC 28608 Jennifer Galovich Associate Professor of Mathematics St. John's University Collegeville, MN 56321 and The College of St. Benedict St. Joseph, MN 56374 Elio Ramos Assistant Professor Department of Mathematics University of Puerto Rico at Humacao Rene Salinas Tim Comar Assistant Professor of Mathematics Benedictine University Lisle, IL Mike Martin Professor of Mathematics Johnson County Community College Overland Park, KS Renée Fister Associate Professor of Mathematics Murray State University Murray, KY

MAA Digital Classroom Resources Editor

Doug Ensley
Department of Mathematics
Shippensburg University
Shippensburg, PA 17257

Copyright 2005, All Rights Reserved, The Mathematical Association of America.
 

Implementing NRC Bio 2010's Recommendations for More Mathematics in Undergraduate Biology Education

In 2002, the National Research Council made eight major recommendations for the improvement of undergraduate biology education in its publication: BIO2010: Transforming Undergraduate Education for Future Research Biologists. The first two of these recommendations both emphasized the need for additional attention to the inclusion of more mathematics:

“It is important that all students understand the growing relevance of quantitative science in addressing life-science questions. Thus, a better integration of quantitative applications in biology would not only enhance life science education for all students, but also decrease the chances that mathematically talented students would reject life sciences as too soft …  Most biology majors take no more than one year of calculus, although some also take an additional semester of statistics. Very few are exposed to discrete mathematics, linear algebra, probability, and modeling topics, which could greatly enhance their future research careers. These are often considered advanced courses; however, many aspects of discrete math or linear algebra that would be relevant to biology students do not require calculus as a prerequisite. While calculus remains an important topic for future biologists, the committee does not believe biology students should study calculus to the exclusion of other types of mathematics.”

Explicit strategies for implementing these recommendations were the subject of a follow-up conference entitled “Meeting the Challenges: Education Across the Biological, Mathematical and Computer Sciences” and a book published by the Mathematics Association of America entitled: Math & Bio 2010: Linking Undergraduate Disciplines.

Members of the BioQUEST Curriculum Consortium were funded to develop modules to address these challenges through a new initiative: Biological ESTEEM (Excel Simulations and Tools for Exploratory, Experiential Mathematics). The recommended areas: “discrete mathematics, linear algebra, probability, and modeling topics” will be illustrated through materials that were developed in biochemistry, bioinformatics, biometrics, developmental biology, ecology, evolution, genetics, microbiology, and physiology. All materials are easily run on economical microcomputers equipped with Microsoft Excel and a web browser. Biological ESTEEM modules are downloadable at no charge.