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Every few months the Center spotlights a topic
of significance to research university faculty and administrators. Its
approach is Thoughts and Models. The Thought consists of a short essay
on the particular topic being highlighted. The Models represent different
campus approaches to the topic.
THOUGHT:
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BioMath Project
The Reinvention Center recently completed a study, funded by the
NSF, to determine the extent to which and how research universities
are modifying their undergraduate education in the biological, mathematical
and computer sciences to reflect the increasing intersections of
these disciplines in much biologically-related research. The study
was driven by two key questions:
- How are undergraduate biology, computer science and mathematics
programs teaching students to understand the complexity of modern
biology and the critical role mathematical and computer sciences
play in addressing the complexity?
- How do these programs bring together what is happening scientifically
and what is happening educationally to foster change? How do they
translate what is happening in research labs into what is happening
in the classroom?
The goals were:
- To ascertain the ways in which undergraduate biology programs
at research universities are incorporating quantitative approaches
into the curriculum and, conversely, how undergraduate programs
in mathematics, statistics, and computer science are making students
aware of the increasing opportunities for the application of quantitative
concepts and techniques in biological research.
- To develop an information base that can be used to inform both
curricular changes and faculty development activities in order
to strengthen connections between biology and quantitative sciences
in the undergraduate curriculum.
The project had two components:
- A survey designed to elicit information on current approaches
to connecting the biological and quantitative sciences in the
undergraduate curriculum. Three versions were created, each tailored
to a different targeted population: Directors of Undergraduate
Studies of Biology, Directors of Undergraduate Studies in Mathematics,
Applied Mathematics, and Statistics, and Directors of Undergraduate
Studies in Computer Science. Twenty-two biology directors, 24
mathematics directors and 22 computer science directors responded.
- In-depth interviews with faculty in the biological, mathematical
and/or computer sciences who collaborate in their teaching or
in their research. Thirty-four faculty (21 biologists, 10 mathematicians
and statisticians, and 3 computer scientists) participated in
the interviews.
Major Findings:
- Undergraduate education in biology, mathematics, applied mathematics
and computer science is changing, as evidenced in the significant
and continually-growing numbers of new and revised courses and
programs that are at the nexus of biology and the quantitative
sciences, the increase (though still small) in joint offerings
with this emphasis, and the increasing participation of undergraduates
in research involving interdepartmental collaboration.
- Ironically, the change is being driven by factors unrelated
to undergraduate education, most notably research advances which
have created a need for faculty with new skills and specializations,
increasing interdisciplinary research collaborations, new computational
technology, and increasing interdisciplinarity in graduate programs.
Few departments that participated in the study for example have
undertaken a systematic examination of their undergraduate curriculum
for the specific purpose of strengthening the connections between
the biological and quantitative sciences.
- As a result, the changes in curricula that are occurring are
primarily evolutionary, stimulated largely by the research collaborations,
personal interests of faculty, an increasing presence of faculty
with interdisciplinary specializations, and grant funds that support
the development of new initiatives. They are also motivated by
the increasingly common recognition that undergraduates will need
interdisciplinary skills and perspective as preparation for graduate
study.
- Departments face several persistent challenges that prevent
a more comprehensive approach: Existing demands on individual
departments which in some instances are struggling to cover their
basic courses; lack of funds for new positions; time constraints;
different orientations and level of interest among faculty in
different disciplines; and few incentives (for mathematics and
computer science faculty in particular) to develop new courses
directed primarily at undergraduates in biology. Several individuals
also cited administrative problems such as determining which department
receives credit for a jointly taught course and figuring out how
new courses with blended emphases related to other departmental
offerings. The most pervasive challenge however relates to how
interdisciplinary courses of this type should be conceived and
what the goals and content should be.
- Despite these challenges, change in this direction will continue
to occur. This perhaps is best evidenced in recent faculty hiring,
as departments have made the recruitment of individuals whose
training and/or current work is at the cutting edge in these areas
a priority and are increasingly seeking faculty with these skills.
Many departments have been hindered in this effort by the shortage
of candidates with both biological and quantitative expertise.
- The pressure to modify the curriculum appears much greater on
biology departments than on mathematics or computer science departments
because of the centrality of quantitative approaches to modern
biology.
- A major concern of biology faculty, as well as mathematics and
computer science faculty, is the weakness they perceive in biology
students' reasoning and quantitative skills. Because of this weakness,
many faculty, including those in biology, indicate a preference
for bringing mathematics/statistics or computer science majors
into their research, rather than biology majors, on the grounds
that they can learn the relevant biology more quickly and easily
than biology majors can develop quantitative skills.
- There was consensus that curricular efforts to connect biological
and quantitative sciences would continue and expand, especially
as departments have more faculty to teach the new courses and
all faculty begin to recognize the benefits to themselves as well
as their students. Some of the benefits cited were the formation
of networks; new opportunities to collaborate in research and
teaching with colleagues from other departments; a new, reinvigorating
way of looking at one's own research; a change in research focus
or even a new focus; and gaining an appreciation of other disciplines
and of how other disciplines approach problems.
An overview of the study and its findings appears in the chapter,
"Building Connections in Research Universities," in Math
& Bio 2010: Linking Undergraduate Disciplines, ed. Lynn
Arthur Steen, The Mathematical Association of America, Washington,
DC, 2004 (2004).
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MODELS: NEW
AND INNOVATIVE COURSES
Departments by themselves or in collaboration with other departments
are creating new courses or revising existing ones to emphasize quantitative
applications in biology. Six examples are described below. Other universities
have also created exciting and exemplary courses and initiatives designed
to educate undergraduates about the connections between biology and mathematics,
statistics and computer science. While space does not permit us to profile
all of them, we refer you to our Resources
page on Connecting
Biology and the Quantitative Sciences for links to additional courses.
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Biology Courses
The new or revised biology courses fall roughly into three groups:
1) Revised introductory mathematics courses, geared for prospective
life science majors, that replace the standard calculus sequence;
2) Revised introductory biology courses that incorporate substantial
quantitative elements; and 3) Advanced courses on topics that are
at the intersection of the biological and quantitative sciences.
The introductory courses almost uniformly address the concern that
biology students are not being adequately prepared in quantitative
concepts and techniques to continue the study of biology. These
courses typically retain the traditional lecture format in order
to accommodate the large number of prospective biology majors research
universities typically teach.
(1)
Introductory-level Mathematics Courses for Life Science Students
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Example:
Contacts:
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"Biology,
Models, and Mathematics"
University of Toronto
Professor Joe Repka, Department of Mathematics Professor James
Rising, Department of Zoology |
This one-year introductory mathematics course was developed jointly
by biology and mathematics faculty in response to the perception
that the standard calculus sequence was not serving the need of
biology students to understand essential mathematical concepts and
see the relevance of these concepts to biology. Team-taught by a
mathematician and 2-3 biologists, the course consists of lectures
accompanied by weekly tutorials (recitation sections). Students
must also enroll in an Introductory Biology course as a co-requisite.
The co-requisite was introduced to ensure that undergraduates who
take this course are genuinely interested in biology. Approximately
100 students enroll in the course per semester.
During the lecture component, a biology professor typically introduces
a problem that requires certain mathematical tools to solve. The
problems are selected from the areas of population genetics, conservation
biology, evolution, growth, population dynamics, physiology, or
cell biology that. The mathematics professor then educates the students
about the theory surrounding the tool and teaches them how to use
it and how to apply it specifically to the biological problem. The
mathematics topics covered during the two semesters include linear
regression, logarithms, power functions, logarithmic graph paper,
exponential and logistic growth, elementary probability, derivatives,
integration, dynamical programming, differential equations, Markov
chains, and a brief introduction to chaos theory. Students can earn
credit in biology for this course, but they may not earn credit
in mathematics.
(2)
Introductory-level General Biology Courses
Example:
Contact: |
"General Biology"
University of Tennessee
Professor Louis Gross, Department
of Ecology and Evolutionary Biology |
This revision of the existing 100-level "General Biology"
course revolves around two types of instructional materials developed
specifically for the course. The first is a set of 50 high school-level
mathematical modules that are designed to correspond to topics in
General Biology, namely either ecology and evolution or cell and
molecular biology. The modules, which all have the same structure,
start with an underlying biological question, move to a discussion
of why that question is important, and then describe the appropriate
mathematical approach to be used to answer the question. Typically,
students are presented with a set of equations that represent the
key variables and are taught how to measure the variables. They
are then given data sets to analyze. At the conclusion of an exercise
they are asked to respond to questions that require them to demonstrate
some understanding of the mathematics that they did not understand
prior to the exercise. Since the lectures can have anywhere from
200 to 500 students and instructors vary from semester to semester,
instructors are given great flexibility in determining how to apply
the modules. Some incorporate small pieces of modules in lectures,
others use individual modules as mini-components of the course,
and others adapt them for homework assignments or extra-credit assignments.
The use varies from instructor to instructor and from semester to
semester.
The second instructional material is a lab manual that focuses
on quantitative methods, particularly statistical applications,
and is used in the lab sections that are offered in conjunction
with the lectures. The labs include components that give students
experience working with graphs and computer software.
(3)
Advanced Courses: Directed at majors in biology, mathematics, applied
mathematics and computer science, these courses typically serve
two functions: To further the quantitative training of biology majors
and to introduce biological applications to mathematics and computer
science majors.
Example:
Contacts: |
"Applied Mathematics in Biology"
Utah State University
Professor James Haefner, Department
of Biology
Professor James Powell, Department of Mathematics and Statistics
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This advanced interdisciplinary elective is team taught by faculty
in biology and mathematics. It evolved from informal discussions
between a biologist and a mathematician who were concerned about
the lack of understanding among biology majors of basic mathematics
concepts that are critical to study in a wide range of biological
fields and a similar lack of knowledge among mathematics majors
of modern biology, which increasingly relies on quantitative applications.
The course has two components: lectures in which students study
a series of mathematical topics and a corresponding wet laboratory
in which they relate these topics to actual laboratory experiments.
The course is listed by both the biology and mathematics departments
and attracts students majoring in both. The students collaborate
in both the lecture and laboratory study phases of the course.
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Mathematics, Statistics, Applied Mathematics and Computer Science
Courses
The new quantitative courses that have been developed with an eye
toward biology also fall into three categories: 1) Introductory
calculus or statistics courses that target prospective biology majors;
2) Advanced electives offered by individual departments; and 3)
Advanced interdisciplinary or joint offerings. The advanced courses
often enroll graduate students as well as undergraduates-a practice
reflective of the small enrollment these courses typically have
and the shortage of faculty available to teach them.
(1)
Introductory-level Courses that Replace the Standard Calculus Sequence
Example:
Contact: |
"Calculus with Biological
Emphasis"
University of Minnesota
Professor Claudia Neuhauser, Department of Ecology, Evolution
and Behavior |
This two-semester variant of the standard introductory calculus
course, taught entirely by faculty in mathematics, was developed
by a mathematical biologist in response to the concern among biology
faculty that the standard course was not giving prospective biology
majors the quantitative background they would need for further study
and research in biology. Although this variant covers many of the
same topics as the regular calculus course, it also includes differential
and difference equations, matrix models, and some probability and
statistics. It is further distinguished by its emphasis on applications
in the biological sciences and its use of word problems taken from
biological research papers. The sequence is taught in a traditional
lecture/recitation section format. The text, Calculus for Biology
and Medicine (Prentice Hall, 2003), was written especially for calculus
courses that have a biological emphasis.
(2)
Advanced Electives Offered by a Department and Geared for its Majors,
as well as Majors in Related Disciplines
Example:
Contact: |
"Mathematical Biology"
University of Utah
Professor Frederick Adler, Department of Mathematics |
This course, created by the Mathematics Department for its advanced
majors and first-year graduate students, is designed to introduce
students to some of the basic models and methods of mathematical
biology that are not usually seen in standard mathematics courses.
The course covers models of population dynamics, reaction kinetics,
diseases, and cells that can be written as ordinary differential
questions, delay-differential equations, and discrete-time dynamical
systems.
(3)
Interdisciplinary Electives for Majors in Biology, Mathematics,
Applied Mathematics, Computer Science and Related Disciplines, such
as Bioengineering
Example:
Contact: |
"Computational Biology"
University of Pennsylvania
Professor Warren Ewens, Department
of Biology |
A joint offering of the Departments of Computer Science and Biology,
this team-taught course focuses on computational problems in molecular
biology such as sequence search and analysis, informatics, genetic
mapping and optimization. The course was developed as part of a
training grant for graduate students in computational biology and
thus is officially a graduate level course that advanced undergraduates
are permitted to take. It attracts majors in biology, computer science,
and statistics. Biology undergraduates who choose to take the course
are typically concentrating in mathematical biology or computational
biology.
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If you have a course you would like listed on the Resources page, please
send
us a brief description (250 words maximum). Be sure to include the
name of the program as well as a link to a Web site or the name and email
address of a contact person.
AN
INVITATION: We invite you to take the lead in framing
future Thoughts and Models.
If you're interested and have a "Thought" in mind, please
send us an e-mail: reinventioncenter.
We will identify "models" that relate to it.
THOUGHT: The
Thought will consist of a short essay focusing on an issue central to
undergraduate education at research universities. The specific topic to
be addressed may vary. It may for example relate to an institutional challenge,
an aspect of student learning, a societal need, or a recent research finding
that may influence the way undergraduate education generally or in a specific
discipline is conceived and delivered at research universities.
MODELS: Each
Thought will be accompanied by reports on programs and experiences that
exemplify or expand upon the Thought. The models will be drawn from different
research universities, utilize different strategies, and, to the extent
possible, focus on different disciplines. Collectively, they will become
part of a database that will yield insights into what works or does not
work and why.
Together, the Thoughts
and Models will be incorporated into reports to be distributed through
this web site, professional society newsletters and our own mailings.
We welcome your comments and look forward to hearing from you.
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