Course Proposal for Math 807T: Using Mathematics to Understand our World
Prerequisites: Admission to the MAT-MScT program in mathematics or to a graduate
program in the College of Education and Human Sciences.
Catalog description: Students in this course will examine the mathematics underlying
several socially-relevant questions from a variety of academic disciplines. Students will
construct mathematical models of the problems and study them using concepts and skills
developed in this or previous mathematics courses (such algebra, linear and exponential
functions, statistics and probability). Sources will include original documentation whenever
possible (such as government data, reports and research papers) in order to provide a sense of
the very real role that mathematics plays in society, both past and present.
Course Goals: In this course the students' mathematical perspectives will be broadened and
strengthened as they are exposed to a variety of interdisciplinary settings to which
mathematical topics can be applied. The mathematical topics include exponential growth and
decay, logarithmic functions, Newton’s Law of Cooling, simulations, graphing data, making
predictions, analysis of the effects of error, probability and quality control. The disciplines to
which the mathematics will be applied include biology, medicine, natural science, forensics,
and industry. In addition to broadening the participants’ mathematical perspectives, these
experiences will provide the teachers taking this course with concrete examples of how they
might collaborate with colleagues in other disciplines in their own classrooms and schools.
The course goals are threefold:
Mathematical Modeling and Problem Solving: Students in this course will learn to identify
the mathematics found in questions stemming from a variety of real-world settings and
academic disciplines. Complex problems in which the mathematics is not readily apparent
will be modeled and analyzed from a mathematical perspective, providing a very real
application for concepts and skills which will be developed in the course or were acquired in
previous mathematics courses. As is the case with mathematicians who apply their expertise
to a variety of scientific and industrial settings, students will be required to synthesize
considerable background information in order to make sense of and identify the mathematics
in the project problems.
Reading ScientificResearch: Students will be able to read professional mathematical reports,
such as reports from the Center for Disease Control or elementary research articles. Students
will prepare for this by reading background information provided to them by the instructor
and by analyzing problems which are similar too, but simpler than the problem discussed in
the professional report. Students will gain an appreciation for the way in which mathematics
is used to solve these very real problems and at the same time recognize how an
understanding of a simplified problem leads to an enhanced understanding of a more
complicated one.
Communication: Students will strengthen their communication skills in mathematics by
working collaboratively, sharing ideas on discussion boards, and submitting written
descriptions and justifications of their mathematical models and solutions. Participant’s
written reports will incorporate mathematics into language intended for non-mathematical
audiences, thereby developing students’ skills in articulating the connections between a
mathematical study and its concrete applications.
The emphasis on articulating
mathematical explanations in both verbal and written forms will address the NCTM process
standard of Communicating Mathematics.
Course Outline:
Face-to-Face Session: linear functions (review), exponential functions, logarithms,
exponential growth and decay, modeling with linear and exponential functions, problem
solving
A partial list of projects includes:
Measuring Temperature, Newton’s Law of Cooling and Determining Time Since Death
Description: In this project students will examine methods for the derivation of number
scales for measuring temperature, construct their own thermometer and determine its
temperature scale. Students will learn how Isaac Newton first measured very high
temperatures (temperatures which exceeded the boiling temperature of his thermometer) and
how Newton's Law of Cooling came out of this study. Participants will see Newton's
original paper on cooling (in Latin and in English), use his ideas to predict the temperatures
of simple cooling objects, and study methods for adapting Newton’s Law to more
complicated objects. In particular, students will examine how these mathematical ideas are
used to estimate time of death of a human body and use standard coroners’ algorithms to
solve a murder mystery!
Mathematical Tools:
exponential functions, logarithms, modeling, graphing, linear
functions, proportional reasoning, conversions between scales, basic statistics
Project 2: Containing Infectious Diseases
Description: Due to concerns about bioterrorism that have resulted from the September 11
attack, the U.S. government commissioned the CDC (Center for Disease Control) to come up
with recommendations for how to react in the event of a smallpox attack. With the goal of
containing the outbreak to prevent an epidemic, the CDC came up with a plan that involves
quarantining infected individuals and vaccinating a percentage of healthy individuals (since
the vaccination itself is dangerous it is not recommended to vaccinate everyone). The CDC
used mathematics to solve this problem and the goal of this project is to understand it.
Students will begin by analyzing the simpler (fictitious) disease, schoolpox, and along with
various strategies for containing schoolpox outbreaks. After the simplified problem is
understood, students will read (and try to understand) the actual CDC smallpox report.
During this project, students will study strategies (based on mathematics) employed to
contain cholera outbreaks in the 1800’s, strategies which virtually eliminated cholera
epidemics and saved literally tens of thousands of lives.
Mathematical Tools: modeling, iterative processes, basic statistics, interpretation of graphs,
linear functions
Project 3: Childhood Growth Charts
Description: In this project students will study the development of growth charts used by
pediatricians and how they are utilized to predict health risks in children. The charts
produced by the CDC) and the report containing the data which led to the development of the
charts will be studied. Students will use data from the CDC to construct their own growth
charts, analyze data from children in their own classrooms, and learn how to use their charts
to determine the risk of obesity for real children.
Mathematical Tools: basic arithmetic, metric conversions, percentages, statistics, graphing
and interpreting graphs, error analysis
Course Structure: The course will be structured around a series of projects problems. For
each project, participants will complete a pattern of activities that is similar to what follows:
1. Read the problem and essential background information (using original
documentation whenever possible).
2. Identify the mathematical aspects of the problem in order to develop an appropriate
mathematical model.
3. Analyze the mathematical model and connect the results to the problem at hand.
4. Read further documentation of the problem, using the model and analysis to
synthesize information in a research document describing a more complicated
situation (again, using original documentation whenever possible).
5. Provide written reports which include mathematical explanations and justifications
for solutions and recommendations for the problems.
Schedule:
This course, offered as a “blended” distance education course, will have two components.
Face-to-Face Component:
Participants will meet on campus for a 2-day intensive weekend in which they have 16 hours
of class time. The course will begin with a study of exponential and logarithmic functions to
provide the necessary background for the first project problem.
During the face-to-face component of the course, instruction will be offered by an
instructional team consisting of two faculty, two graduate students and one master teacher.
Each member of the instructional team will serve as the “advisor-coach” for approximately
6-7 participants. The advisor will check in with their participants regularly and offer
comments about the homework solutions. In addition, participants will be able to meet
individually with their advisor at various times during the day to discuss assignments, review
material that has been presented and to discuss the successes or difficulties the participant is
having in the course. In addition, advisors will meet with participants in the evenings to offer
help with assignments.
On-Line Component: The remainder of the material during the semester will be
communicated using Blackboard. One faculty member and one graduate student will
continue to oversee the course during this time. Homework will be collected at the end of
each project and given feedback. Participants and instructors will actively communicate via
email, Blackboard, telephone, face-to-face meetings, and Breeze (an internet conferencing
system) meetings with one another about the course content, assigned projects and written
reports.
End of Course Requirements: At the conclusion of the course, participants will be required
to complete two final assignments; the End-of-Course Problem Set and a final draft of one
project. The End-of-Course Problem Set, which is a collection of problems that covers the
areas of mathematics covered in the course, will be distributed as the course comes to a close.
Students will be required to submit solutions to these problems as part of a course portfolio.
Students will also be required to select one of the projects they have completed during the
course and make revisions based on instructor feedback. The revised version of the project
will be included in the course portfolio as an example of the participant’s finest work.
Participants and instructors will actively communicate via email, Blackboard, telephone,
face-to-face meetings, and/or Polycom with one another about the course content during this
time period.
Grading: Grades will be based on course projects submitted throughout the semester, class
participation, the End-of-Course Problem Set, and the revised project.
A sample rubric for grading the homework and end-of-course problem set:
1. A project submitted with no mathematics or incorrect mathematics or little to do
with problem. F
2. Project contains essentially correct mathematics but with little explanation of
reasoning. B-/C+
3. Mathematics in the project is essentially correct with some logical explanations.
B/B4. Project contains correct mathematics with coherent logical explanations. A/A/B+
5. Project contains correct mathematics with well-written logical explanations and
motivation and proposed alternate solutions when appropriate. A+/A/A-