Course Description:
This course introduces students to the process of developing mathematical
models as a means for solving real problems. The course will encompass
several different modeling situations that utilize a variety of mathematical
topics. The mathematical fundamentals of these topics will be discussed,
but with continued reference to their use in finding the solutions to problems.
Connections to the NCTM Standards and current curriculum projects will be
made continually through the course.
Course Goals:
Students will be required to work with and apply a variety of mathematical
concepts, processes, and relationships. Students must be able
to connect, through creative problem solving, their understanding of specific
content to the modeling situation. Students will
promote the processes of problem solving, reasoning, communicating,
and connecting mathematical concepts and principles using modeling as a medium
relate modeling concepts to the NSF developed programs being used in
schools
model and solve significant problems in our society
apply technology to develop concepts and relationships
develop methods for teaching the content areas as outlined in the Standards
develop strategies for effective teaching of mathematical modeling
learn alternative assessment and evaluation techniques that are realistic
while promoting quality mathematics for all students.
Resources:
Mathematics Methods and Modeling for Today's Mathematics Classroom:
A Contemporary Approach to Teaching Grades 7-12 by Dossey, Giordano, McCrone,
Weir, COMAP, Brooks/Cole Publishing.
NCTM Principles and Standards for School Mathematics
Microsoft Word and Excel
Fathom or Minitab (a statistical software package)
Topics: Part 1:
Modeling Change with Discrete Systems
Approximating Change with Difference Equations
Discrete vs. Continuous Change
Project #1
Examine The Standards and Curriculum Projects: A First Glance - Journal
#1
Part 2:
Dynamical Systems
Systems of Difference Equations
Project #2
Doing Mathematics - Journal #2
Part 3:
NCTM Standards: Number and Operations
Review sample lessons - Journal #3
NCTM Standards: Patterns, Functions, and Algebra
Review sample lessons - Journal #4
NCTM Standards: Geometry and Measurement
Project #3
Review sample lessons - Journal #5
NCTM Standards: Data Analysis and Probability
Project #4
Review sample lessons - Journal #6
Part 4:
Model Fitting and Empirical Model Construction
Project #5
Linear Programming
Project #6
Part 5: Final Project on a topic of student's choice
Part 6:
Strategies for Effective Teaching of mathematical modeling
Assessing and Evaluation
Course Portfolio
Assessment:
Exercises: Homework exercises will be assigned regularly
but will be not be collected. The exercises are examples similar to
in-class activities. They are designed to reinforce the in-class examples.
Projects: There are two types of projects in this course.
Mini-projects will be assigned regularly. Each min-project will be
graded on mathematical content as well as the written communication.
You should prepare the projects as a professional document. The final
project will be an individual modeling project on a topic of a students own
choosing. Each student will present their project to the rest of the class.
Journal Reflections: Students will be required to reflect
frequently on how the course content ties together with the NCTM Standards
and curriculum projects for grades 7-12.
Course Portfolio: Students will submit a final course
portfolio that includes sample modeling activities developed through the
course and modeling activities from curriculum projects in which they will
integrate into their classrooms.
Grades:
Course grades will be based on the following.
Projects 45%
Journal Reflections 20%
Final Project 15%
Course Portfolio 20%