[Back up to Course Information]    [Back up to Dr. Green]

Resources for GMST 570:

Modeling Change in Mathematics and Science

What is this course?

GMST 570 is a content enrichment course for 7-12 teachers of mathematics and science. The idea of the course is simple: to study mathematical modeling. This is a topic that touches on every area of mathematics. The potential problems that can be addressed range from simple proportional reasoning to complicated models for how fast two chemicals react to form a third chemical. Students in the course will become familiar with the mathematical tools needed (difference equations, algebra, matrix techniques, graphing, etc.), some of the science involved (population dynamics, flow of heat, motion of objects, etc.) and the techniques of modeling (use of software, process of setting up a model, etc.)

New York State Standards

The New York State Standards for Teaching and Learning Mathematics, Science and Technology contain many expectations that students in K-12 will experience the use of mathematics. The best place to look for these is to scroll down and examine the "MST Performance Indicators" for the standards. Note: All information is in PDF formatting, which requires Adobe Acrobat Reader to display. Most computers have this already installed. If you do not, it is a free download. There is a link on the NYS MST standards page to get the download.

Class Notes

These are actually just the PowerPoint presentations that I am using to guide the class. Right-click and select "Save Target As..." to copy them to your disk. Or, just left-click and view them in your browser with a PowerPoint plug-in (the plug-in is free, and is installed automatically with more recent versions of Internet Explorer).

Day 1
Power Point Pres		 Day 2
Power Point Pres		 Day 3
Topic Outline
Excel File: Logistic Growth		 Day 4
Homework		 Day 5
Squirrel Data
Homework
Day 6 Day 7 Day 8 Day 9  

Web Resources

Modeling in the curriculum (high school and college)

  1. Core Plus Mathematics Program (this one is in use in many 9-12 districts): http://www.wmich.edu/~coreplus/
  2. Math modeling core course; some basic math and some modeling:    http://www.math.uga.edu/104/

  3. Math modeling course for teachers – 500 level! – leads to #7:    http://www.math.montana.edu/frankw/modeling.htm

  4. The connected curriculum project at http://www.math.montana.edu/frankw/ccp/modeling/topic.htm

  5. A two-semester, math modeling course for liberal arts curriculum:    http://math.la.asu.edu/~hauk/tport/tport6html/node50.html

  6. Teaching modeling in High School:    http://www.indiana.edu/~hmathmod/index.html

  7. Definition of a function, with a discrete example

  8. More to come...

Mathematics background for different types of models

  1. Two good papers on difference equations (PDF format); Excel activities with Lotka-Volterra: http://lochsa.lcsc.edu/ma330
  2. Markov chain models and information: http://www.math.nyu.edu/phd_students/campbelm/stuff/random/markov.html
  3. More Makov chains: http://www.cc.gatech.edu/~jamesv/7001/proj2/ and definitions http://mathworld.wolfram.com/MarkovChain.html
  4. Information on the quadratic formula http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html
  5. More information on quadratic equations, with tools for solving them http://www.mathnstuff.com/math/spoken/here/2class/320/quadequ.htm

Examples, projects and worksheets that show modeling in action

  1. Good problems and projects from the Mathematical Contest in Modeling:    http://www.comap.com/highschool/contests

  2. Mathematical look at evolution; pretty high level stuff, but laid out well:    http://pespmcl.vub.ac.be/MATHME.html

  3. Software linking matrices and dynamical systems; has a great layout:    http://www.learn.motion.com/lim/mathmod/MathMod1.html

  4. Poor layout, but lots of good examples from biology and chemistry:    http://www.hhmi.princeton.edu/grp2/mathl_modeling.htm

  5. Good links in many science areas:    http://library.cmsu.edu/sboone/mathmodellinks.html

  6. Excel worksheets for epidemics:    http://www.scibridge.sdsu.edu/coursemats/introsci/mathmodeling

  7. High school example – using curve fitting to predict basketball statistics:    http://www.leyden212.org/Depart/Math/weinart/alg2/model.htm