What is Mathematical Modeling?
What is modeling?

Modeling, in the context of this course, is another representation of numbers and operations on numbers with physical materials.
  • You have learned to do mathematics with a pencil.
  • You have learned to do mathematics mentally.
  • You have learned to do mathematics with a calculator. 
  • Now, you are about to learn to do mathematics a new way--with simple materials.
    		•
    When  modeling a mathematical operation on numbers, the numbers are represented by physical models, action is taken on the models, and the result is read from the model.

    [The only need for a pencil is to draw pictures to describe each step in the process or to have a written record of the mathematical operation.]
    Steps in Mathematical Modeling
  • Select the model, the physical materials
  • Identify which piece is to represent one (the unit) & then determine the value of all other pieces in the model
  • Model the appropriate number(s)
  • Perform an action on the model
  • Interpret the mathematical result from the model
    		•
    Modeling is ...
     
  • representing mathematical ideas with physical materials.
  • giving meaning to mathematical symbols. 
  • clarifying understanding of mathematics ideas.
  • doing mathematics.
    		•  Modeling is an experience with physical objects that leaves mental images, or referents, in the memory of the learner.

    The actions on the objects are associated with mathematical operations so well that when abstract, mathematical symbols are encountered, one can respond to the symbols without a model but by using its mental images as referents of thinking.
    Benefits of Modeling


  • referents for thinking mathematically
  • tools for explaining mathematics
  • a better understanding of mathematics
  • an added perspective on mathematics
  • more effective teaching techniques
  • greater ease in learning mathematical ideas
    		•
    Communicating Modeling

    Tell a story, like a cartoonist, with pictures, symbols, and words.

    Draw a picture of your beginning model

    Draw pictures showing the results of the steps in the action process
    Draw indicators of the action(s) taken
    Use words to assist when necessary

    Record with symbols what has been done