David Hestenes wrote these comments about basic particle models in 2011 to high school teachers:

 

“I have enclosed a slide about basic models that I use in talks about Modeling Instruction.
Let me add some comments for teachers.

Mechanics can be divided into kinematics (description of motion) and dynamics (causal explanation of motion). Accordingly, I have two sets of names, depending on which aspect is of interest. Newtonian theory says that all causes of motion are forces, so causal models are classified by types of force.

 

More about this in "Modeling Games in the Newtonian World," where Kepler’s laws are identified as kinematics, which is explained causally by the gravitational force.”
            ---------------------------------------------------------------------------------------


Notes by Jane Jackson:

(See also the slideshow at the bottom of the modeling home page for his 2011 invited talk on “Remodeling STEM Education” in Taiwan. See slide #22 on basic models.)

 

Each basic particle model should be correlated with the appropriate basic mathematical model. David Hestenes' list of mathematical models is in two documents on the modeling website.

 

1. On page 6 in  "Modeling Instruction for STEM Education Reform", a major proposal by David Hestenes (2009) (at http://modeling.asu.edu. Scroll to the bottom of the webpage.) I quote:

 

Basic Mathematical Models:

1. Constant rate (linear change): graphs and equations for straight lines (proportional reasoning, constant velocity, acceleration, force, momentum, energy, etc.)

2. Constant change in rate (quadratic change) graphs and equations for parabolas (constant acceleration, kinetic and elastic potential energy, etc.)

3. Rate proportional to amount: doubling time, graphs and equations of exponential growth and decay (monetary interest, population growth, radioactive decay, etc.)

4. Change in rate proportional to amount: graphs and equations of trigonometric functions (waves and vibrations, harmonic oscillators, etc.)

5. Sudden change: stepwise graphs and inflection points (Impulsive force, etc.)

 

These models characterize basic quantitative structures that are ubiquitous not only in physics but throughout the rest of science. Their applications to science and modern life are rich and unlimited. Accordingly, we regard skill in using these models in a variety of situations as an essential component of math and science literacy.

 

2. In the PHS 542 syllabus, at http://modeling.asu.edu/MNS/MNS.html.  I quote David Hestenes:

"These are the basic models at the foundations of the Modeling Instruction Program. This is shown explicitly in the syllabus for PHS 542, a course we developed to get physics and math teachers talking together about common essentials. These models are employed over and again in different contexts throughout the Modeling Program. Modeling pedagogy is designed to actively engage students in using the models to characterize physical phenomena quantitatively and evaluate the results."