**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):*

*2. Constant
change in rate (quadratic change)*

*3. Rate
proportional to amount*

*4. Change
in rate proportional to amount*

*5. Sudden
change*

* *

*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."*