**David
Hestenes wrote these comments about basic particle models**

in
2011 to high school teachers:

*ÒI
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 KeplerÕs laws are identified as kinematics, which is explained
causally by the gravitational force.Ó****
* ---------------------------------------------------------------------------------------

Notes by
Jane Jackson:

David
Hestenes asks that teachers **introduce your students to his name of each
particle model**,
even though you start out with a different name. *You should eventually replace the Òbalanced force
particle model (BFPM)Ó with Òfree particle modelÓ.* *Likewise, the Òunbalanced force
particle model (UFPM)Ó should be replaced with Òconstant force particle
modelÓ. These names are standard
terminology, and your students should leave your course using accepted terminology, Dr. Hestenes
said.*

David
Hestenes has written that each basic particle model should be correlated with
the appropriate basic mathematical model. **His list of mathematical models** is in two documents on
the ASU modeling website.

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

__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 original PHS 542 syllabus, in 2001. 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."*

* *

David
HestenesÕ original PHS 542: Integrated Mathematics and Physics syllabus (2001)
states:

* *

*Course
content:*

*Abstract
mathematical concepts, such as variable, function and rate, are learned and
studied within the context of mathematical models with concrete applications to
physics and other subjects.*

*Statistical
concepts, such as mean and standard deviation, are learned and applied within
the context of matching models to data collected by students using calculators
and/or computers.*

* *

*Basic
models:*

*(1) Constant rate, linear
change*

* Graphs
and equations for straight lines*

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

* Graphs
and equations for parabolas*

* Accelerated
motion*

*(3) Rate proportional to
amount, doubling time*

* Exponential
function*

* Population
growth and radioactive decay*

*(4) Change in rate
proportional to amount *

* Trigonometric
functions and harmonic oscillations*

* *

*Other
models will be studied as extensions and/or elaborations of the basic models.*

*References:
A. A. Bartlett, Physics Teacher 34: 342 (1996), and many articles cited
therein. *

http://modeling.asu.edu/MNS/PHS542IntMath&Phy-2001DH.pdf
.

*
The slide that David Hestenes provided (at http://modeling.asu.edu/modeling-HS.html
, in pdf at http://modeling.asu.edu/modeling/Hestenes
BasicParticlModels.pdf ) is
the same as slide #22 in his slideshow at http://modeling.asu.edu (near the
bottom of the page) of his 2011 invited talk in Taiwan, called ÒRemodeling
Science EducationÓ. The URL to
download that slideshow is

http://modeling.asu.edu/Hestenes
RemodlngSciEd11.pdf

**
You can download David HestenesÕ publication, ÒModeling Games in the Newtonian
WorldÓ, at http://modeling.asu.edu/R&E/Research.html
.

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to Modeling Instruction in high school sciences webpage: