Summary: Wells, et al.Summary of “A modeling method for high school physics instruction,”
Malcolm Wells, David Hestenes, and Gregg Swackhamer, pp. 162–175.OVERVIEW:This paper describes the creation, development, initial test-
ing, and preliminary dissemination of a physics instructional
approach that has come to be called Modeling Instruction.
The instructional design is centered on models, defi ned as
conceptual representations of physical systems and proc-
esses; these representations may be both mathematical and
non-mathematical. There is a particularly strong emphasis on
the use of qualitative reasoning aided by a diverse array of
representational tools such as motion graphs, motion maps,
force diagrams, etc. Such representational tools are consid-
ered essential for competent modeling and problem solving.
The modeling approach organizes the course content
around a small number of basic models, such as the “harmonic
oscillator” and the “particle subject to a constant force.”
These models describe basic patterns that appear ubiquitously
in physical phenomena. Students become familiar with the
structure and versatility of the models by employing them in
a variety of situations. This includes applications to explain or
predict physical phenomena as well as to design and interpret
experiments. Explicit emphasis on basic models focuses stu-
dent attention on the structure of scientifi c knowledge as the
basis for scientifi c understanding. Reduction of the essential
course content to a small number of models greatly reduces
the apparent complexity of the subject. In modeling instruc-
tion, physics problems are solved by creating a model or,
more often, by adapting a known and explicitly stated model
to the specifi cations of the problem.
Students begin each laboratory activity by specifying the
physical system being investigated, and then identify quan-
titatively measurable parameters that might be expected to
exhibit some cause/effect relationship, some under direct
control by the experimenters, others corresponding to the
effect. The central task is to develop a functional relation-
ship between the specifi ed variables. A brief class discussion
of the essential elements of the experimental design (which
parameters will be held constant and which will be varied)
is pursued, following which the class divides into teams of
two or three to devise and perform experiments of their own.
Computer tools are frequently employed for data acquisi-
tion and analysis. Students are guided in their activities and
discussion through Socratic questioning and remarks by the
instructor. For a post-lab presentation to the class, the instruc-
tor selects a group which is likely to raise signifi cant issues
for class discussion—often a group that has taken an inap-
propriate approach. At that time, the group will outline their
model and supporting argument for public comment and dis-
cussion by the other students.
Modeling instruction is strongly guided by research on stu-
dents’ ideas and misconceptions in physics. These research
fi ndings are used for course planning, both to improve
the coherence of the overall course structure and to ensure
that class activities provide repeated opportunities for stu-
dents to confront all serious misconceptions associated with
each major topic. Specifi c misconceptions are targeted and
addressed in connection with each activity in a way that fl ows
naturally from the manner in which the activities themselvesare structured. In both problem-solving and laboratory activi-
ties, students are required to articulate their plans and assump-
tions, explain their procedures, and justify their conclusions.
The modeling method requires students to present and defend
an explicit model as justifi cation for their conclusions in every
case; verbal, mathematical, and graphical representations are
all employed in this analysis. As students are led to articulate
their reasoning in the course of solving a problem or analyz-
ing an experiment, their naïve beliefs about the physical world
surface naturally. Rather than dismiss these beliefs as incor-
rect, instructors encourage students to elaborate them and
evaluate their relevance to the issue at hand in collaborative
discourse with other students. In pursuit of this goal, substan-
tial amounts of class time are allotted to oral presentations by
students, including “postmortems” in which students analyze
and consolidate what they have learned from the laboratory
activities. In these presentations student groups outline their
models and their supporting arguments for joint examination
and public discussion.
This paper outlines how initial testing of the effectiveness
of the modeling instruction methods was done in high-school
classes by author Wells and in college classes by a collabo-
rator of the authors. Wells’s students increased their scores
on research-based mechanics diagnostic tests by about 35%
in comparison to their pre-instruction scores. This is far
higher than the 13-21% observed in comparable high-school
classes taught with traditional methods by other instructors,
and higher even than Wells’s own students in classes he had
previously taught using other methods. Similarly, students in
the college classes taught with the modeling methods showed
pre- to post-instruction improvements of about 25%, well
above the 11% observed in comparable classes taught with
traditional methods.
To develop a practical means for training teachers in the
modeling method, a series of NSF-supported summer work-
shops for in-service teachers was designed and conducted. The
fi rst fi ve-week summer workshop was held in 1990, followed
by similar workshops in 1991 and 1992 which incorporated
increasing amounts of teacher-developed written curriculum
materials and greater focus on the pedagogical methods. After
the fi rst year, scores on the “Force Concept Inventory” diag-
nostic test by the students of the participating teachers were
greater than they had been before the workshop, but only by
4%. After the improvements incorporated in the second year,
these gains had risen substantially to 22%.
During more than two decades following the initial activi-
ties reported in this paper, several thousand high-school phys-
ics teachers throughout the U.S. have participated in Modeling
Instruction workshops. Data refl ecting learning gains by these
teachers’ students have been very consistent with the initial
observations reported in this paper. Further details and docu-
mentation are available on the Modeling Instruction website
at http://modeling.asu.edu.HISTORICAL NOTE, BY DAVID HESTENES:This paper serves as a published account of Malcolm Wells’
1987 doctoral thesis. Since I regard that work as the mostAPS-AJP-11-1001-Book.indb 28APS-AJP-11-1001-Book.indb 28 27/12/11 2:56 PM27/12/11 2:56 PM