**Introduction:**

David Hestenes' modeling approach to
physics
instruction^{1-3} has become a well-implemented
and highly
effective teaching methodology that is used by several
hundred teachers
trained in modeling. The original modeling papers
provide great detail and
theoretical background about modeling
instruction. This article addresses
practical issues of implementation
and describes the modeling approach from
a modeling teacher's
point of view.

**Why use modeling instruction?**

The need for physics teaching reform
is well summarized by
Lillian McDermott. "Teaching by telling
is an ineffective mode of
instruction for most students. Students
must be intellectually active to
develop a functional understanding."
"A coherent conceptual
framework is not typically an outcome
of traditional instruction. Students
need to participate in the
process of constructing qualitative models that
can help them
understand relationships and differences among
concepts.^{4}"
Numerous studies^{5} (in addition to
observation and experience^{6})
support Dr. McDermott’s
statement. "Results of lecture
and demonstration type instruction are
uniformly poor for all
teachers . . . independent of the teacher's
experience and academic
background.^{2}" The reason for this
failure is that
"most students systematically misinterpret what they
hear
and read in traditional introductory
physics.^{3}"

One tool
that has been used extensively
to evaluate instructional effectiveness is
the Force Concept Inventory
(FCI)^{7}. Dr. Richard Hake's studies
of Force Concept
Inventory scores of over 6000 students^{8}
confirmed that
in a lecture-demonstration classroom environment, the skill
of
the instructor does not affect the amount that the students
learn.
Typical normalized FCI gains are .24. However, Hake found
that
various methods of interactive engagement resulted in
typical
normalized FCI gains of .48. Modeling teachers achieved the
higher
gains in Hake’s study and experienced modeling teachers
have
produced even higher gains, demonstrating that within
interactive
engagement instructional modes, the skill of the instructor
does
make a difference.

Effective
instruction requires a variety
of interactive engagement tools such as
Socratic dialogue, individualized
instruction, multiple representations of
phenomena, kinesthetic
experiences, cooperative learning and emphasis on
coherency of
concepts^{9}. Numerous research-informed curricular
materials^{10}
that employ interactive engagement methods are
available; they
are typically lab and workbook based. Students are required
to
make predictions, elucidate misconceptions, observe phenomena
and
reconcile their understanding with what they observe while
following the
curriculum's carefully structured concept development.
Although
research-informed curricular materials are excellent,
they do not teach
themselves, and more importantly, most of them
are necessarily aimed at a
specific audience, making them rather
inflexible.

In contrast, Modeling Instruction is
a curriculum
__design__, rather than a fixed curriculum. Modeling
provides teachers
with an overall instructional methodology that
enables effective
utilization of physics education research and
curricular reform, which
ultimately helps students to learn more
effectively. Within a
"modeling mindset" the instructor
can flexibly adapt the
conceptual development strategies from
research-informed curriculum to best
suit their own course level
and student ability.

**What is modeling?**

The way we make sense of the world is to construct mental models to organize natural phenomena. A model is a primary unit of coherently structured knowledge. For example, as physics teachers we want our students to understand the effect of a constant force on a particle. However, when we teach traditionally, we seldom explicitly structure our curriculum and class activities to guide students through the construction of a constant force model. Instead, we teach a long list of topics like force diagrams, force vectors, Newton’s second law, gravitation and friction. Although the coherence of these topics is clear to us, students see a fragmented picture of disconnected ideas.

In Modeling, on the other hand, instruction is organized around a storyline of concept flow specifically designed to develop a model. A variety of representations of natural phenomena are used, and connections between conceptual representations and the physical model are explicitly developed.

**How does the modeling
approach affect
the classroom?**

Modeling instruction is based on the modeling cycle, which is a refinement of the learning cycle. Development of a model begins with a paradigm lab in which students define the system and develop verbal, diagrammatical, graphical, and mathematical representations for the phenomenon being studied. For example, pendulum motion could serve as the paradigm lab for the simple harmonic oscillator model. Students would identify the relevant system as the earth and pendulum, describe the motion in words, create diagrams to represent the motion, identify variables in order to collect data and produce a graphical representation and finally describe the graph mathematically.

Students further develop the model through worksheets, readings and additional labs. At each step of the process, extensive "post-mortem" analysis is conducted. Working in collaborative teams, students write their lab results or homework solutions on 24" x 32" dry-erase whiteboards and explain their solutions to the class, subject to Socratic questioning.

The teacher-student and student-student discourse around the whiteboards is the most critical aspect of modeling instruction, and the quality of this discourse is what ultimately determines instructional success. The questioning strives to reinforce key ideas and definitions; confront misconceptions; and provide students with opportunities to elucidate the model, extend the model to new situations, applications and contexts, and establish connections among the verbal, diagrammatical, graphical, and mathematical representations of phenomena.

The students’ model is then tested. Lab practica require the model to be put into practice, and written and oral tests emphasize problem solving through application of the model.

**How is modeling instruction
different
from curricular reforms?**

Modeling is not a curriculum. Modeling is an approach to teaching in which a small number of key models of physics are explicitly developed. Modeling can flexibly utilize a variety of curricula that the instructor finds conducive to developing the models.

Although modeling is not a curriculum, example models and supporting materials have been prepared to provide teachers with working examples while learning the modeling approach. These materials (which are available at the modeling project website: http://www.modeling.la.asu.edu) have a rather traditional appearance, but remember that these materials merely form the starting point for the rich classroom discourse in which learning really occurs.

**What are the advantages of
modeling?**

Trying a new teaching approach for the first time is a bit nerve-wracking. However, even in my first year of modeling I found the approach highly successful and satisfying, as did my students.

My students developed a better grasp for the physics content and were better able to apply it. Their Force Concept Inventory scores partially quantify that statement. Before I began Modeling, my students’ FCI posttest mean score was 53%. Using modeling, my regular physics students’ posttest score averaged 65% with a normalized gain of .56, which is quite good according to Hake’s study. (Experienced modelers have even higher average gains.) Additionally, students learned Socratic questioning by my example and got used to asking productive questions of their peers and of themselves, helping them to become self-directed learners. Knowing they had to present ideas to their peers, they also became very involved in presentations made by their classmates to make sure they understood what was going on.

My students liked the classroom interaction and recognized why it helped them learn. One student said, "I thought [the whiteboards] were worthwhile because they forced you to understand the answers you got rather than just following examples. They helped me tie things together (which I think is really important) with all the questions [the teacher] asked. You don’t really understand something until you can explain it, and the whiteboards gave us the opportunity to do this." As a result, I got to know my students far better. I write many reports and letters of recommendation for my students, and the active role of the students in modeling made me intimately aware of each student’s strengths and weaknesses.

Modeling fills a need for high school physics teachers since the research-informed workbook curricula are designed for particular audiences, often not fitting the many-varied contexts of high school. However, my experience with modeling has helped me to better analyze, adapt and use the concept flow from various research-informed curricula.

Modeling also helped me to better define and become aware of the models I use in physics. Models are quite different from textbook unit titles, and seeing physics in terms of explicit models was a fascinating discovery for me.

Other modeling teachers have many of the same positive responses to modeling that I did. What I find striking is the success of modeling with junior high physical science courses, regular, honors and AP high-school courses and university courses, all taught in very different situations to very different students by very different teachers. This demonstrates that the successes of modeling are portable to teachers who learn and implement modeling instruction.

**What
training is needed to use modeling
instruction?**

If there's a drawback to modeling, it's that modeling takes a significant amount of time to learn to do well. I participated in the modeling workshops, requiring a month of training in each of two consecutive summers. I also had prior experience with microcomputer-based labs and a number of excellent research-informed physics curricula, which I found instrumental in my smooth transition to modeling instruction.

Getting involved in a modeling workshop is essential to learning modeling. In the workshop environment, teachers become students and the workshop leaders teach the models just as they do with their own students. In this environment you get a feel for leading paradigm labs, the modeling cycle, whiteboarding, questioning strategies, lab practica and the structure of the example models. At the same time, you have the opportunity to use microcomputer-based lab equipment and learn how to use it effectively in your class. Homework for the course includes readings to better understand student difficulties and misconceptions in various areas of physics.

The second summer of the modeling workshops focuses on identifying and developing models for "second semester" physics topics. This exercise helps teachers get to the heart of modeling theory. Understanding the structure and essence of models enables teachers to revise or build models carefully tailored to their own classes. As part of the process, teachers study exemplary curricula with an eye for concept flow and the kinds of questions and activities used.

Over the past five years, 200 teachers nationwide have participated in Leadership Modeling Workshops. A goal of the modeling project is for these teachers to lead workshops through partnerships with local universities. To bring a modeling workshop to your area, begin a conversation between local university and high school physics teachers to establish a group of interested persons. Also, contact the modeling project director for information on logistics, funding and workshop leaders.

For more information about modeling, browse the modeling project web page http://modeling.la.asu.edu