Keynote 7
"Gaps" in Problem Solving. From theory to practice, from researchers to teachers:
A point of view
Zulma Gangoso
Faculty of Mathematic, Astronomy and Physics
National Cordoba University
Argentina
Abstract
In spite of many changes in conceptions of teaching and learning, problem solving
remains a core activity for teaching, learning and assessment of skills in physics at the
university level. However most of the assigned problems appear not to have been
designed to encourage the development of these skills. In some topics the presented
problems perhaps do not meet the explicit instructional objectives for promoting
deeper understanding of the subject.
It is useful to describe the context in which the studies presented were developed. The
"gap" between proposing tasks of solving problems such as modeling activity or as
routinary activity, often is explained supposing teaching physics and research in physics
as if different professionals coordinated them. On one hand, researchers in physics and
on the other hand physicists, perhaps with the same initial training as above, but who
have made teaching physics their main task. In this talk, studies developed in a
Department of Physics are presented. There, its members use most of their time doing
research in theoretical or experimental physics. In the Department there is also a
Physics Education Research Group composed of physicists too. The university that hosts
this department requires that all the full time teachers carry out teaching, research and
activities linking physics to the social environment. This fact would suggest that the
mentioned "gap" should not exist. Since their professional practice, researchers in
physics would be competent enough to teach problem solving as a modeling activity.
One of the difficulties of studying problem solving in specific disciplines has been the
complexity of the process brought into play and the lack of theoretical frameworks that
could account for it. A proposal was made to study the process of problem solving as an
understanding and modeling activity, which we call Physics Problem Understanding
Model (PPUM). From this perspective, the solution to a problem begins with the reading
of the statement resulting in a Situational Model. By changing ontological characteristics
this model evolves in a Conceptual Physical Model. Depending on the requirements of
the problem, the solver also builds a Formalized Physical Model of the situation. The
latter is expressed in abstract language and mathematical equations that enable to
quantify. From this theoretical proposal, certain indicators can be defined to assess the
modeling skills of problem solvers. An experimental study found that a measured of the
level of development of these skills correlated positively with the grades awarded to
student by teachers of the Department of Physics.
In part of this talk experimental studies using a sample of instructional material will be
presented and analyzed to distinguish between two hypotheses. On the one hand, on
topics of basic physics, the claim that academic problems do not bring all types of skills
into play is examined. There is a tendency to emphasize problems that are already
structured into a certain physics model, allowing the student just to use mathematical
expressions sometimes uncritically, to solve them. Furthermore, when restricted to
quantum physics, the assertion that these problems are not oriented to deeper
understanding but rather, to emphasize methodological aspects limited to mathematical
language.
In the second part of this talk, two studies of the problem-solving process itself will be
presented. Two types of experimental problems were developed using the proposed
‘Physics Problem Understanding Model’. A small group of experts solved those
experimental problems in an interview and some selected features of the process of
solution were studied. On one hand, it was found that expert subjects developed
different processes when faced with different statements to solve. Furthermore,
analyzing the type of inferences made by the subjects, evidence that could be crucial for
the development of problem solving skills appeared. The subjects seemed to "evoke" a
physical model, previously learned, to create a Conceptual Physical Model of the
situation stated in the problem. The Situational Model, created from reading the
statement, serves as proof of suitability of the physical model evoked, but is not by itself
a basis for direct construction of a Conceptual Physical Model. Some instructional
alternatives are discussed, as it is reasonable to ask how the former conceptual model
was built.
It is plausible to assume that the success of the construction of a rich model for the
problem depends on the flexibility with which the conceptual model was developed.
NOTE: The material of this presentation has been developed in a PhD thesis and by
undergraduate students supervised by the author.