Effective use of models
in physics teaching and learning
Andy Buffler
UCT Physics
Bibliography
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construction of energy models in physics.” Instructional Science 24 259-293.
E. Etkina, A. Warren and M. Gentile (2006). “The role of models in physics
instruction.” The Physics Teacher 44 34-39.
I.M. Greca and M.A. Moreira (2000). “Mental models, conceptual models, and
modelling.” International Journal of Science Education 22 1-11.
I.M. Greca and M.A. Moreira (1997) “The kinds of mental representations-models,
propositions and images-used by college physics students regarding the
concept of field.” International Journal of Science Education 19 711-724.
A.G. Harrison and D.F Treagust (2000). “A typology of school science models,”
International Journal of Science Education 22 1011-1026.
D. Hestenes (1987). “Toward a modeling theory of physics instruction.” American
Journal of Physics 55 40-454.
I. Houlloun (1996). “Schematic modelling for meaningful learning of physics.” Journal
of Research in Science Teaching 33 1019-1041.
P. Johnson-Laird (1983). “Mental Models.” (Cambridge: Harvard University Press).
G. Possner (1982). ”Accommodation of a scientific conception: toward a theory of
conceptual change.” Science Education 66 211-227.
K. Raghavin and R. Glaser (1995). “Model-based Analysis and Reasoning in
Science: the MARS curriculum.” Science Education 79 37-61
Physics courses at UCT
First year courses for:
physics majors (PHY1004W)
other science majors (PHY1031F+PHY1032S)
engineers (PHY1010W)
health science students (PHY1025S)
GEPS (PHY1023H)
... 60 students
... 150 students
... 450 students
... 180 students
... 150 students
Second year:
physics majors (PHY2006H+PHY2013H)
... 25 students
Third year:
physics majors (PHY3021F+PHY3022S)
... 15 students
... 98% of our clients are with us for only one year.
… more than 1000 first year students pass
through us each year …
… what do we want them ...
... to “know” ?
… mechanics, properties of matter,
thermodynamics, waves, electricity
and magnetism, modern physics
… at an “international level”
(Halliday and Resnick) … ?
... to “do” ?
… solve problems, practical work,
use a computer, write … ?
… we think that physics is good for all scientists,
engineers, medics, …
… why?
… what are the features in our first year courses
that appear attractive / useful so that students want
to take our courses and other programmes include
physics in their curricula?
Our teaching and learning context has infinite
complexity (but with some useful generalities)
Our students (in 2007): …backgrounds (social, cultural, …)
…schooling …expectations …learning abilities …
Us (in 2007): …backgrounds (social, cultural, …)
…expectations …physics knowledge …teaching abilities …
The physical teaching environment (in 2007): …lecture
theatres … tutorial rooms …laboratories …digital teaching
UCT (in 2007): …expectations …structure …RFJ …workload
Cape Town / South Africa (in 2007): … local idiosyncrasies
The wider (physics) community (in 2007): …fewer physics
graduates? …physics departments closing?
…exciting “cutting-edge” physics …
The modern world (in 2007): …digital everything
…new technologies …overload of visual stimuli …uncertainty
Digital teaching / educational technology
Modern textbooks
…colour! …photographs!
… look (and learn?)
Digital slides (PowerPoint) …passive lectures
…printed copies
Animations / movies / simulations
…click and watch (and learn?)
Web pages …with…
…tutorial solutions
Computer-based assessment
…multiple choice
Easier (?) tutorials/weekly problem sets
… where “problem solving” = “pattern matching”
Recipe-based laboratories
…digital labs?
Are students still encouraged to think
in our introductory physics courses?
The main feature of physics that both defines physics a
discipline and is a useful life skill for student scientists /
engineers / medics is that…
… a small number of abstract ideas (principles and
theories) can be applied to a wide range of physical
applications, which allow description / explanation /
predication of natural phenomena.
… the “beauty” of physics …
… the nature of physics as a modelling enterprise
should be a defining theme in our introductory courses
…
…and … there is growing evidence that sense-making
in general can also viewed as a modelling exercise
… physics is the most suitable science discipline to
deal with the development of a number of important
scientific skills
What is a “model” ?
… a surrogate object, a representation
… a simplified version of a real object
… can be descriptive or explanatory
… has predictive power
… has limitations
… is subject to change
… many different types (proliferation of usage in the literature)
What is the relationship between
physics and nature ?
Three worlds or “spaces” are relevant:
• The real world of phenomena
• Physical theories
• Physical models
A few comments on the
Real world
• Concrete
• World of phenomena, observation, experience and technology
• Perception of the real world is not unique
… (personal experience)
The heart of physics is defined by the collection of
Physical theories
• External (shared)
• Produced by experts according to agreed rules
and “principles” (e.g. conservation laws)
• Abstract
… manifested in mathematical or linguistic form
• Acontextual
• Always can be expressed in terms of mathematical
models which constitute deductively articulated axiomatic
systems, and which express statements of the theory in
terms of equations
• By themselves are not descriptions of phenomena since
they lack a frame of reference (semantically blind)
… require interpretation through physical models …
Physics modelling (by experts) results in the production of
Physical models
… which mediate between theory and reality
• Are statements of the theory applied to a simplified and
idealized physical system or phenomenon
• Develop the potentiality of the theory
• Determine the way in which classes of physical
phenomena linked to particular theories should be
perceived.
• Constitute powerful heuristic pictures
• Allow visualization of explanatory principles of the theory
[Jammer, Greca & Moreira]
Physical theories
Abstract, acontextual, external.
Manifested in mathematical or linguistic form
particularization,
application
Physical models
Concrete, contextual, external
Manifested in many (conceptual) forms
idealization,
simplification
Real world
(Phenomena)
Concrete, experience, observation
visualization !
Physical models are manifested as
Conceptual models
• Didactical versions of a physical model
• Generated by experts, to explain, communicate or teach.
• External (shared)
• Precise and complete
• Consistent with accepted scientific knowledge
• Have predictive power
• May be mathematical, analogical or real (material artifact)
Linguistic
Mathematical
G
G µ0 I ∆ l × rˆ
∆B =
4π
r2
Numerical /
graphical
Scale models
Conceptual
models
Diagrammatic
(still or animated)
Simulations
... pictures ?
... movies ?
... demonstrations ?
... laboratories ?
• photographs
• movies
• demonstrations
Physical theories
Physical models
Real world
???
Physical theories
• mathematical
model
Physical models
comparison of applied
theory and modeled
data (measurands)
pdf
Real world
• experiment
(apparatus and
observation)
• data (numbers!)
Some comments on “visualization” …
Only physical models, not the underpinning physical
theories, can be visualized.
… not a pictorial relationship in which each element of
the model corresponds to an element in reality
[Dirac: “…the main purpose of science is not to provide
images…”]
Some physicists claim that they “see the physics of a
problem when it is expressed in equation form”
… (no dispute, but what is going on in your mind when
you think about the physics in terms of mathematical
models?)
(i)
(ii)
(iii)
Some comments on “representations” …
… any notion or sign or set of symbols which “re-presents –
both externally and internally – something to us in the
absence of that thing” [Eysenck and Keane]
Therefore a scientific theory is a representational system
... re-presenting externally (mainly in the form of
mathematical formulism) and internally (in the minds of
those who understand it)
… and so are all models …
… and so are all internal constructs in the mind.
(Think of “multi-representational” problem solving which has gained
recent prominence in the literature and textbooks.)
… what about how people make
sense of things (physics) ?
[mainly the realm of cognitive psychology]
Johnson-Laird (1983):
Three forms of mental (internal) representations:
Mental models
…structural analogues of situations or processes
Propositional representations
… strings of symbols linked to each other by a
particular syntax, whose truth depends on their
interpretation according to a mental model
Mental images
Visualizations of mental models from a given
perspective
Human beings understand the world by constructing
Mental models
… constructed through perception and interpretation,
or acts of imagination.
… analogical representations of reality
… dynamic and recursive (continuously enlarged and
improved as new information and experiences are
incorporated)
… the means through which we construct an
understanding of phenomena or act accordingly to
the resulting predictions
Propositional representations are be interpreted
through mental models, and in turn mental images
correspond to views of models.
Thus models, images and propositional
representations are functionally and structurally
distinguishable form one another.
For example:
“The cat is in the hat”
Propositional representation
... is undetermined :
The ... cat ... is ... in ... the ... hat
Mental model
... is required for specific meaning
Mental image
... contains detailed visual-spatial information
“Understanding” physics
“Understanding” a physical theory requires
construction of mental models that include
both the fundamental aspects of the theory
and the predictions that follow from working
with scientifically-appropriate physical
models.
Mental models in teaching and learning
Students bring to the classroom the working models that
they have constructed in order to understand the
physical world in which they live.
... these models may be culturally-induced,
school-induced, home-induced, etc … and may have
been carefully cultivated over many years.
Mental models which are not consistent with physical
theories may result from erroneous internal visualization
of physical models.
Mental models in teaching and learning
Students’ mental models may be largely analogical
… mainly qualitative understanding, using images,
manifested in drawings, hand movements, etc.
or largely propositional … mainly use of verbal
definitions and mathematical relationships.
… but knowing the right definitions and formulae does not
imply that the student has the appropriate mental models
in place.
Mental models in teaching and learning
… physical theories are often interpreted by
students by using mental models which they have
about the world which is not scientifically
accepted.
…result is that these scientific conceptions do not
result in a change in mental model, and are soon
discarded or forgotten.
Mental models in teaching and learning
Most physics textbooks (and courses?) present physics
theories as finished structures of knowledge, with the
mathematical models presented according to some logical
deductive criteria.
…and so physical theories are presented in courses in forms
which have been rationally deconstructed
… but it does not mean that reconstruction and
comprehension are achieved by the student with same logic.
… presenting a series of postulates and “inferring” the theory
from them, as if it were a branch of mathematics, does not
means that the phenomena explained by the theory will be
understood physically.
?
Mental
model
?
?
Mental
model
Mental
model
Conceptual
model
Modelling in physics teaching
These ideas suggest that it will be useful in teaching
and learning to facilitate processes for the
construction of scientifically appropriate mental
models.
Novices often do not have the necessary knowledge
of the domain to interpret as conceptual models
those presented to them, or to impose upon the
modelling process the necessary constraints, but do
have the basic tools to generate mental models …
Some broad consequences for teaching
Some practical suggestions for teaching
Open questions
Some broad consequences for teaching
1. Teaching should recognise that students already
have the basic tools to generate mental models,
make analogies, idealizations and abstractions, even
though to a great extent they are used tacitly.
2. The semantics of theories should precede the learning
of syntax (in happens in the case of a new language) …
... mathematization should not come first ...
… the “learning” of mathematical procedures in
themselves cannot guarantee that appropriate mental
models are retained.
Some broad consequences for teaching
3.
Because mental models are personal constructions,
a more effective path to meaningful learning in
physics would be related to the teaching and
learning of construction processes for these
representations – modelling – which might be more
important than teaching the conceptual models
themselves.
4. Teaching should start with presenting the
essence that defines physics as a modelling
enterprise ... that a small number of
fundamentals can be applied to a wide range of
physical systems
Some practical suggestions for teaching
1. Foreground physics as a modelling enterprise by
explicitly identifying where various elements under
discussion are located (theory, physical model,
phenomenon).
Physical theories
Physical models
Phenomena
Some practical suggestions for teaching
2. Identify to students different conceptual models as such.
3. Foreground the fact that everyone might have different
mental models … but the goal of (this course) is for
everyone to be able to construct mental models which
are scientifically appropriate.
Some practical suggestions for teaching
4. Be careful of setting tutorial “problems” that require little
more than pattern matching …
Ask students to identify the physics principles that are
important when making sense of a particular physical
model (e.g. when solving a problem) … tutors can be
asked to do this too in group tutorials.
5. Be alert for visual overload
… which movies, demonstrations,
simulations, etc. will aid building
good mental models?
... be critical of your own use
of visual elements and teaching aids.
Open research questions
Mental models are personal and constrained by
cognitive capabilities and perception biases … doubtful
that an establishment of a closed catalogue of initial
models is possible.
... but the observation of these personal mental models
poses interesting problems ...
…explore the heuristics of images and mental simulations
in the process of creation and comprehension of physical
theories … can the “tools” and “skills” of modelling be
identified and taught?
Open research questions
Work presently underway in this department:
In the context of the foundation physics course ...
... explore the variation in the ways that introductory physics
students interpret and visualize key conceptual models
... what are the tools and skills needed for the effective
interpretation and visualization of conceptual models?
... and should they be explicitly taught?
[Bashirah Ibrahim]
Open research questions
In the context of the
new PHY1004W course ...
... explore the variation in the mental models generated by
students in the process of producing their own (VPython)
simulations.
... develop and teach tools and skills to students in order for
them to use simulation more effectively in their own learning
of physics.
[Seshini Pillay]