Effective use of models in physics teaching and · PDF fileEffective use of models in physics teaching and learning Andy Buffler ... tutorial rooms ... “The cat is in the hat

Effective use of models in physics teaching and learning

Andy BufflerUCT Physics

Bibliography

R. Devi, A. Tiberghien, M. Baker and P. Brna (1996). “Modelling students’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) ... 60 studentsother science majors (PHY1031F+PHY1032S) ... 150 studentsengineers (PHY1010W) ... 450 studentshealth science students (PHY1025S) ... 180 studentsGEPS (PHY1023H) ... 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” ?

... to “do” ?

… mechanics, properties of matter, thermodynamics, waves, electricity and magnetism, modern physics … at an “international level”(Halliday and Resnick) … ?

… 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 teachingUCT (in 2007): …expectations …structure …RFJ …workload Cape Town / South Africa (in 2007): … local idiosyncrasiesThe 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 solutionsComputer-based assessment …multiple choiceEasier (?) tutorials/weekly problem sets

… where “problem solving” = “pattern matching”Recipe-based laboratories …digital labs?

Are students still encouraged to thinkin 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 enterpriseshould 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 theoriesAbstract, acontextual, external.

Manifested in mathematical or linguistic form

Physical modelsConcrete, contextual, external

Manifested in many (conceptual) forms

idealization,simplification

particularization,application

visualization !

Real world(Phenomena)

Concrete, experience, observation

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)

LinguisticMathematical Scale models

Conceptual models

... pictures ?

... movies ?

... demonstrations ?

... laboratories ?

Numerical /graphical

Diagrammatic(still or animated)

Simulations

02

ˆ 4

Ir

µπ

∆ ×∆ =

l rB

• photographs• movies• demonstrations

???

Real world

Physical theories

Physical models

• experiment (apparatus and observation)• data (numbers!)

• mathematical model

comparison of applied theory and modeled data (measurands)

pdf

Physical theories

Physical models

Real world

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

Propositional representations

Mental images

…structural analogues of situations or processes

… strings of symbols linked to each other by a particular syntax, whose truth depends on their interpretation according to a mental model

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 imagescorrespond 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

Mental model

Mental image

... is undetermined : The ... cat ... is ... in ... the ... hat

... is required for specific meaning

... 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.


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.


… 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.


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


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.


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


1. Foreground physics as a modelling enterprise by explicitly identifying where various elements under discussion are located (theory, physical model, phenomenon).

Phenomena

Physical theories

Physical models


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.


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?


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]


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]

Documents

Effective use of models in physics teaching and · PDF fileEffective use of models in physics teaching and learning Andy Buffler ... tutorial rooms ... “The cat is in the hat