What Can Linguistics Tell UsAbout Knowledge Structures in

Physics?

David Brookes

Rutgers University

Outline1. Quantum Mechanics: Historical Analysis2. Constructivism: A Theoretical Framework3. Linguistics4. Metaphors5. Metaphors in Physics6. A Model of a Conceptual System7. The Conduit Metaphor8. Implications for Teaching

ObservationExperiment

Model

Testing Experiment

Applications

YesNo

Schrödinger

†

(—L)2 = n2

†

—W( )2= 2m E -V( )

L - optical path lengthor phase of the wave

W - Hamilton’s characteristic function

Lines of constant Win configuration space

Lines of constant L

†

fiParticle trajectories perpendicular to const.W lines

†

p = —W“Rays” of light.

Hamilton-Jacobi Eqn Eikonal Equation

Hamilton’s analogy between classical mechanics and geometrical optics (descriptive)

[“Quantisation and Proper Values II” Annalen der Physik (4) 79 (1926)]

…Schrödinger

• Schrödinger supposed that the analogy was “exact” in thefollowing sense:

A different perspective

Geometrical optics

Wave theory of light Wave theory of matter

Classical mechanics

Limit of Replacewith

Breaks down in similarmanner to geometricaloptics.

†

fi

…Schrödinger

†

j = e2pi L

l-nt

Ê

Ë Á

ˆ

¯ ˜

†

—2j -1u2

∂ 2j∂t2 = 0

†

(—L)2 = n2

†

S = W - Et

†

y = e2pih

S

†

Ll

-ntÊ

Ë Á

ˆ

¯ ˜ Proportional toTotal phase

†

fi n =Eh

, lparticle =hp

†

H qk,∂S∂qk

Ê

Ë Á

ˆ

¯ ˜ +

∂S∂t

= 0†

h2

8p 2m—2y -Vy =

h2pi

∂y∂t

Reduces in smalll limit to:

Reduces in smallh limit to:

Plug into Plug into

Patterns in Schrödinger’sThinking

• Use of analogical modeling.• Use of knowledge which is familiar to

him.• Small extensions of existing ideas.• A case for an “historical approach”?

Cognitive-historical Approach(Nancy Nersessian)

• “Continuum” hypothesis.• Physicists use of analogical reasoning

methods extensively.• Students generate models similar to the

models that physicists generated at somepoint in history.

• QM inventors present a looseanalogical model of students’cognitive processes.

A model of student reasoning?

Born

Analogy

confusion

argument

Base knowledge

Schrödinger

Mental modeling

misconceptions

explanationsLanguage use

Studentsconfusion

Inventorsof quantum mechanics

Students learningquantum mechanics

Base Target

M ? preconceptions

Primitive knowledge

Theoretical Framework forAnalogy

Gentner, D. (1983). Structure-mapping: A theoretical framework foranalogy. Cognitive Science, 7, 155-170.

b1

b2b3

bibn

t1t2

t3 tj

tm

• Not a “literal similarity”• Map objects so as to preserve the relational structure (Just like an isomorphism)• Systematicity Principle: (Map based on the deepest possible relations)

M

Base space (familiar) Target space (unfamiliar)

Rk Rk

Hypothetico-Deductive Reasoning

This aspect of the analogy works (positiveanalogy)/The analogy breaks down at this

point (negative analogy).THEREFORE

It did happen/It did not happenAND/BUT

We predict something will happen in Tbased an analogous process in BTHEN

System B (base) is analogically related tosystem T (target)IF

Lawson, A. (2000). How do humans acquire knowledge? And what does that imply about the nature of knowledge? Science & Education 9 577-598

A model of student reasoning

Born

Analogy

confusion

argument

Base knowledge

Schrödinger

Mental modeling

misconceptionsexplanations

Language use

Studentsconfusion

Inventorsof quantum mechanics

Students learningquantum mechanics

Base Target

M ? preconceptionsPrimitive knowledge

A model of student reasoningPositive Analogy

• Students struggling with classical notions.Generation of conceptual change.

• Notions about types of models whichstudents will generate.

Negative Analogy• Experts reason productively from classical

knowledge.• Expert background strong, student

background weak

Discussion

Terms like: “This apparentlycorresponds to diffraction”

Terms like “electroninterference”

Emphasis on “understanding”and interpreting QMEmphasis on “doing” QM

Scientific modelingemphasisedCalculation strategies

Extensive use of metaphor andanalogyAbsolute truths

Vague ideas, somemisconceptionsAxiomatic knowledge

QM InventionQM Instruction

Conclusion• What does an “historical” approach really

mean in practice?

Quantum Mechanics

Base space (familiar) Target space (unfamiliar)

• Build up the base• Find new base spaces

TransitionBuild intermediate

base space.

Theoretical Framework: Aims“…well, let’s compare it to electricity and magnetism which is

also a fairly technical subject that has quite a lot of math init…wave guides, resonating cavities, you name it…Well,you want the student to have dived into all of that andlearned the major aspects and techniques of things and beable to swim around in it so that when he is a professionalphysicist and something concerning Maxwell’s equationsor electrodynamics comes up, he is able to draw on thatknowledge and go back to his textbook…and be able toread those books because he has enough knowledge…youwant the students to have the same kind of virtuosity withQuantum Mechanics…”

…AimsEducation as transmission and internalization of

knowledge• Focus on the knowledge. How is it effectively

conveyed? Testing focused on knowledgeacquisition.

Learning as a dimension of social practice• Focus on how knowledge is acquired and used.• Aims focused nurturing expert though processes.• Student participation in and creation of knowledge

structures of physics - environment created allowsaccess.

Social Practice ModelObservations

• Studies of traditional apprenticeship.• Hake’s paper.

ModelLearning is dependent on the environment. Focus on

the effectiveness of the learning environmentcreated rather than the effectiveness of instructorstransmission techniques.

Social Practice ModelCognitive Apprenticeship• Learning physics in the way in which physicists do

physics.Legitimate Peripheral Participation• Participation in the knowledge structures of

physics.• Peripheral implies starting at the surface.• Decentralization of student/teacher roles, focus on

the structuring of learning resources and learningenvironment.

C.A. vs L.P.P.

Need to understand knowledgestructures of physics

Need to understand expertreasoning process

Centripetal access toknowledge structuresGenerate knowledge structures

Transparency of knowledgestructures

Transparency of reasoningprocess

Top down approachGround up approach

L.P.P.C.A.

Linguistics• What is the role of written and spoken language in

learning and thinking about Physics?• Vygotsky: Thought is mediated by language.• Sapir and Whorf:

– Language is not objective– Language reflects culture and experience rather than

objective reality

– How is language restricting/facilitating our thought

processes?

MetaphorBlack (1962), “Models and Metaphors”

• Substitution View: A metaphorical expression Mmay be replaced by a literal expression L which isequivalent in meaning.

• Example: “The chairman ploughed through thediscussion.”

• Substitute: “The chairman ruthlessly suppressedirrelevant arguments.”

• Counterexample: “Electron is a wave.”

Metaphor

• Comparison View: Special case of substitutionview - metaphor is a condensed simile.

• Example: “Richard is a lion.”• Substitute: “Richard is like a lion with respect to

cunning and courage.”• Counterexample: “Time is money”• Assumption of an objective reality on which

comparison can be based.

Metaphor

• Interaction View: Objects interact throughmetaphor. Metaphor creates similarity.

• It is a cultural creation, a reflection of what asociety considers to be real.

• Analogy: metaphor is a filter or a lightwhich projects out a silhouette or shadow.

What is a metaphor?Lakoff and Johnson, (1980): “Metaphors we Live By”

• Our conceptual system is fundamentallymetaphorical in nature.

• “The primary function of metaphor is toprovide a partial understanding of one kindof experience in terms of another kind ofexperience.”

Argument is War• Your claims are indefensible.• He attacked every weak point in my argument.• His criticisms were right on target.• I demolished his argument.• Who won that argument?• He shot down all my arguments.• Such a strategy will not help you win the

argument.

Time is Money• You are wasting my time• This technique will save you hours.• How do you spend your time these days?• That mistake cost me an hour.• Living on borrowed time.• You should use your time profitably.• I have invested a lot of time in this project.

A Model of Human ConceptualSystem

• Language is largely metaphorically structured.• Metaphors highlight aspects of meaning.• Metaphors are often rooted familiar/physical

experience and describe abstract concepts.• Metaphorical structure of language suggests

metaphorical thought processes andmetaphorically grounded conceptual system.

Metaphors in Physics

Metaphors highlight certain aspects ofbehavior of a physical system.

• Heat is a fluid:– We talk about “heat flow”.

• Electrons are waves:– We talk about “electron interference”

Metaphors in Physics

Metaphors highlight ways of visualizingabstract ideas and abstract systems.

• Atom is a solar system:– We talk about “electron orbitals”

• Bound systems are water wells:– We talk about “potential wells” and “energy

levels”

Primitive Encoding

• Students reason using phenomenologicalprimitives. Eg: Force as mover:– Objects always move in the direction of the applied

force.• Experts use primitive concepts as labels for

complex physics. (“Distributed encoding.”)• Example: “normal force”.

diSessa (1993) Toward an Epistemology of Physics. Cognition & Instruction 10

Towards a Model…• Bono: “metaphors are constitutive of

scientific thought.”• The imprecision of language is necessary for

theoretical change and development.

Metaphorical Language

Metaphorical humanConceptual system

Encoding of physics knowledge

Metaphorical Language

reflects Reflected in

†

fi

reflects Reflected in

A Model of the Structure ofExpert Knowledge in Physics?

Hypotheses• In physics, metaphors are surface encodings of deep

relational structures and prototype classes.• A metaphorical analysis of physicists’ language will

reveal their productive ways of thinking/modeling.• Experts are able to use this encoding effectively (use

productively/see limitations) through either/both1. Experience - deep schemas, many connections.2. Hypothetico-deductive reasoning.

Example: Newtonian Mechanics“Objects exert forces”, “What is the object’s

weight?”• Personification metaphor (object is actively

“exerting”)• Force is a commodity which is exchanged.• Container metaphor: force is a property

contained by the object.• Causal syntax imposed on a system which is

not always causal. (An ontologicalframework)

Example: Newtonian Mechanics

Predictions• Passive objects will not exert forces

(inanimate).• Weight is an invariant property of the

object.• Larger objects contain more force, exert

more force.• Are “misconceptions” caused by the

teachers?

The Conduit MetaphorMichael J. Reddy (1979), “The Conduit Metaphor” in “Metaphor and Thought”

(Andrew Ortony, ed.)

Words contain meanings/ideas andcommunication is the act of sending.

• I hope these ideas are coming across beautifully.• The ideas you seek are in the the book

“Metaphor and Thought”.• Look, the meaning is right there in the words.

Toolmakers Paradigm

An allegory with two morals• The language in which the model is

encoded can confound the model and leadto confusion

• Teaching is about communication.Communication is not necessarily aboutsending meaning. It is about constructionof meaning from the signals and thisconstruction is culturally, socially andenvironmentally dependent.

Implications for TeachingCase for two approaches

• Cognitive apprenticeship: Build conceptsfrom bottom up w/o confusing language.

• Take a top-down approach: Can studentsbe made aware of the confusions whichlanguage cause? Gradually deepeningperipheral participation in the linguisticstructures of the experts.

Traditional Approach

•Methods of solving•Examples of solvable problems

Student Repertoire•Wave notions, classical notions

Traditional Applications•Hydrogen atom•Scattering

SchrodingerEquation

•Limitations of classical ideas•Observations (eg: line spectra.)

TeacherCommunicates

Construction of Meaning

Develop•Methods of solving•Classes of problems•Own interpretation

Student Repertoire•Wave notions•Classical notions

Applications•Transistors•LED’s•QM teleportation

SchrodingerEquation

Multiple Reps:Students haveDifferent ways ofunderstanding

Environment•Limitations ofclassical ideas•Observations (eg:line spectra.)

Are these notionsSufficientlyDeveloped?

TeacherCommunicates

TeacherFacilitatesFeedback

Summary

Characterize expertReasoning processes

Analogy

Cognitive Apprenticeship Leg. Peripheral Participation

Characterize expertKnowledge structures

H-DReasoning

ReflectiveJudgement

Social Practice Model

New model ofknowledge structures

misconceptionsParticipation?