What Can Linguistics Tell Us About Knowledge Structures in Physics? David Brookes. Rutgers University

Transcription

1 What Can Linguistics Tell Us About Knowledge Structures in Physics? David Brookes Rutgers University

2 Outline 1. Quantum Mechanics: Historical Analysis 2. Constructivism: A Theoretical Framework 3. Linguistics 4. Metaphors 5. Metaphors in Physics 6. A Model of a Conceptual System 7. The Conduit Metaphor 8. Implications for Teaching

3 Observation Experiment Model No Yes Testing Experiment Applications

4 Schrödinger [ Quantisation and Proper Values II Annalen der Physik (4) 79 (1926)] Hamilton s analogy between classical mechanics and geometrical optics (descriptive) Hamilton-Jacobi Eqn ( W ) 2 = 2m( E -V ) W - Hamilton s characteristic function Lines of constant W in configuration space p = W Particle trajectories perpendicular to const. W lines fi Eikonal Equation ( L) 2 = n 2 L - optical path length or phase of the wave Lines of constant L Rays of light.

5 Schrödinger A different perspective Schrödinger supposed that the analogy was exact in the following sense: Geometrical optics Classical mechanics Limit of Replace with Breaks down in similar manner to geometrical optics. Wave theory of light fi Wave theory of matter

6 Schrödinger Total phase Ê Á Ë L l -nt ˆ Proportional to S = W - Et fi n = E h, l particle = h p j = e 2pi Plug into Ê L Á Ë l -nt ˆ 2 j - 1 u 2 2 j t 2 = 0 Reduces in small l limit to: ( L) 2 = n 2 y = e 2pi h S Plug into h 2 8p 2 m 2 y -Vy = h Reduces in small h limit to: 2pi Ê H q k, S ˆ Á + S Ë q k t = 0 y t

7 Patterns in Schrödinger s Thinking Use of analogical modeling. Use of knowledge which is familiar to him. Small extensions of existing ideas. A case for an historical approach?

8 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 some point in history. QM inventors present a loose analogical model of students cognitive processes.

9 A model of student reasoning? Inventors of quantum mechanics Students learning quantum mechanics Base knowledge confusion Born argument Schrödinger Mental modeling Analogy M? misconceptions preconceptions confusion Students Primitive knowledge Language use explanations Base Target

10 Theoretical Framework for Analogy Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, b 2 b 3 b 1 b n R k b i M R k t 1 t 2 t m t 3 t j Base space (familiar) Target space (unfamiliar) 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)

11 Hypothetico-Deductive Reasoning Lawson, A. (2000). How do humans acquire knowledge? And what does that imply about the nature of knowledge? Science & Education IF THEN AND/BUT THEREFORE System B (base) is analogically related to system T (target) We predict something will happen in T based an analogous process in B It did happen/it did not happen This aspect of the analogy works (positive analogy)/the analogy breaks down at this point (negative analogy).

12 A model of student reasoning Inventors of quantum mechanics Students learning quantum mechanics Base knowledge confusion Born argument Schrödinger Mental modeling Analogy M? Primitive knowledge preconceptions confusion Students Language use explanations misconceptions Base Target

13 A model of student reasoning Positive Analogy Students struggling with classical notions. Generation of conceptual change. Notions about types of models which students will generate. Negative Analogy Experts reason productively from classical knowledge. Expert background strong, student background weak

14 Discussion QM Instruction Axiomatic knowledge Absolute truths Calculation strategies Emphasis on doing QM Terms like electron interference QM Invention Vague ideas, some misconceptions Extensive use of metaphor and analogy Scientific modeling emphasised Emphasis on understanding and interpreting QM Terms like: This apparently corresponds to diffraction

15 Conclusion What does an historical approach really mean in practice? Base space (familiar) Transition Build intermediate base space. Quantum Mechanics Target space (unfamiliar) Build up the base Find new base spaces

16 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 in it wave guides, resonating cavities, you name it Well, you want the student to have dived into all of that and learned the major aspects and techniques of things and be able to swim around in it so that when he is a professional physicist and something concerning Maxwell s equations or electrodynamics comes up, he is able to draw on that knowledge and go back to his textbook and be able to read those books because he has enough knowledge you want the students to have the same kind of virtuosity with Quantum Mechanics

17 Aims Education as transmission and internalization of knowledge Focus on the knowledge. How is it effectively conveyed? Testing focused on knowledge acquisition. 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 allows access.

18 Social Practice Model Observations Studies of traditional apprenticeship. Hake s paper. Model Learning is dependent on the environment. Focus on the effectiveness of the learning environment created rather than the effectiveness of instructors transmission techniques.

19 Social Practice Model Cognitive 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 learning environment.

20 C.A. vs L.P.P. C.A. Ground up approach Transparency of reasoning process Generate knowledge structures Need to understand expert reasoning process L.P.P. Top down approach Transparency of knowledge structures Centripetal access to knowledge structures Need to understand knowledge structures of physics

21 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?

22 Metaphor Black (1962), Models and Metaphors Substitution View: A metaphorical expression M may be replaced by a literal expression L which is equivalent in meaning. Example: The chairman ploughed through the discussion. Substitute: The chairman ruthlessly suppressed irrelevant arguments. Counterexample: Electron is a wave.

23 Metaphor Comparison View: Special case of substitution view - 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.

24 Metaphor Interaction View: Objects interact through metaphor. Metaphor creates similarity. It is a cultural creation, a reflection of what a society considers to be real. Analogy: metaphor is a filter or a light which projects out a silhouette or shadow.

25 What is a metaphor? Lakoff and Johnson, (1980): Metaphors we Live By Our conceptual system is fundamentally metaphorical in nature. The primary function of metaphor is to provide a partial understanding of one kind of experience in terms of another kind of experience.

26 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.

27 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.

28 A Model of Human Conceptual System 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 and metaphorically grounded conceptual system.

29 Metaphors in Physics Metaphors highlight certain aspects of behavior of a physical system. Heat is a fluid: We talk about heat flow. Electrons are waves: We talk about electron interference

30 Metaphors in Physics Metaphors highlight ways of visualizing abstract 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

31 Primitive Encoding disessa (1993) Toward an Epistemology of Physics. Cognition & Instruction 10 Students reason using phenomenological primitives. 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.

32 Towards a Model Bono: metaphors are constitutive of scientific thought. The imprecision of language is necessary for theoretical change and development. Metaphorical Language reflects Reflected in Metaphorical Language reflects Reflected in Metaphorical human Conceptual system fi Encoding of physics knowledge

33 A Model of the Structure of Expert 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/both 1. Experience - deep schemas, many connections. 2. Hypothetico-deductive reasoning.

34 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 ontological framework)

35 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?

36 The Conduit Metaphor Michael J. Reddy (1979), The Conduit Metaphor in Metaphor and Thought (Andrew Ortony, ed.) Words contain meanings/ideas and communication 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.

37 Toolmakers Paradigm

38 An allegory with two morals The language in which the model is encoded can confound the model and lead to confusion Teaching is about communication. Communication is not necessarily about sending meaning. It is about construction of meaning from the signals and this construction is culturally, socially and environmentally dependent.

39 Implications for Teaching Case for two approaches Cognitive apprenticeship: Build concepts from bottom up w/o confusing language. Take a top-down approach: Can students be made aware of the confusions which language cause? Gradually deepening peripheral participation in the linguistic structures of the experts.

40 Student Repertoire Traditional Approach Wave notions, classical notions Limitations of classical ideas Observations (eg: line spectra.) Schrodinger Equation Methods of solving Examples of solvable problems Teacher Communicates Traditional Applications Hydrogen atom Scattering

41 Construction of Meaning Student Repertoire Wave notions Classical notions Environment Limitations of classical ideas Observations (eg: line spectra.) Are these notions Sufficiently Developed? Teacher Communicates Schrodinger Equation Teacher Facilitates Feedback Multiple Reps: Students have Different ways of understanding Applications Transistors LED s QM teleportation Develop Methods of solving Classes of problems Own interpretation

42 Summary Social Practice Model Cognitive Apprenticeship Leg. Peripheral Participation Characterize expert Reasoning processes Characterize expert Knowledge structures Analogy Reflective Judgement New model of knowledge structures H-D Reasoning Participation? misconceptions