MIRIAM REINER
A LEARNING ENVIRONMENT FOR MENTAL VISUALIZATION IN ELECTROMAGNETISM?
1. INTRODUCTION Much of the research in physics learning is based on verbal or verbalizable processes. For instance, research on alternative frameworks, problem solving and conceptualization are all concerned with verbal processes. However, physics learning involves more than verbal processes. In analyzing expert problem solving, Clement (1988) identified observable behaviors that could be defined as “references to intuition, references to imagery, depictive hand motion, and imagistic predictions . . .’. He suggests that knowledge embodied in perceptual motor intuitions can play a powerful role in expert thought. At least two other resources are, then, involved in physics learning: knowledge stored in the body, due to years of muscular learning as in playing tennis or riding a bicycle, and knowledge achieved through imagery thought processes. These types of knowledge, are of a non-propositional nature, in the sense that they have no easily articulated syntax and semantics. This paper concentrates on the second type – the role of imagery in physics learning. Many conceptual innovations in physics originate in imagery reasoning (Nersessian, 1995; Miller, 1986; Shepard, 1978; Wertheimer, 1959). For instance Einstein claimed to construct his insights on the relativity of simultaneity (a major principle in the special theory of relativity) by means of thought experiments (Einstein, 1960). These thought experiments were based on a mentally visualized system consisting of idealized objects, imagined entities such as light waves, measuring devices (e.g. clocks), and events that happen in an imagined world. Similarly, Galileo’s thought experiment on falling bodies of different weights (Galileo Galilei, Stillman trans., 1974) Kekule’s vision of the benzene molecule and Faraday’s analysis of imagined material field lines, are all based on imagery reasoning. ? I would like to thank an anonymous reviewer for his many insightful comments. Many
thanks to Menahem Finegold too, for many helpful comments.
International Journal of Computers for Mathematical Learning 2: 125–154, 1997. c 1997 Kluwer Academic Publishers. Printed in the Netherlands.
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The usefulness of imagery reasoning in physics, is further supported by the existence of a set of visual symbols used to support communication in physics. The left and right hand rule relating the direction of force, magnetic field and current, Feynman’s diagrams, representations of particle collisions, of equilibrium states, or of light as rays, are all pictorial, dynamical representations, part of the culture of communication within the science community. Though learning has recently been viewed as enculturation, a process of progressive familiarization with the culture of the scientist (Lave, 1988; Lave and Wenger, 1991; Brown, Collins and Duguid, 1989), imagery has hardly been employed in physics teaching. Simulations are introduced, and examined as tools for learning, (diSessa, 1995; Reiner, 1995), but not much is known about their role in generating images in physics. How students generate images and employ them in communicating about physics, is the main focus of this study. The hypothesis tested in this study is that features of the learning environment have an impact on collaborative processes of problem solving in physics. In particular, we test the hypothesis that a graphical-dynamical learning environment supports the generation of mental imagery, which is then employed in the design of hands-on solutions to physics problems. A second hypothesis tested is that imagery representations are employed in communicating about problem solving, turning personal-mental images into social constructs. The study evolves in three stages: a. analysis of a case study of three students discussing a problem. This analysis identifies evolving patterns of use of mental imagery and verbal representations in different types of learning environments, and offers readers an insight into the nature of such discussions. b. analysis of fifteen groups collaboratively designing a solution to a problem, in an attempt to test and modify the pattern of use of imagery identified in the case study. c. identification of relations between the pattern of imagery and the nature of solution offered by the participating students. Results of this study show that the features of a learning environment have a major impact on students’ problem solving processes. Students who collaboratively interacted with an animation and hands-on lab, end up developing an insight into the microscopic causality of the physics involved, by imagining the moving particles and induced force-lines as part of the visible system. Students discuss and ‘see’ more than the physical objects. They develop a qualitative view of the underlying events, based on imagery, thus turning the physical set-up from a black box into a glass box. They communicate through images, shared by the collaborative
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team, but not necessarily by outsiders. These images are often reflections of computer-based dynamic representations, sometimes reflections of lab set-ups, or reflections of learning situations. Mental images are treated similarly to physical object; they are ‘visible’, are rotated, manipulated in space, and shared by the collaborating team. We conclude with a suggestion that students form and create associations between two representational schemes: the imagery constructs and the hands-on, physically perceived objects. We speculate that these mental links provide students with insight into the phenomena necessary for a solution design. Solutions based on imagery are thus related to microscopic deep structure processes, rather than to surface features and observables of the physical system. We further suggest that in the absence of links made across representational schemes, conceptual meaning is fragmental, local, limited within each scheme only. 2. MENTAL IMAGERY AND LEARNING Research on imagery suggest that mental images are manipulated in ways similar to visual perception. An imagined object in space changes in a linear manner with the extent of spatial transformation (Block, 1992; Shepard, 1978, 1994). Metzler and Shepard (1971) claim that people rotate mental images at measurable speeds, that these speeds may be constant, that mental images being rotated can be ‘caught’ precisely at a particular angle, that these can be scanned, stored and retrieved in parts or whole (Kosslyn, 1995), that they can be enlarged causing the imaginary picture to overflow, and that the mind’s eye ‘sees’ a picture overflowing at a particular angle. These images are not mere inner representations, but can interfere with concurrent visual tasks (Kaufman, 1979; Craver-Lemely and Reeves, 1992), affecting the manner of operation and learning. The cognitive similarity between mental imagery and perception of physical objects, is supported by physiological research as well. Positron emission tomography (Roland and Eriksson, 1987), event related potentials (Farah, Peronnet, Gonon and Giard, 1988) and regional cerebral blood flow imaging (Goldenberg, Podreka, Steiner and Willmes, 1987), have implicated common processing sites and similar potential patterns for both imagined and real visual objects. Indeed, self-reflections reported by physicists suggest a mode of visual-mental experimentation that, though of a similar nature, was not carried out in a physics laboratory, but occurred as thought processes (Brown, 1991; Gribbin, 1988; Sorenson, 1992; for an extensive review, see Shepard, 1978; Beiser, 1960; Miller, 1986). What then are the features of mental visualization, and what claims have been made for it? Typically, mental visualization is a cognitive strategy,
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classified as a type of elaboration used by learners to construct meaning that can constrain and guide the individual’s intuitive reasoning (Comstock, 1927; Johnson-Laird, 1983; Mayer, Bove, Bryman, Mars and Tapaganco, 1986; Hodes, 1992; Schwartz and Black, 1996). For instance, students who visualize current as a flow of juice, think of batteries as a pool of juice consumed by bulbs and other electrical equipment (Shipstone, 1984, 1985; McDermott, 1985). Differently stated, “visualization is the word that describes the process of forming mental images depicting a content of a production” (Connelly, 1993). Mental images are individual, conceptual interpretations of symbols, constructed through interaction with external stimuli, part of a personal world model (Finke, Pinker and Farah, 1989). Compared to verbal memory, visual memory is superior when recalling (Bagget, 1989; Mayer and Anderson, 1992). Images shown to the learners and perceived by them as congruent with a learning situation, are assimilated into the learning process (Segal, 1972). The original mental image is changed according to features of the situation. Hence the construction of images is not a passive revivification of past experience, but an enlivening of the situation, including sensory data, students’ ideas and habits of reasoning. 2.1. Imagery – A Mental Animation Employed in Problem Solving Imagery is explored in this study through problem solving. Imagery is common in problem solving and has been studied much in that context (Comstock, 1927; Kaufmann, 1979; Forbus, Nielsen and Faltings, 1990; Hagerty, 1992, 1993; Schwartz and Black, 1996; Rumelhart, 1995). Hagerty (1992) for instance, examined the subgoals people constructed in understanding pulley systems. She found that her subjects used a type of inferring-prediction system to describe the behavior of pulleys, which favored the forward, rather than the backward, flow of events. Hagerty suggested that these inferences are based on spatial imagery processes that imitate the mechanical event, which she termed “mental animation”. Ferguson (1992) in his review of the development of engineering, claims that many technological inventions are based on mental animation. For example, Evans, the inventor of the automatic flour mill, claimed to have completed an “arrangement” in his mind before he began to build it in physical detail: “I have in my bed viewed the whole operation with much mental anxiety”. Nasmyth, a nineteenth-century English engineer, said that the machine “was in my mind’s eye long before I saw it in action.” He explained that he could build mechanical structures in the mind and set them to work in imagination, observing beforehand the various details performing the respective function, as if they were in absolute material form
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and action. Similarly, the founder of Chrysler Corporation (the automobile company) claimed that he built his first machine without any drawing, by following a model that existed in his mind “so real, so complete that it seemed to have three dimensions” (Ferguson, 1992, pp. 48, 50). Strategies for thinking with images were studied by Schwartz and Black (1996). They explored how students manipulate a two-wheel gear system. Their subjects appeared to coordinate their gear images by predetermining the appropriate angular velocities. They suggest that people can think about physical events by manipulating analog visual mental models of the world. According to Schwartz and Black (1996 p. 207) “lack of visual information that can constrain and guide the individual’s intuitive reasoning” may act as an obstacle in physics problem solving. For example, novices tend to approach a problem according to its most salient surface features (Chi, Feltovich and Glaser, 1981) and jump to analytic solutions without considering the underlying forces (Larkin, MacDermott, Simon and Simon, 1980). One attempt to explain the role of imagery in problem solving is the “dual code theory” (Paivio, 1971, 1986; Clark and Paivio, 1991). Paivio argues that information is processed through two distinct, yet linked memory systems, verbal and imagery systems. Though not clarifying the exact nature of imagery, or of the related memory systems, he suggests that the two act in parallel, can be accessed independently, and interact extensively and continuously in any learning situation (Paivio, 1971, 1986; Clark and Paivio, 1991; Hodes, 1992). The study reported here suggests that students relate two schemes, not verbal with imagery, but the physically perceived objects with imagery constructs. 3. UNDERSTANDING ELECTROMAGNETISM AND IMAGERY Understanding electromagnetism involves imagery (Shepard, 1990; Maxwell, 1873; Miller, 1986; Wertheimer, 1959) and the use of pictorial symbols such as arrows, geometrical patterns and three dimensional finger positioning that describe conceptual relations. Lines of force, for instance, are not physical entities in space. These are mental images of a particular shape in space, that describe the intensity of the field in terms of the density of lines. Faraday, an experimentalist with no formal mathematical training invented the concept of lines of force, a central concept in understanding fields (Maxwell, 1873). Faraday’s lines behave as if they have definite physical properties. In his attempts to understand electromagnetic induction, he thought about the field as if iron filings occur near magnetic poles. Though part of a whole system, each
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individual line has a continuous existence in space and time. When a piece of steel becomes a magnet, or when electric current begins to flow, the lines of force do not suddenly appear each in its own place, but as the intensity increases, new lines develop within the magnet (or conducting wire) and gradually grow outwards. The whole system expands dynamically from within. From the conception of geometrical lines of force, Faraday moved to physical lines of force. These lines behave as though under tension, and exert a transverse repulsion on one another. The tendency of the lines of magnetic force to spread out laterally and to shorten themselves is explained by visualizing the system of rotating lines. The centrifugal forces change the shape of the lines of force, as if they were actual curved rods. According to Maxwell, “by means of this new symbolism, Faraday defined with mathematical precision the whole theory of electromagnetism, in language free of mathematical technicalities and applicable to the most complicated as well as simple cases” (Maxwell, 1873, p. 112). Maxwell, following the same line of thought, conducted a series of thought experiments in which he visualized an infinite array of cylinders whose direction of rotation represented magnetic force, and intervening ball bearings, whose correlated motion at right angles represented electrical force (Shepard, 1995). The cylinders and balls are imagined immersed in a flexible, non conducting material called ether, that can transfer mechanical disturbances. Moving one of the cylinders or one of the balls creates a disturbance in the flexible medium that generates a force pushing the cylinder back into its original position through a series of vibrations. This is similar to moving an object connected to many springs. The cylinder will vibrate until finally settling back into its original position. Maxwell saw the propagation of disturbances in the ether, in the form of two perpendicular fields, electrical and magnetic, that induce each other. The velocity of propagation is that of light. Mathematical modeling and empirical observations, despite their importance, do not convey the meaning hidden in a mental animation similar to the one just described. We hypothesize that the mental animation is tested and continuously refined against hands-on experimentation and mathematical models. Based on historical processes of understanding electromagnetic fields, we assume that understanding electromagnetic fields involves generating imagery, verbal, laboratory and mathematical representations, and linking them together.
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4. PURPOSE OF THE STUDY Given the possibility that meanings of concepts in electromagnetism are at least partly determined by images as conceptual entities, we have designed a learning environment that provides an opportunity to study the evolution of imagistic representations of phenomena related to transmission and reception of electro-magnetic fields, in a collaborative setting. We look at: – the role of imagistic representations in collaborative problem solving – the nature of mental image interference with concurrent tasks – links between perceived physical objects, and imagined objects. This requires examination of conversations among the participants, in order to find out: – How are images communicated, and how do they evolve into social constructs? – What are the relations between the images communicated and the images represented by the animation? – How is are meanings of images and words constructed socially? 5. THE LEARNING EXPERIMENT The learning experiment took place in a university physics lab. Thirty-two 16–17 year old students were enrolled in an extensive problem-solving activity on electromagnetism. The activity consisted of eight meetings, each of two and a half hours, twice a week. The students worked together in teams of two or three on each assignment. An observer collected data on students’ activities. Verbal interaction was recorded. Six progressive problem-solving tasks were introduced. Only two of these are discussed here. Each group was asked to collaboratively design a situation that may count as a solution. Each problem dealt with designing a physical, hands-on situation in which reception of electromagnetic radiation is strongest. The problem-situations are based on a computer learning environment and a physical lab set-up, provided for design. The tasks and components of the learning environment are described below. 5.1. The Tasks Task A: Quality of reception and relative direction of transmitter and receiver. To broadcast, one basically needs a transmitter and a detector (receiver) of electromagnetic fields. The receiver is sometimes affected by winds and so its direction may change. As a result, the quality of reception
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Figure 1. Laboratory set-up for Task A – Relative direction of transmitter and receiver for best reception
changes. The kit that was provided included a transmitter and receiver of electromagnetic fields in the range of microwaves (wavelength of about 2 cm). Reception is best when the transmitter and receiver are parallel. Students were asked to design a situation to improve the reception, if the relative direction between the transmitter and receiver changes. Task B: Quality of reception and reflecting materials. Broadcasting in a particulr area is sometimes influenced by accidental reflection by materials present in the environment, similar to the situation described in Figure 2. Students were asked to find out which materials affect quality of reception and design a situation to improve reception. 5.2. Components of the Learning Environment Following views of situated learning, students were provided with two types of media to construct, represent and question their ideas: computer animation of electromagnetic phenomena, and relevant hands-on equipment. The software (animator) allows the construction of two major situations: 1. One or two antennas (wires) are constructed on the screen, a grid of parallel wires is positioned in the space between the transmitter and receiver. The antenna can be activated. If it is, two sine functions describing the electrical and magnetic fields appear on the screen, drawn in red and green, respectively. The two representations are dynamic, and are drawn on seemingly perpendicular planes. Objects such as a grid of parallel wires can be positioned on the screen in various places. The functions describing the fields are affected by the
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Figure 2. Laboratory set-up for Task B – Direction broadcasting according to materials that reflect electromagnetic fields
presence of the grid (or another antenna), depending on the angle of the grid relative to the antenna. If parallel, the field is absorbed in the wires of the grid and there is no output signal from the grid. The grid can be rotated. The transmitted output signal, observed on the screen, decreases as the relative angle between the antenna and the grid increases. An infinite number of situations which consist of the above constructs may be designed on the screen. 2. An animation of interference and diffraction of the electromagnetic waves is presented. This is similar to patterns occurring in water tanks with one and two wave generators. The participating students spontaneously used the first situation only. The components of the hands-on system are a transmitter, a receiver (each with a built-in device to measure induced current), a metal plate, a metal grid, and various metal plates with adjustable slits. These are meant to provide students with the opportunity to construct the actual hands-on situations described in each of the tasks. 5.3. The Subjects All the thirty-two participating students were enrolled in the eleventh grade of a prestigious technological high school in a special class that took
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electrical engineering as a focal discipline. Twenty five were boys. They spent ten hours per week in an electronics laboratory, and five hours per week on theoretical aspects of electronics. Though it may seem inconsistent with their special program, students had only a limited course in physics of three hours per week, without any lab activities. Based on discussion and interviews it seemed as if the school had decided not to invest too many hours in physics courses. Based on analysis of students’ curricular materials and interviews with the teacher, we found that physics was integrated in the electronic courses on a technical level only, which was mainly focused on acquaintance with a set of equations, without any deep understanding of causal relations and models. The participating students separated into fifteen teams of two or three each. Eight teams spontaneously began their work with the first task, seven with the second. Some teams chose to work with both hands-on and visual representations. Some chose to work with the hands-on only. This enabled us to identify patterns of use of imagistic information for each problem, by comparing students who used animation with those who did not. 6. RESULTS Results are reported in three parts: use of imagery in a collaborative problem solving set-up: a case study use of imagery in a collaborative problem solving set-up: analysis of fifteen groups discussing a solution. The results were used to test and modify the pattern of use of imagery identified in the case study patterns of use of imagery as related to the nature of students’ solutions
6.1. The Use of Imagery in a Collaborative Problem Solving Set-up: A Case Study The following is a description of the problem solving conversation that took place in a group of three students (denoted G-1 in Table 1). It is based on solving the first task on quality of reception. This team of students chose to work first with the hands-on set-up, then with the computer environment, concluding with the hands-on set up and the computer animation. The discussion evolved through three distinctive phases, each consisting of a set of acts. Though the first phase deals mainly with physical objects and the second with imagery, the overall pattern of the first two phases is similar. The third integrates imagery and physical objects. The phases and set of acts identified is described in the following. (for a list of the phases and categories identified see appendix 1).
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6.1.1. Phase a: Components of the Discussion While Interacting with the Hands-on System The discussion evolved from categorization of equipment and seemingly unrelated, fragmented situations, towards designing complex situations, identifying a problem and discussing the potential ability to construct a solution. It consists of the following acts: a-1: Labeling, Categorizing and Testing Features of Equipment A fragmented view of the conceptual features of the physics lab set-up is exhibited by students. This discussion took place when the students first encountered the equipment. They were familiar with transmitters, receivers and gauges, but not with the particular type used in this experiment. They examined the equipment, holding it, touching the buttons, examining the connections, comparing it to other devices, sharing doubts as to what each part was. The discussion dealt mainly with features of each particular device, unrelated to the other components of the system. In this sense the ideas reflected in this state are fragmented. For example. D: These [transmitter and receiver] look similar [: : : ] they do different things [: : : ] it says [reads the label] electromagnetic micro-wave transmitter. E: this sends like electrical signals, like a signal generator [: : : ] signal, I guess this [points at the receiver] receivers it [: : : ] D: remote control A: what’s micro [: : : ] D: its like, what sort of waves these are. A: microwave oven? D: like specs [specification] of the signal E: : : : meters, [points at meters located on the sides of the transmitter and receiver] what for? mili amperes, I guess current. D: if [: : : ] current is present : : : at least we know that it works.
a-2: Designing, Labeling, and Testing Variables of Situations. A System View Students design situations according to particular goals, such as a situation in which the transmitted signal is received by the receiver. Once the receiver detects the signals, current should be induced in the wire which acts as a receiver, and the meter should show non-zero current. Designing situations while aiming towards particular outcomes, requires that students consider the function of each component of the system relative to other components. They view the components as a system rather than as a collection of fragmented components. This is revealed in the segments below – students discuss how to make the system work:
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A: D: A: D: E:
This is no good. I can’t make it work. You should put it so they face each other. Why? It’s open in the front only : : : not open in the back : : : don’t know. [: : : ] and also turn it on : : : [D. looks at the receiver. A. moves the receiver and transmitter. E. sits back in his chair.] D: OK. I got current.
Students also examined variables that may affect the “working state” of a physical set-up: E: If the receiver is blocked : : : [a few metal devices were accidentally placed on a pile of books in between the receiver and transmitter] : : : Do you get current? [addressing D. who watches the meter on the receiver] D: zero : : : I got current before E: [partly removes the plate.] D: Funny, the needle, : : : current goes up and down D: [removes the pile of books and devices]. D: The books : : : block the current. A: : : : it works
D.’s conclusion, though wrong, is interesting. The students assumed that current flows in space, and that the books blocked it. The view of what propagates between the receiver and transmitter changed dramatically in the second phase to a field view employed in an interesting way in the third phase to explain underlying processes. a-3: Identifying and Agreeing on a Problem – a System-relational View Students need to translate the verbal representation of the problem into the physical set-up. The design of the situations was goal oriented (students check the current when the receiver is horizontal), and was based on what was learnt previously. The students thus consider relations between situations as a basis for the design of new situations. The following is a segment of the conversation in which students negotiate a problem: D: Suppose it falls. [D. relates to the receiver. He changes the position of the receiver, as if it fell] A: If this really works [receiver is horizontal, transmitter is vertical] there should be current in this wire [points at the wire in the receiver] It might be too far away from the transmitter. [A. looks at the meter on the receiver] : : : [moves the receiver closer to the source, current in the receiver is still zero] D: The contact is probably off E: [checks the electrical contacts.] D: All the contacts I can see work E: One of the contacts may be weak in this position only. Try it again when it’s vertical D: Right. [rotates the horizontal receiver until it is vertical. Current increases gradually].
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D: It works. So it just does not get the current when it is horizontal, for some reason horizontal is dead [: : : ] It gets some current in between : : :
No solution was suggested. E: [: : : ] how much can we rotate it and still get good reception. A: [: : : ] should find how we cancel the effect of rotation on the current in the receiver
a-4: Testing the Potential Ability to Construct a Valid Design – a Meta-cognitive View of the System Students don’t really believe they have the epistemological ability to respond to the problem: A: How would I know if current goes in circles [: : : ] unless somebody tells us or we guess [: : : ] E: [: : : it’s not even fair to expect us to make it up [: : : ] any guess I make is stupid, and I can’t know how wrong I am [: : : ]
We term this as a meta cognitive view of the system because it is tested against the conceptual capabilities owned by the group. The recognition of the gap between these capabilities and the behavior of the system forms a basis for the search for other sources of information. An interesting case of evolution of meaning is the differentiation between measured current and induced current: D: No, I mean that the current does not reach the meter [: : : ] like it, the current goes in circles in the wire [: : : ] like not along the wire [: : : ] we always think it goes along [: : : ]
The student imagined a situation in which the measured current is not identical to the actual current in the wire. The “current in circles” does not reach the meter. The “current in circles” is an imagery construct, not perceptually observable. 6.1.2. Phase b: The Nature of Discussion While Interacting with the Computer Animation The general structure of this part is identical to the previous. Yet most of the terminology is new. The two representational schemes – the one constructed with hands-on representations and the other constructed with imagery representations, seem to be only weakly linked. While in the previous situations students used terms such as receiver, transmitter and current, here they say “wire”, “antenna”, “particles”, “force”, “strength of push”. There is no indication as to the origins of these terms, other than some, such as “antenna”, which appear on the screen. The representations
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on the screen include two straight lines termed by students as wires (or antennas), an object that could be rotated between the two antennas with the shape of a grid, and mathematical representations of the changes in induced current in the grid of parallel wires, or/and the second antenna. Almost all discussions are based on the animated imagery. There is no evidence that the animated imagery representations are linked to hands-on objects. Analysis shows the following components: b-1: Labeling, Categorizing and Testing Features of Imagistic Representations. A Fragmented View Similar to the previous discussion, this part also starts by attaching words to pictorial representations on the screen. Terminology not used previously begins to emerge: line, I guess a wire it has two waves like an antenna field peak of wave this wave is taller : : : may be not strength of field. strength of force the force travels the wave travels it looks like a sin : : : two sin.
In general, terms such as “force”, “push”, “particles” are used to impart a meaning to words such as “current” (linked to moving particles) and “induction of current” (linked to force exerted on charged particles). Note that the participating students were in an electrical engineering class in a well established school. They had had classes on induction coils. They seemed to be somewhat familiar with several concepts, such as induction, but the situation/context seemed to be completely unfamiliar. Students’ discussions were not heavily based on mathematical representation, but were rather qualitative, based on imagined particles on which imagined forces are exerted (no particles are represented on the screen). b-2: Designing, Labeling and Testing Animated Situations. Testing Variables. A System View Two different screen situations are brought as an example. In the first, students watch the radiating antenna, the receiving antenna and a curve that represents the intensity of the induced current (in the second antenna) as a function of time. The second antenna can be rotated. The changes in the current are represented simultaneously with the angle of rotation.
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Figure 3. Direction of current in the wire according to D.
Students discuss what generates the current in the second antenna, explore the effect of the transmitter-receiver relative positions, and construct a possible imagery model that explains the decline in the current. D: [: : : ] the force pushes the current [: : : ] particles, in the receiver. if you rotate the transmitter, the force pushes the particles in the new direction A: The galvanometer should still feel the current. D: [: : : ] may be it goes like across the wire. D: [When the data was collected, scanning was not available yet, thus Figure 3, is a version of the student’s diagram] E: What I really don’t get is why the current does not go along the wire, but it did before. D: [: : : ] the force of the wave (points at the line on the screen that describes the direction of electrical field) pushes the particles across the antenna, not along [: : : ] [A few minutes later on] D: [: : : ] I guess if you rotate the receiver it like feels only part of the field
Features of the situation such as field symmetry and polariziation are constructed: A: The electrical force [: : : ] of the wave, is in a [: : : ] single direction. Like it is aimed at one target. It is not all over [surprised – probably expects the pattern of an electrostatic field]
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B: So, It means it will make the electrons move to where the force goes : : : I mean opposite to that. D: [: : : ] the force is not along the wire but across the wire. it pushes inside, maybe like in circles.
b-3: Identifying and Agreeing on a Design Problem, a Relational System View D: [: : : ] need to find how to make the first wire generate a field in all directions [: : : ] no matter how we put the antenna it will always feel the whole field.
b-4: Suggest Appropriate Design (Solution), a System Cognitive View Students view the system that may behave according to the information the group constructed previously, and now shares. They suggest an explanatory model to the problem, which later triggers a solution: D: [: : : ] you need to generate many electrical fields, like in all directions : : : no matter what the direction of the antenna is, there is always an electrical field parallel to the antenna.
6.1.3. Phase c: The Nature of Discussion while Interacting with the Hands-on Experiment after Using Computer Animation The major event in this phase is the links created by students across two schemes: the physical scheme, and the animated representations. Students worked with the physical equipment twice, before and after interacting with the animator. The first encounter with the physical system lead to a dead end. (see a-4). The second led to the development of relations between the terminology of the animation world and the physical world. Students relate single objects and screen drawings (c-1), as well as processes and systems (c-2). The discussion in this section reveals a system view. It includes the following acts: c-1: Attaching Imagistic Representation of Objects to Physical Objects: A System View The following is an example of how students relate animated systems to physical systems. They create relations between systems, across representational schemes. This is a description of how the team agreed that the transmitter and receiver were actually antennas and/or wires: A: I need a wire for the antenna. D: no [: : : ] E: [: : : ] this is supposed to be the antenna [pointing at the transmitter, A held the transmitter, examining it] I guess this also an antenna. [pointing at the receiver]
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A: How do I find the direction of the antenna? D: Look for a wire [: : : ] it’s like a conducting wire. You need current for transmission [holds the transmitter in his hands. Examines an inner visible wire].
c-2: Designing Situations, While Linking Visual Representations to System Processes. An Imagery View of the System In this part students view the lab system through the physical constructs and conceptual imagery capabilities shared by the group. The process of linking imagery representations and physical representations is constrained by the ability to manipulate images. Five types of manipulations were identified: I. Mimic and manipulate imaginery ‘drawings’ in the air: E: [: : : ] suppose I turn this on [turns on the transmitter] so we get current in the antenna of the transmitter. it creates two waves. [holds his hands perpendicular to each other, placed along the line connecting transmitter and receiver] Two waves, is this like two forces? D: I don’t think so. the B [magnetic fields] creates a force perpendicular to its motion. the forces add up in this direction [draws a line on D.’s hand that represents the electical field] E: [working with the physical equipment] the wave goes this way : : : [draws with his finger an upwards arrow, in the space between the transmitter and the receiver] A: the force goes up [Points at the directgion perpendicular to the line connecting the receiver transmitter] [: : : ] means that the current is upwards [points along the wire in the receiver upwards]
II. Rotate and transform imagery representations: Two segments in which students relate direction of field (or force) to direction of current: E: [: : : ] the force could go exactly the opposite A: ??? E: The current may go either upwards or downwards. I don’t know. so the force could too. [draws a sin function in the air, and points to the negative part] D: [: : : ] this is not dc. [direct current]. It’s ac, [alternating current] so it goes forwards and backwards
Students repeat a discussion they had before in the animated world (see D’s comments in both cases) on the effect of rotating the antenna on the induced current. This time, the discussion is in the physical world: D: If I put this [receiver] wire this way : : : [holds the receiver at a 60 degree angle with the desk] the waves, force still goes like before, I mean vertical, like this [draws a vertical sinx wave in the air]
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E: [holds his hand in the air to represent the direction of the field] only part of the force moves the electrons [: : : ] the current should be smaller. [checks the actual current] right. D: [: : : ] when you rotate the source, the force rotates too [rotates the source, with his hand placed at 45 degrees towards the source]
III. Compare sizes of imagery representations: A: [: : : ] the force [looking at the screen] changes too. it’s smaller in the beginning, gets bigger, then smaller again. [: : : ]
IV. Constructing coherency across representations: A: How come we can’t see it [the changes in the current due to the change in direction of the field] on the meter [: : : ] too fast? D: [: : : ] like a 100 times per second.
V. Remember history of drawings: E: Suppose you have many wires, in all directions [: : : ] [draws a circle, perpendicular to the line that connects the transmitter and receiver] You get force, in all directions around the axis. [draws a second circle, parallel to the previous] which means even if the receiver of the wire falls, one of the wires will transmit in the right direction, and current is induced [: : : ] D: [: : : ] but, it may fall backwards, you need to have wires transmitting in all directions in space not in plane. You had a circle, [: : : ] I think it should be a sphere. Like this [use his palms to create a sphere around the transmitting wire]
c-3: Construct a Solution: An Imagery – System View Beyond the physical system, students construct an imagery situation that may act as a solution, based on the imagery representation of polarized waves, discussed and thus shared by the group: D: You need to have wires transmitting in all directions in space not in plane [: : : ] you had a circle, I think it should be a sphere. [. . .] like this [uses his palms to create a sphere around the transmitting wire]
It is important to note here that a field going in all directions at once is impossible. A spherical antenna as students imagine would not work here. 6.1.4. Summary of the Discussion Analysis Two major points are reflected in the above observations:
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Figure 4. D. and E. discuss direction of current by using imaginary drawings on top of the physical system.
a. Imagined objects are treated like physical objects and thus become part of the situation: Just like perceived objects, imagistic representations are rotated, replaced and memorized and sizes of parts are compared, ‘zoomed in’ and examined in detail. As such, these become part of the situation. Though invisible, these representations have a cognitive shared ‘presence’ in the environment similar to the presence of physical objects. Students collaboratively ‘see’ and construct the imagistic representation in space. They use the mentally visualized representation of the field in order to communicate, negotiate, justify and construct ideas through the problem solving process. Transmitter and receiver now have the meaning of an antenna which is a transmitting wire. The decrease in current when the transmitter and receiver are not parallel is explained by ‘seeing’ the direction of the electrical force relative to the wire, and as a result ‘seeing’ the changes in the induced current. b. The depicted shared mental images represent concepts that when combined with the physical perceived objects have a propositional nature, in three perspectives: 1. Imagistic representations can encode a direction. 2. Represented entities add-up, like vectors. 3. Directions of the waves are coordinated with directions defined by the physical set-up, e.g., electrical and magnetic fields are perpendicular to the line between transmitter and receiver.
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This process of mental visualization, allows students to ‘see in their mind’s eye’ the imagistic representation on top of the physical equipment. They visualize one type of representation while physically examining another type. The steps within each phase are not completely distinguishable, nor are they precisely ordered. Phases a and b are similar in their structure. In both cases students become familiar with the concepts of electromagnetism. However the nature of the concept constructed is different, and so is the information obtained about the nature of electromagnetic fields. Hands-on representations trigger mainly discussions in terms of the measured currents both in the transmitter and in the receiver, while the simulator triggers mainly visual representations. In the first case electromagnetic fields seem to be identical to the induced current in the receiver. In the animation discussion, electromagnetic fields were conceptualized as different from current. They are identified as the wave that propagates in between. The electromagnetic field, rather than current, is considered to be the cause of the current induced in the receiver. 6.2. The Use of Imagery in a Collaborative Problem Solving Set-up: Analysis of Fifteen Discussions The pattern identified in the case study was used to analyze fifteen discussions in an attempt to determine whether other groups revealed a similar use of imagery. The results are displayed in Table 1. This table has the form of a matrix. The horizontal axis displays number of the group. The vertical axis shows the categories identified in the case study. An x in a cell shows that the particular group performed the corresponding act. Eight groups worked with both hands-on equipment and with the animation (G-1 to G-8 in Table 1). Seven groups worked with hands-on equipment only (G-8 to G-15). The most obvious result is that all groups that used the animator, constructed imagery representations coupled with the physical set-up. Other than a few incidental sentences, no imagery was exhibited by students who interacted with the physical system only. This supports the hypothesis that students generate imagery representations based on animation, and that the pattern of imagery identified in the analysis of the case study is not accidental. The animator was crucial in order for the students to generate and use imagery for communication. This, however, implies nothing about the quality of solutions. Thus the next step was to examine the extent to which imagery was employed, and relate it to the quality of the solutions.
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6.3. Imagery and Nature of Solution In an attempt to obtain a preliminary indication of the extent of use of mental visualization, we counted the events in which imagistic and handson representations are used simultaneously. Our conclusion is limited both because of the sample size, and the problematic definition of what counts as coupling of visual and hands-on representations. For instance, is a pointing act, simultaneously mentioned with current, a visualization act? We decided it was, if the student ‘draws’ the direction of the current on top of the equipment during the hands-on experiment. This indicates that the student has the ability to ‘see’ through the equipment. If it was generally mentioned without an explicit reference to a component of the experiment, it was ignored. The electromagnetic wave, drawn within the space of the physical system, the force drawn on top of the receiver, or exemplifying the plane of rotation of the electrical field by using the palm, are all considered coupling processes associated with the two representational schemes. Each time a specific integrated concept – visual attached to hands-on – was mentioned in the discussion, it was considered as using an imagistic event. Table 2 displays roughly the number of visualization events for each conceptual theme for each group, (G-1 to G-8) as reflected in the analysis of the discussion. Though not totally satisfactory, this counting strategy of visualization acts does seem to lead to the conclusion that the more visualization acts are displayed, the better the chances of constructing a conceptual working solution. All groups suggested a solution. Only four groups (1, 2, 3 and 7 in Table 2) realized that here electromagnetic fields are directed in a particular direction. Their solution was based on canceling the effect of polarization; an electrical field is transmitted in all directions, thus no matter where the antenna points, there is always one transmitted field parallel to that of the antenna. All other groups suggested mechanical solutions aimed at keeping the receiving antenna in a steady position. Figure 5 shows that these four groups had indeed involved more visualization acts in the discussions. Thus, the use of imagery to ‘see’ the inner processes helped students design a solution based on the deep structure features, the physics of the system, rather than on surface mechanical features. 7. SUMMARY AND CONCLUSION This study shows that: a. Imagery representations are generated by students who interact with an animator, and hardly occur when students do not interact with a visual representation.
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X
X
X X X
a-4: Testing cability to design – a solution, system cognitive view b-l: Labeling, imagistic representations. A fragmented view b-2: Designing animated situations. A system view. b-3: Identify, a problem a system view b-4: Suggest imagery solution: a system view
X
a-2: Designing, situations. A system view. X
X
a-1: Labeling, of equipment A fragmented view
a-3: Identifying a problem – a system view
G-1
Group no: Acts:
TABLE 1 Activities performed by each group
X
X
X
X
X
X
X
X
G-2
X
X
X
X
X
X
X
X
G-3
–
–
X
X
X
X
X
X
G-4
X
X
X
X
–
–
X
X
G-5
X
X
X
X
–
X
X
X
G-6
–
X
X
X
X
X
–
X
G-7
X
X
X
X
X
X
X
X
G-8
–
–
–
–
X
X
X
X
G-9
–
–
–
–
X
X
X
X
–
–
–
–
X
–
X
X
–
–
–
–
X
X
X
X
–
–
–
–
X
X
X
X
–
–
–
–
–
X
X
X
G-10 G-11 G-12 G-13 G-14
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X
X
X
X
X X X X
c-1: Linking imagistic shapes to hands-on objects – a system view c-2: Linking imagery to physical processes- a system imagery view I. manipulate imaginary ‘drawings’ in the air II. Rotate and transform imagery representations III. Compare sizes of imagery representations IV. Construct coherency across representations V. Remember history of drawings c-3: Construct a solution – a system imagery view
Table 1 (continued)
X
X
X
–
X
X
X
X
X
X
X
X
X
X
X
X
X
X
–
–
–
X
–
X
X
X
X
X
X
X
X
X
X
X
–
X
–
–
–
X
X
X
X
X
X
X
X
–
X
X
X
X
X
X
X
X
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
X
–
X
X
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
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TABLE 2 Construction of diagrams in the air or on top of the physical equipment, or referring to equipment by pointing at a symbol on top of the screen at least once during the following activies Group no:
G-1
G-2
G-3
G-4
G-5
G-6
G-7
G-8
1. current in the transmitter causes/pushes current in the receiver
3
1
2
1
1
1
2
1
2. current affected by distance of receiver-transmitter
1
1
1
0
0
1
2
1
3. current affected by relative angle of receiver-transmitter
1
2
1
1
1
1
3
1
4. measured current in the transmitter is different from induced current
1
1
1
0
0
0
1
0
5. antenna radiates a wave-like entity
3
3
3
2
3
2
4
1
6. the wave has an electrical part and a magnetic part
3
2
2
1
2
1
2
1
7. the wave is probably an electromagnetic field
1
1
2
0
0
0
1
1
8. the wave propagates
2
2
3
2
1
2
1
2
9. it affects the second antenna
3
2
2
4
3
1
3
1
10. changing the direction of the current in the antenna changes the direction of the wave
1
0
0
1
0
0
1
0
11. symmetry in radiation
1
1
1
0
0
0
1
0
12. electromagnetic field is unidirectional – polarized 13. multi-polarized field is required in order to cancel the angle affect
3
2
3
0
0
0
1
0
3
3
1
0
0
0
2
0
Activities: With hands-on objects
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Figure 5 Total number of visualization acts for each group.
b. These images are treated similarly to objects. They are ‘visible’, manipulated, and shared by the collaborating team. Thus the images are an extension of the communication system. c. Imagery has a central role in designing problem solutions. Deep structure designs of solutions were more frequent among groups that tend to communicate with extensive imagery. d. Generating imagery is not sufficient for deep structure collaborative design of solutions. More important are the links that learners create between imagery constructs and the hands-on, physically perceived mental constructs, that extend the communication tools. The meaning constructed in an imagery environment is limited, different from the one constructed with hands-on experiments. The association of an image and the corresponding physical object allows construction of both the phenomenology and explanations. We speculate that in the absence of the links made across schemes, conceptual meaning may be fragmented. For instance, in the absence of
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hands-on experimentation, the meaning of an antenna is situated only within the animation. New terminology emerges through the various types of learning environments. In discussing the physical system, students used words such as current, transmitter, meter, receiver, relating to physically measurable entities and physically perceived objects and processes. In discussing the animated system, students used terms relating to visual representations such as, wave, mathematical functions, forces, current, particles and direction of entities. The third part of discussion is based on both. Sentences such as “the force pushes particles in the wire” create conceptual associations between the observable physical system and the hidden, only mentally visible “particles” and “push”. Therefore we suggest that it reflects linkages created between the two vocabulary systems, the physical and the visual, thus integrating the two schemes into a webbed, associated system of perceived objects and imagery. The third part of the discussion reveals a communication system which goes beyond links between words and imagery. Students relate imagery rooted in the animation with imagery rooted in the physical system. The imagery rooted in the animation is linked to a set of rules. The imagery based on the perceived objects captures an equipment set-up, a ‘real world’ situation. This is termed depictive (Kirby and Kosslyn, 1992). Thus in the process of discussing a solution, students generate two types of imagery representation, based on the animation, and based on ‘real world’ situations. The later are based on the hands-on set up, phenomenological in nature, reflecting the shape, color, and other features of the hands-on equipment. Depictive representations use ‘points’ as their sole class of symbols, combined with spatial relationships and convey meaning by visual resemblance (Kirby and Kosslyn, 1992, Sterelny, 1992). It seems that students use images of two kinds. The first is images of vectors, mathematical curves, is associated with some rules of manipulation (e.g. vector addition) which seem to be based on the animation. The second is images of the perceived physical equipment in the lab, and is depictive in nature. In the course of communication about physics, students map each part of the first, e.g. a vector describing the field, to a part of the hands-on set-up. Hagerty (1993) suggests that when reasoning about mechanics problems students run mental animation to make sense of the system. In this case students run the animation in relation to the hands on system. By constructing this correspondence between the depicted and the propositional images, understanding of the phenomenon is constructed. Furthermore, generalization may happen by constructing a double corresponding resemblance, between depictive images and animation-rooted
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images of experienced situations and new situations. The animation image suggests direction of force, motion of particles, relations between the two fields, and thus provide tools to construct an interpretation of the phenomenon and a design for the solution. These images on top of the physical set-up images, turn the mere physical objects into conceptually transparent entities. By mentally visualizing inner processes, students turn ‘black boxes’ into transparent ‘glass-boxes’ providing a possible imagery picture of otherwise invisible processes. Components of a situation, such as objects, act as cognitive tools for problem solving (Lave and Wenger, 1991; Lave, 1988; Brown, Collins and Duguid, 1988). It seems that the animated rooted symbols (e.g. vectors) act similarly to physical objects as cognitive situated tools for empowering reasoning and communicating in collaborative settings.
8. IMPLICATIONS FOR TEACHING The features of the environment dominate the terminology and the meaning attached to the imagery symbols. Therefore the design of the environment has a major impact on meaning construction. One of the major difficulties in learning is related to the fragmental nature of representations. The mathematical or imagistic representations are not related to the students’ past experience or lab hands-on experience. This study suggests that conceptual fragmentation in students’ ideas may be a result of the fragmentation embedded in the learning environment. Animations as a sole component in the learning environment enable learners to create only a single type of relations within the verbal-imagery system. Learners have no opportunity to create links between physical objects, processes and occurrences, and the corresponding imagery representations. Thus a preferred design of the learning environment needs to be based on a multiple representational, rather than a single representation system.
APPENDIX 1: EVOLUTION OF A PROBLEM SOLVING DISCUSSION – A CASE STUDY (GROUP 1 IN TABLE 1) Phase a: a-1: a-2: a-3: a-4:
Labeling, categorizing and testing features of equipment. A fragmented view. Designing, labeling, and testing variables of situations. A system view. Identifying, and agreeing on a problem – a system view Testing the potential ability to construct a valid design – a system cognitive view (view the system through the conceptual capabilities owned by the group)
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Phase b: b-1: Labeling, categorizing and testing features of visual representations. A fragmented view. b-2: Designing, labeling and testing animated (screen) situations. Testing variables. A system view. b-3: Identify, and agree on a design problem: a system view b-4: Suggest appropriate design (solution): a system cognitive view (view the system through the conceptual capabilities owned by the group) Phase c: c-1: Attaching visual representations of objects to hands-on objects – a system-view c-2: Designing situations, testing variables. while attaching visual representations of processes to system processes – a system imagery view (view the system through the imagery capabilities of the group) I. II. III. IV. V.
Mimic and manipulate imaginary ‘drawings’ in the air Rotate and transform imagery representations. Compare sizes of imagery representations: Construct coherency across representations: Remember history of drawings:
c-3: Construct a solution – a system imagery view
REFERENCES Baggett, P.: 1989, Understanding visual and verbal messages. In H. Mandl and J. R. Levin (Eds.), Knowledge Acquisition from Text and Pictures (pp. 101–124). Amsterdam: Elsevier. Beiser, A.: 1960, The World of Physics. McGraw-Hill. Block, N.: 1992, The imagery Issue. In W. G. Lycan (Ed.), Mind and Cognition. A reader. Camrbridge MA: Blackwell Publishers. Brown, J. S., Collins, A. and Duguid, P.: 1989, Situated cognition and the culture of learning. Educational Researcher 18(1). Brown, J. M.: 1991, The Laboratory of the Mind: Thought Experiments in the Natural Sciences. Routledge. Clark, J., M. and Paivio, A.: 1991, Dual coding theory and education. Educational Psychology Review 3: 149–210. Chi M. T. H., Fletovich, P. J. and Glaser, R.: 1981, Categorization and presentation of physics problems by experts and novices. Cognitive Science 5: 121–152. Connelly, J. O.: 1993, Visualization. Technical Communication, Fourth Quarter. Comstock, C.: 1921, On the relevance of imagery to the process of thought. American Journal of Psychology 32: 196–230. Craver-Lemely, C. and Reeves, A.: 1992, How visual imagery interferes with vision. Psychological Review 99: 633–649. diSessa, A.: 1995, Designing Newton’s laws: Pattern of social and representational feedback in a learning task. In R. J. Beun, M. Baker, M. Reiner (Eds.), Dialogue and Instruction. NATO series of Advanced Technology in Education, Berlin, Heidelberg: Springer-Verlag GmbH & Co. KG.
ijco8.tex; 15/11/1997; 3:23; v.6; p.28
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Einstein, A.: 1960, Relativity: The Special and General Theory. London: Mathuen. Ferguson, E.: 1992, Engineering and the Mind’s Eye. Cambridge MA: MIT Press. Farah, M. J., Peronnet, F., Gonon, M. A. and Giard, M. H.: 1988, Electrophysiological evidence for a shared representational medium for visual images and visual percepts. Journal of Experimental Psychology: General 117: 248–257. Finke, R. A., Pinker, S. and Farah, M. J.: 1989, Reinterpreting visual patterns in mental imagery. Cognitive Science 13: 51–78 Forbus, K. D., Nielsen, P. and Faltings, B.: 1990, Qualitative kinematics: a framework. In D. S. Weld and J. de-Kleer (Eds.), Readings in Qualitiative Reasoning about Physical Systems (pp. 562–567). San Mateo, CA: Morgan Kaufman. Gribbin, J.: 1988, In Search of Schrodinger’s Cat. New York NY: Bantam Books. Galileo Galilei: 1974, Stillman Drake trans., Dialogue Concerning the Two New Sciences, (trans.). Madison Wisconsin: University of Wisconsim Press. Aspects of Understanding Electricity, IPN (Institut Fur Padagogik Naturwissenschaften) Kiel. Goldenberg, G., Podreka, I., Steiner, M. and Willmes, K.: 1987, Patterns of regional cerebral blood flow related to meaningfulness and imaginability of words – an emission computer tomography study. Neuropsychologia 25: 473–486. Hagerty, M.: 1992, Mental animation: Inferring motion from static displays of mechanical systems. Journal of Experimental Psychology: Learning, Memory, and Cognition 18: 1084–1102. Hagerty, M.: 1993, Constructing mental models of machines from text and diagrams. Journal of Memory and Language 32: 717–742. Hodes, C., L.: 1992, The effectiveness of mental imagery and visual illustrations: a comparison of two instructional variables. Journal of Research and Development in Education 26(1): 46–56. Johnson-Laird, P. N.: 1983, Mental Models. Cambridge, Mass.: Harvard University Press. Kaufman, G.: 1979, Visual Imagery and its Relations to Problem Solving. Columbia University Press. Kirby, K. N. and Kosslyn, S. M.: 1992, Thinking visually. In Humphreys G. W. (Ed.), Understanding Vision. Blackwell Cambridge U.S.A. Kosslyn, M. S.: 1995, Image and Brain: The Resolution of the Imagery Debate. The MIT Press. Larkin, J. H., McDermott, J., Simon, D. and Simon, H. A.: 1980, Expert and novice performance in solving physics problems. Science 208: 1335–1342. Lave, J.: 1988, Cognition in Practice. Cambridge University Press. Lave, J. and Wenger, E.: 1991, Situated Learning: Legitimate Peripheral Participation. New York: Cambridge University Press. Mayer, R., E. and Anderson, R., B.: 1992, The instructive animation: helping students build connections between worlds and pictures in multimedia learning. Journal of Educational Psychology 84(4): 444–452. Mayer, R. E., Bove, W., Bryman, A., Mars, R. and Tapaganco L.: 1986, When less is more: meaningful learning from visual and verbal summaries of science textbook lessons. Journal of Educational Psychology 88(1): 64–73. Miller, A. I.: 1986, Imagery in Scientific Thought. MIT Press. Maxwell, J. C.: 1873, Action at distance. In Beiser A. (Ed.) 1960: The World of Physics. New York, NY: McGraw Hill. Metzler, J. and Shepard R. N.: 1971, Mental rotation of three dimensional objects. Science: 701–703.
ijco8.tex; 15/11/1997; 3:23; v.6; p.29
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Nersessian, J. N.: 1995, Should Physicists preach what they practice? Science and Education 4: 203–226. Paivio, A.: 1971, Imagery and Verbal Processes. Hillsdale, NJ: Holt Rinehart and Winston. Paivio A.: 1986, Mental Representations: A Dual-coding Approach. New York: Oxford University Press. Reiner M.: 1995, Tools for collaborative learning in Optics. In R. J. Beun, M. Baker, M. Reiner (Eds.), Dialogue and Instruction: NATO series of Advanced Technology in Education. Berlin, Heidelberg: Springer-Verlag GmbH & Co. Roland, P. E. and Eriksson, L.: 1987, Does mental activity change the oxidative metabolism of the brain? Journal of Neuroscience 7: 2373–2389. Rumelhart, D. E.: 1989, Toward a microstructural account of human reasoning. In S. Vosiadou and Ortony (Eds.), Similarity and Analogical Reasoning (pp. 298–312). Cambridge, MA: Cambridge University Press. Schwartz, D. L. and Black J. B.: 1996, Analog imagery in mental model reasoning: Depictive models. Cognitive Psychology 30: 154–219. Segal, S. J.: 1972, Assimilation of stimulus in the construction of an image. The Perky effect revisited. In. P. W. Sheehan (Ed.), The Functional and Nature of Imagery. New York Academic Press. Shepard, N. S.: 1978, The mental image. The American Psychologist, February, 1978, 125–137 Shepard N. R.: 1994, Perceptual-cognitive universals as reflections of the world. Psychonomic Bulletin & Review 1(1): 2–28. Shipstone, D.: 1984, A study of children’s understanding of electricity in simple DC circuits. European Journal of Science Education 6: 185–188. Sterelny, K.: 1992, The Imagery Debate. In W. G. Lycan (Ed.), Mind and Cognition. A reader. Cambridge, MA: Blackwell Publishers Wertheimer, M.: 1959, Productive Thinking. New York Harper enlarged edition.
Department of Education in Technology and Science Technion, Haifa, Israel e-mail:
[email protected]
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