MULTIMEDIALE LEERMIDDELEN --- HOOFDSTUK

Mental models

Acquisition of a mental model by means of computer simulation

Het opbouwen van mentale modellen bij het werken en leren met computersimulaties

Deze tekst is van oorsprong een literatuurscriptie in het kader van de studie Toegepaste Onderwijskunde bij de Universiteit Twente.

1. INTRODUCTION

2. MENTAL MODELS

Figure 1.Instruction or observation from a target system leads to a mental model.

To acquire a mental model of a system which is not easily observed (e.g. molecules, national economy, energy), a conceptual model has to be presented to a learner. This is a mental model of an expert, condensed in some medium, e.g. a text, a computer program or a drawing.
Norman (1983) distinguishes for this purpose a target system, the conceptual model of that target system, the user’s mental model of the target system and the scientist’s conceptualization of that mental model. A conceptual model is invented to provide an appropriate representation of the target system, appropriate in the sense of being accurate, consistent and complete. These characteristics are not necessarily held by a mental model. A scientist’s conceptualization of a mental model is a mental model of a mental model. Norman introduces a notation of these concepts:

t target system
C(t) a conceptual model of the target system
M(t) a mental model of the target system
C(M(t)) a conceptualisation of a mental model

Figure 2. The different models according to Norman (1986).

In a later discussion of these issues, Norman (1986) also introduces a design model, a user’s model and a system image. Other authors also contributed to what Streitz (1988) calls the Mental Model Zoo. Streitz tries to systemize the different views on mental and conceptual models.
He starts with a functionality f. This functionality can be realized by a system S, leading to a system’s realization of the functionality, S(f). A functionality cannot exist without a realization of this functionality. Streitz argues that a functionality can be realized in different systems. His assumption is that people can abstract the basic features of a function from their experience with a variety of system realizations.
The mental model of this functionality calls Streitz U(f). U stands for user. This model is based on experiences with a variety of the realizations, Si (f). This is a different concept from the mental model Norman mentioned. His mental model in the terminology of Streitz would be: U(S(f)). This model is a second order model. For conceptual models, Streitz wants to distinguish between models of designers, D(f) and those of psychologists P(f). This distinction accounts for the difference in conceptualization in models implemented in S(f) and those studies by psychologists. Thus, Streitz considers four models; U(f), S(f), P(f) and D(f).

Figure 3. The first order model (f) and 3 second-order models D(f), S(f) and U(f) according to Streitz (1988).

If U(f), S(f), P(f) and D(f) are seen as operands and S, U, D and P are seen as operators, a range of second-order models appears when the operators are applied to the operands. This situation is represented in the last four rows of Figure 4. The first row contains the first-order models.

Figure 4. Classification of first and second-order models of a functionality f. (Streitz, 1988).

If scientists talk about mental models of users, a third-order model is needed: P(U(S(f))); the psychologist’s mental model of the users mental model of the systems realization of a functionality. This model is influenced by the P(S(f)) and the P(f).
Communication about a third-order model will result in a fourth-order model. One can question the usability of these and higher order models.
The central model in this study is the user’s mental model of the system’s realization of the function f; U (S(f)). This is the model the user refers to when actually interacting with a system.
The concept of a mental model is used in different fields of science and lends itself for many definitions. A diversity of terminology is used to refer to different models for example: surrogates, metaphors and glass-box machines. A surrogate is a mental model that has the same input/output functions as a system in reality, but it’s internal causal structure is different. It’s obvious that a surrogate carries the danger of malfunctioning in some (maybe important) situations. A metaphor is a comparison between a unknown system in reality and a known system in the mind of a user or learner. Knowledge of one domain is transferred to another domain. A glassbox-model lies in the middle of the continuum from surrogate to metaphor. The description of this model is not very clear: The glass box model share the mimicry quality of surrogates whilst offering a semantic basis for understanding the system, as do metaphors, by providing information about the internal processing and mechanics of the system. (Bibby, 1992).
One explanation for this diversity is that different disciplines of cognitive psychology and cognitive ergonomics/human factors independently developed a notion of a mental model (Goei, 1994). Another explanation is that the notion of a mental model can be molded in any form a researcher would like to have. Bainbridge (1992) concludes that the domain in which the mental model is used, largely affects the elements that are considered as necessary.
A problem with the concept of mental models is the form in which they are represented in the head. It is not likely that they are similar to photographs; it would require a homunculus to perceive these pictures (Johnson-Laird, 1980). In general, two perspectives on knowledge representation and problem solving can be found in literature; a propositional one and a depictive one. The propositional one is described in the next paragraph, the depictive view in paragraph 2.3.

The propositional perspective
Before the theories of mental models were introduced, the classical view on skill acquisition was dominated by the propositional viewpoint. In this view cognition is modeled by productionsystems that are easily simulated by computer programs.

Propositionalists see cognition as a collection of facts and rules represented in a sentence-like structure in the head. They differ from natural language sentences, a reason why it is sometimes difficult to put an idea into words. Another argument for a difference with natural language is that young children are able to understand concepts they are not able to explain. Some propositionalist allow the formation of a picture on the basis of propositions. This mental picture can not contain more information than the propositions itself. (Stillings et. al., 1987).
Newell and Simon (1972) popularized a way of representing knowledge, which has become a universal standard in psychology (Payne, 1988). Their system is known as the production system representation. Production systems are convenient languages to model learning. Learning is seen as a transition from novice to expert. An expert does know the same as a novice, but he is able to use his knowledge in a more efficient way.
To understand this, two kinds of knowledge are distinguished: declarative knowledge and procedural knowledge. Declarative knowledge consists of facts, concepts and principles. Procedural knowledge is knowledge about how to process or manipulate information to accomplish tasks. According to Anderson (1987), procedural knowledge accounts for all mental and physical activities.
The knowledge base of an expert and a novice can be the same (Shih & Alessi, 1993). It consists of declarative knowledge. The expert has more procedural knowledge, in production system terms: more specific production rules. The production rules consist of domain specific procedural knowledge. This knowledge is acquired through a synthesis of domain general procedural knowledge and domain specific declarative knowledge.
Production systems consist of a set of rules (productions), that communicate by way of a working memory. Productions in a production system are condition-action pairs that specify what action occurs under which condition. A novice in this view uses general-purpose, weak-search methods to solve a problem or acquire a cognitive skill. These search strategies can be made more efficient and faster. This is done by various mechanisms that mutate production rules. These mutating mechanisms model the learning mechanisms that occur with practice. (Payne,1988).
The modular structure of production systems allows the adding of new code to the existing system, without complete rewriting of this system. Provided that there is sufficient redundancy in the ruleset, it is also possible to delete rules without distortion of the reasoning ability of the system. These qualities make the system suitable to model the knowledge-structures of a learner. Since the early designs, many refinements have been introduced, particularly in the pattern matching and conflict resolution strategies. (Payne, 1988). Learning theories have been automated by specifying mechanisms that create new production rules from old, using a variety of transformation techniques. The fundamental approach of the systems is the same. The initial production system solves problems in a domain by some combination of weak search methods (which require only general knowledge). This starting production is designed to model novice problem solving performance. As the novice production system solves problems in a domain, learning mechanisms derive new productions that encode specific knowledge about the domain in their antecedent conditions. The new productions take precedence in the solution of prior problems, allowing knowledge-base heuristics to control search. Expert performance is thus modeled by productions which encode methods for accomplishing tasks (Payne, 1988).
The described approach has been criticized. This critique provides arguments in favor of a more realistic theory of knowledge representation. Payne noticed three major shortcomings of the proposistional view; it (1) neglects context effects, (2) neglects to model mistaken performance, and (3) neglects the role played by rich conceptual representations (Payne, 1988).

(1)Theories have concentrated on the mechanisms of change rather than the conditions of change. The conditions of change lay in a cognitive context.
(2)Mistaken behavior is modeled by adding mal-rules to the rule set. A mal-rule is a rule that leads to an incorrect process of reasoning. A major problem with mal-rules is that they oversimplify the psychological status of regular mistakes. Not all regular mistakes need be caused by buggy procedures. A second problem is that not all problematic misconceptions will be manifest in regular misbehaviors.
(3)The last shortcoming is not soluble within the framework of production system representations. Experts know more than can be easily represented as a collection of method-generating rules; they can reason and argue about their expertise, they can cope with novel problems and their skill transfers to seemingly separate domains.

The conclusion of Payne is:
To interrelate conceptual knowledge with procedural skills appears to demand more powerful constructions than mere networks of facts.

2.3 Building blocks of mental models
The subsystems in the theory of mental imagery are the building blocks for the theory of mental modeling. The debate between proponents of propositional representations and proponents of mental imagery is shortly addressed. With the publication of Image and Brain Kosslyn (1994) tries to resolve the debate.

The central theme in mental model theory is visualizing. People are able to see in the minds eye. They can perform mental simulations to predict target system behavior. The human ability to imagine objects that are not present, corresponds to introspective observations.
Mental imagery is a necessary condition for the proof of mental modeling theories. If mental imagery does not exist, the theory of mental models becomes highly speculative. In other words, mental imagery is the foundation of mental modeling. Imagery is a fundamentally different approach than the one taken in the paragraph on the propositionalist viewpoint. A similarity between both approaches is that they assume that humans do not think in sentences nor in pictures. There is some sort of language of thought. The debate is whether humans are able to think in picture-like structures. The question whether people are able to think in sentence-like structures is not a topic of discussion.
The processes of visualizing are studied in the field of mental imagery.
...imagery is a special purpose component of the cognitive architecture containing representations and processes that are dedicated to processing certain kinds of visual information and that are distinct from the aspects of the architecture that support propositional representations. (Stillings et. al, 1987, p.36)
A sequence of mental transformations makes it possible to predict the behavior of a target system. (A target system is a system that is imagined). This predictive power is one of the characteristics of a mental model. Another resemblance between imagery and mental models is the picture-like form of representation, which appeals to introspective observations. Kosslyn (1973) tried to prove the existence of mental imagery by scanning experiments. He focused on the so-called privileged properties; properties of depictive representations which are not shared by propositional representations.
The subjects in his experiment were asked to close their eyes and visualize previously memorized drawings. For example, subjects might close their eyes and visualize a boat with a motor on the left end, a porthole in the middle and an anchor on the right end. Then, they would focus attention on one end of the object, for example the motor. Next they would hear the name of a part (such as porthole, but also mast and anchor which were not present) and were to look for the named part on the imagined object. The subjects were to press one button if they could see the named part and another if they could not. The further along the object they had to scan, the more time was required, even though the object was no longer present and the subjects’ eyes were closed.
The results of these experiments were seen and understood differently by propositionalists. The time the subject needed was not used to scan the image, but to work down several lists of mental propositions. According to this reasoning, the subjects memorized objects by formulating a series of linked propositions.
As more scanning and mental rotation experiments were conducted, the propositional researchers had to add more rules, lists and symbols to their theories. This means that the propositionalists’ theory lost predictive power. The modifications were according to Kosslyn, ad hoc and post hoc.
In his later work, Kosslyn (1994) uses a cognitive neuroscience approach to explore the concept of mental imagery. His goal is to characterize the subsystems that are responsible for imagery in terms of input, operation and output of a set of neurons.
The mechanisms of imagery are interwoven with those of visual perception. It is therefore that Kosslyn starts with a study of visual perception. He distinguishes between relatively well understood low-level vision, driven on stimuli input and high-level vision, based on previously stored information about properties of objects and events. This last form of perception has deep and pervasive effects during perception.
...I will argue that imagery plays an important role during ordinary perception. (p.53)
He identifies five classes of visual perception abilities his theory has to account for. The goal ... is to infer the subsystems that confer our ability to identify objects (1) in different locations and at different distances; (2) with different, sometimes novel, shapes (3) when the input is impoverished; (4) as specific exemplars, including ones that are not typical for the category; and (5) when we see objects embedded in scenes. Each of these abilities corresponds to a set of more specialized abilities. (p.76)
In the end of his book Kosslyn gives an overview of 16 subsystems of which the mental imagery ability is comprised (p.380). He is able to describe input, operations and output of these systems and gives a suggestion of the localization in the brain. The empirical basis behind his theory is too extensive to describe within the limitations of this paper. It consists of observations of brain damaged patients, experiments with mental rotation, scanning and zooming (also with blind subjects), PET-scans during mental tasks, recognition tasks, research on categorization, prototyping and familiarity, and other research of the past fifteen years.
Phylyshyn is a hard-core propositionalist, and one of the main opponents of Kosslyn in the so-called imagery debates. His critique on Image and Brain is fundamental: ... But the basic problem still stands: as long as the research questions continue to be ill- posed, the problem about mental images will remain unsolved, regardless of how munch brain (or other) data is collected. (Phylyshyn, 1994).
Another critique on Kosslyns book is more positive.
... Evidence for shared mechanisms in imagery and perception is obviously relevant to the debate about the nature of images: if images share brain areas with perception, and these areas are hard-wired (that is, topographically organized) to represent shape depictively in perception, it follows that these areas represent shape depictively in imagery. This hypotheses is further supported by evidence that imagery not only activates homologous topographically organized areas in the human brain but is impaired when these areas are damaged. In summary, the central issue of the imagery debate can now be stated in concrete terms: do areas of the brain that depict visual information represent visual mental images? Yes is an educated answer. How are patterns of activation in these areas formed, manipulated, and used during imagery? With its schematic approach Image and Brain addresses these questions in a precise and challenging, yet enjoyable way. (Georgopoulos, 1995)
A part of Kosslyns work deals with image maintenance, the ability to maintain an image over a period of time which makes it possible to use it in mental operations.
Image maintenance lies at the heart of the use of imagery in reasoning: such tasks usually require at least a few seconds to perform - and hence if one cannot maintain the image, it is useless. For example, one might be told that Sally is smarter than Sam, Sam is dumber than Sheila, and Sheila is dumber than Sally. If one images each person as a dot on a line, with the smarter people being further to the right (and can remember which name goes with which dot), it is easy to decide who is smartest, who is dumbest, and so forth. I think of his sort of imagery as one type of mental model, of the sort discussed by Johnson-Laird (1983). (Kosslyn, 1994, p. 324)
Kosslyn (1994) identifies three reasons why not all theorists are convinced that mental models represent the actual processes in the brain better than production rules do. The first is that their intuitions have developed over years of working with computers trying to program their ideas in LISP. Second, the successes of Artificial Intelligence impressed researchers so much that they saw no reason for change. The last reason is the attractivity of the apparent simplicity of a single-representation system.

2.3.1 Conclusion
Kosslyn tries to prove mental imagery with the results of neuroscientific research. This seems a successful approach although hard-core propositionalists are not convinced. The subsystems of the brain that are responsible for depictive thinking are outlined in a systematic way, but more research is needed to prove the correctness of this particular model. The ability of people to think depictive is sufficiently proven. This means that the mental model theory can be build on an empirical basis. This way of thinking is not so easily modeled in a system, or simulated on a computer as propositional thinking is.

2.4 Benefits of a mental model
Is there a good reason for investing mental effort in acquiring a mental model? This is the central question in this paragraph. There have been reported influences on problem solving, on learning speed and on inferring procedures.

The way in which knowledge is represented has an influence on the outcome of problem solving. During an experiment with 36 high school and college students, Gentner and Gentner (1983) asked their subjects to make qualitative predictions about changes in voltage and current in simple electrical circuits. The circuits differed in the amount of resistors and batteries and the way they were connected (parallel or sequential).
Genter and Genter concluded that subjects who imagined electricity as a flowing fluid made good predictions about the problems with batteries. Subjects who imagined electricity as a moving crowd made good predictions about resistor-problems. The interaction between mental image and the type of combination (batteries or resistors) was significant. No other effects were significant. Kieras & Bovair (1984) studied how a mental model of a device influenced the learning of procedures to operate this device and if a mental model was responsible for inferring operating procedures. By a mental model they mean some kind of understanding of how the device works in terms of its internal structure and processes. They do not claim any visual or propositional representation.
In simple cases it is clearly unnecessary to know how a device works. A familiar example is a telephone. Many people use it easily, without knowing anything about the underlying system. Even a complex telephone system requires only how-to -do -it knowledge. However in more complex cases the situation may be different. Kieras & Bovair designed a control panel for a device based on the science fiction series Star Wars. It contained switches and indicators for useful contrivances as shipboard power, energy boosters and a phaser firing indicator.
In their first experiment they tested the influence of a mental model on the learning rate of procedures. The model group (n=20) received instruction about the internal working of the device. Both model en control (n=20) group received the same procedure training. The learned 10 procedures. Four of these procedures where designed to be inefficient. Then a retention test was taken and in a second test subjects were asked to look for short-cuts. One week later a second retention test was taken.

Table 1. Summary of results on learning procedures with and without a device model.

This experiment shows that understanding a device leads to better performances. The results are similar to those found in experiments with more meaningful learning material. However, the procedures itself are not more meaningful. The hypothesis Kieras & Bovair suggest is that the understanding of the device makes it possible to infer procedures. They test the hypothesis with a second experiment. In this experiment the conditions are the same, but the test is different. Subjects were asked to find two efficient procedures to make the PF-indicator flash. The number of actions was measured.

Table 2. Mean number of actions tried while inferring procedures

The conclusion of this experiment is that a mental model of a device, makes it possible to infer procedures in a efficient way. Thus, the learning of procedures may be made more efficient if the underlying model is known to the student.
This result is consistent with a study of Shih & Alessi (1993). They used graphics and animation to teach programming skills. Programming is a field in which misconceptions are one of the biggest obstacles for students in learning to program. In this experiment seventy nonprogrammers practiced either code evaluation, code evaluation with the aid of conceptual models, or code generation. Conceptual models were provided by a computer based training that used a warehouse analogy and different animations to explain arrays, loops and the sequential evaluation of expressions. In the first sessions (of four) the group that practiced code evaluation with the help of conceptual models (Group EM) took more time to complete the sessions. In the later sessions they were able to solve the problems faster, and spent on the entire course an equal amount of time. The explanation lies in the assumption that group EM spent more time to form mental models, and benefited from these models because the time they needed to find a solution became shorter.
Shih & Alessi found that practicing code evaluation with the help of conceptual models promoted conceptual understanding and facilitated the learning of evaluation skill and transfer to code generation skill. Also the ability to solve transfer problems was highly correlated with the quality of the subjects’ mental models. Should these implications for programming instruction be generalized to other domains? Many things we teach require cognitive skills similar to those used in computer programming. We believe that students being taught any content that requires cognitive skills will benefit from conceptual instruction, including the use of conceptual models to help students develop appropriate mental models. We recommend the development of instructional design models that include the use of conceptual models in teaching cognitive skills. (Shih & Alessi, 1993)
The last experiment that is mentioned is the one Mayer (1989) conducted to investigate benefits of mental models.
Mayer (1989) tested whether the presentation of a conceptual model would influence conceptual recall, verbatim retention and creative problem solving. The conceptual model was presented to a learner before he heard a text about a topic. The conceptual model consisted of a diagram. The topics varied from Ohm’s law to brakes and databases. Mayer suggested that a good conceptual model can provide a assimilative context to build useful mental models. The test results of various experiments led to the overall conclusion that transfer and conceptual recall increase. The verbatim retention decreases.

Table 3. Mayer (1989) observed positive effects offering a conceptual mode before instruction:

3. HOW IS A MENTAL MODEL FORMED?

Table 4. Adjusted means and standard deviations of posttest scores of each educational level and of combined educational levels for treatment combinations:

4. COMPUTER SIMULATION

Table 5. Traditional classification of courseware:

Table 6. Four types of computer simulations according to Gredler (1986):

Table 7. Four main categories of computer simulations according to Alessi & Trollip (1985):

Table 8. Description scheme of simulation learning processes:

5. COMPUTER SIMULATION AND MENTAL MODELS

Table 9. Results on two tests (PNMET 5 & PNMET 7) from three different groups, results indicate a beneficial effect of animation. (Williams & Abraham, 1995):

6. EPILOGUE

7. ACKNOWLEDGMENTS.

8. REFERENCES