Model-Centered Learning and Instruction - Old City Publishing

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Model-Centered Learning and Instruction NORBERT M. SEEL* University of Freiburg, Germany Department of Educational Sciences, Learning Research and Instructional Design

This article focuses on the paradigm of model-centered learning and instruction, which is based on the theory of mental models. According to this paradigm, cognition and learning are the result of mental representations. Individuals form mental representations by organizing symbols of their experience or thought in such a way that they effect a systematic representation of this experience or thought, as a means of understanding it, or explaining it to others. In this article, the focus is on the psychological and epistemological aspects of model-centered learning and instruction. Accordingly, the psychological foundations of modelcentered learning as well as the semantic functions of mental models are described first. Following this, the focus is on types of instruction that help learners to construct mental models. A distinction is drawn between three paradigms of model-centered instruction: (a) Self-organized discovery and exploratory learning, (b) externally guided discovery learning, and (c) receptive learning oriented toward an expert’s behavior or a teacher’s explanation. Then, the state-of-the-art of two scenarios of model-centered instruction is summarized: providing students with model-information and the approach of design-based modeling as employed in discovery learning. Finally, the results of this research are discussed with regard to learning and instruction. Keywords: Mental models, schemata, discovery learning, learning by design, model-centered instruction.

INTRODUCTION Model-centered learning and instruction (MCL&I) is both a new and old paradigm of psychology and education. It concerns a complex phenomenon which occurs not only in classrooms but also in a variety of informal learn____________________________

*e-mail: [email protected]

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ing environments such as museums, zoos, gardens, and activity centres. It also occurs on many levels (individuals, groups of various size and composition, in diverse cultures). Some decades ago, Bandura (1971) developed the paradigm of social model-learning, according to which behavioral changes can occur even when a person is not engaged directly in a learning process but rather observing the behavior of another person. A learner A who has a particular repertoire of behavioral traits (a, b, c, ...) at time t1 observes a model-person B who expresses among others the behavioral traits x, y, z. In examining the behavioral repertoire of A at a time point t2 one can often observe that A has adopted the behavioral traits x, y, z of B. Similarly, in several instructional conceptions, such as the Cognitive Apprenticeship approach of Collins, Brown and Newman (1989), the starting point for cognitive learning is situated in the observation of an expert’s problem-solving behavior (see also Gibbons, 2002). Evidently, these conceptions have a strong psychological background. However, an analysis of the literature indicates that the idea of model-centered learning and instruction also has its origins in the epistemology of neopragmatics (see, for example, Stachowiak, 1973; Wartofsky, 1979), with the focus on both the model-based construction of theories and the meaningful use of models in different fields of instruction. In accordance with the model-theory of semantics, Chapanis (1961) classified models into two broad categories: Reproduction models (i.e. material-semantic models) such as physical objects, diagrams that serve the purpose of communication (e.g. in the context of instruction), and symbolic models (i.e. formal-semantic models) that serve the purpose of mental representation of knowledge. Actually, the central epistemological assumption is that “the person constructs the reality” (Buss, 1979) but not vice versa. Cognition and learning take place in the use of mental representations in which individuals organize symbols of their experience or thought in such a way that they effect a systematic representation of this experience or thought, as a means of understanding it, or of explaining it to others (cf. Seel, 1991). Interestingly, we can find a similar argumentation in various conceptions of model-centered learning which focus on guided discovery and exploratory learning. Such conceptions have been developed in the fields of mathematics, physics, and geography education (cf. Hodgson, 1995; Lesh & Doerr, 2000; Penner, 2001). In all these cases talking about “models” implies asking for the original to be modelled. Globes are models of the earth. Naturally, a globe is not a reduced earth but rather it is supposed to give answers to questions about the locations of different places or distances between places. With regard to the

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chemical composition of the earth, a globe is not relevant. This example illustrates the following: Every model is constructed in accordance with specific intentions in order to simplify its original in several respects. As an idealized reduction to relevant characteristics of its original a model is a concrete, comprehensible, and feasible representation of non-obvious or abstract objects or phenomena. The representation of the objects’ attributes and components comes second to the representation of structural relationships, and the functions of a model are defined on the basis of the explicit intentions of the model-building person. Therefore, in physics and similarly in other disciplines the term model is always used intentionally to refer to the following functions: • Models aid in the simplification of an investigation to particular and relevant phenomena in a closed domain. • Models support the envisioning (visualization) of complex phenomena. • Models aid in the construction of analogies in order to identify relationships within an unknown domain (e.g. quantum mechanisms) with the help of the relationships within a known domain (e.g. Rutherford’s atomic model). Such models are called “analogy models” and are heuristic hypotheses about structural similarities of different domains. • Finally, models aid in the simulation of a system’s processes. This occurs when an individual interacts with the objects involved in a situation in order to manipulate them mentally in such a way that the cognitive operations simulate specific transformations of these objects that may occur in real-life situations. Such simulation models operate as thought experiments, producing qualitative inferences with respect to the situation to be mastered. Moreover, an analysis of the literature shows that there are numerous fields of interest in which the theoretical term “model” plays a significant role: In the context of scientific theory construction, in the theory of measurement, in cognitive psychology with its emphasis on mental models and constructing artifacts, and in different subject matter domains, such as mathematics and physics where models serve to explain phenomena of the physical world. The various field of model-centered research may be summarized as in Figure 1:

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FIGURE 1 Fields of model-centered research

In the following sections I will focus on the psychological and epistemological aspects of model-centered learning and instruction. Here, theoretical concepts such as schemata, mental models and external representations play a central role for the understanding of cognition and learning.

THEORETICAL BACKGROUND OF MODEL-CENTERED LEARNING Evidently, model-centered as well as schema-based learning are theoretical concepts of cognitive psychology, a discipline emerged in the second half of the 20th century. This shift from the normative paradigm of behaviorism to the interpretative paradigm of symbolic interactionism (called the “cognitive revolution” for short) occurred in the 1960s and “focused upon the symbolic activities that human beings employed in constructing and in making sense not only of the world, but of themselves.” (Bruner, 1990, p. 2).


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Thus, cognitive psychology is concerned with the construction of symbolic models of information processing understood generally as the capacity of the human mind to construct knowledge, to interpret the world and to reason in deductive or inductive manner (cf. Seel, 2000). Cognitive learning occurs when people actively construct meaningful representations, such as coherent mental models, that represent and communicate subjective experiences, ideas, thoughts, and feelings (cf. Mayer et al., 1999). By means of mental representations an individual is capable of simulating real actions in the imagination. According to Piaget the fundamental basis for the development of mental representations is based on the development and gradual refinement of assimilative schemata. Schemata and mental models The term schema is one of the central concepts of modern cognitive psychology and is common to the work of Kant, Bartlett, Piaget, Abelson, Schank, Norman, Rumelhart and others. For some cognitive theorists (Neisser, 1979; Rumelhart, 1980), schemata are the basic building blocks of the psychological understanding of cognition. Mandl, Friedrich, and Hron (1988) have defined them as cognitive structures in which general knowledge is represented in memory. More specifically, in the terms of Piaget (1943), a schema of an action (i.e. “enactive schema”) is defined as the structured totality of the generalizable characteristcs of this action, i.e. of those characteristics which allow one to repeat an action and apply it to new contents. Therefore, in modern cognitive psychology schemata (or frames and scripts) are understood as generic data structures which play a central role in the interpretation of perceptions, the regulation of behavior, and the storage of knowledge in memory. However, according to Rumelhart et al. (1986) there is no representational object which is a schema. Rather, schemata emerge at the moment they are needed from the interaction between many simpler elements working in concert with one another in order to interpret the given environment as well as assimilate new information. Actually, in Piaget’s theory of equilibration a schema mainly serves to assimilate new information into existing knowledge structures. The fundamental mechanism in this process is pattern matching, which enables individuals to quickly “settle” on an interpretation of an input pattern. Beyond this, schemata also form the basis of the construction of models, which can be understood in accordance with Piaget as “tools” of accommodation (cf. Seel, 1991). More specifically, Rumelhart et al. divide the cognitive system into two modules (or sets of units). One part—called an inter-

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pretation network—is concerned with the activation of schemata, the other one is concerned with constructing a “model of the world.” This model takes as input some specification of the actions we intend to carry out and produces an interpretation of “what would happen if we did that.” Part of this process could be a specification of what the new stimulus conditions would be like (appearance modeling). The interpretation network (i.e. a schema) takes input from the world (to be explained) and produces relevant reactions whereas the second module, i.e. the constructed “model,” predicts how the input would change in response. In the literature it is common to talk about a mental model that one would expect to be operating in any case, in-asmuch as it is generating expectations about the state of the world and thereby “predicting” internally the outcomes of possible actions. However, it is not necessary for world events to have happened. In the case that they have not, the cognitive system replaces the stimulus from the world with input from the mental model. That means that a “mental simulation runs” envisioning the events in imagination that would take place in the world if a particular action were to be performed. Thus, mental models one allow to perform actions entirely internally and to judge the consequences of actions, interpret them, and draw conclusions based on them. In other words, the cognitive system can build an internal control system based on the interaction between the two modules of the cognitive system. This theoretical conception of Rumelhart et al. (1986) corresponds to a great extent with the theory of mental models that emerged in the 1980s to capture deductive (and inductive) reasoning by “settling” computations of the human mind in a solution rather than to applying logical operations (cf. Johnson-Laird, 1983, 1994; Hinnersmann, 1989). Moreover, it has been argued that comprehension and reasoning in specific situations (e.g., in schools and real-life situations) necessarily involve the use of mental models of different qualities (cf. Greeno, 1989). Accordingly, the theory of mental models has been applied successfully in several domains such as HumanComputer-Interaction (Ackerman & Tauber, 1990), text and discourse processing (Rickheit & Habel, 1999), operating with complex (technical) systems (Kluwe & Haider, 1990), and so on. Mental models play a central and unifying role in representing objects, states of affairs, sequences of events, the way the world is, and the social and psychological actions of daily life. They enable individuals to make inferences and predictions, to understand phenomena, to decide what action to take and to control its execution,


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and, above all, to experience events by proxy. (Johnson-Laird, 1983, p. 397) Historically seen, Craik (1943) introduced the concept of “internal models” into psychology with the notion of a working model. Craik argued that, in contrast to the assumptions of behaviorism, people experience reality only mediated by mental constructions such as internal models. As in the theory of mental models, this idea is based on the assumption that an individual who intends to give a rational explanation for something must develop practicable methods in order to generate appropriate explanations on the basis of principally restricted domain-specific knowledge and a limited information processing capacity. Accordingly, the individual constructs a model that both integrates the relevant domain-specific knowledge and meets the requirements of the phenomenon to be explained—then the model works. Thus, mental models are intentional constructions of the mind which generate access to the observable or imagined world and make it plausible. Mental models reflect the structure of the world because they are generated to structure it, and not because they reproduce or copy a given external structure. They represent and organize the subject’s knowledge in such a way that even complex phenomena become plausible. Models and external representations As Rumelhart et al. (1986) have pointed out, people are not only good at pattern matching (by means of schema activiation) but also at modelling their world and manipulating their environment. The ability of modelling to create expectations by “internalizing” experiences is crucial to learning as well as the skill of manipulating the environment allow us to reduce very complex problems to simpler ones. Interestingly from an instructional point of view, the suggestion has been made (cf. Norman, 1983) that mental models are constructed from the significant properties of external situations, such as designed learning environments and the subject’s interactions with them. According to this view, the external environment becomes a key extension of our mind and its processing is real symbol processing and the primary symbol processing that we are able to do. Accordingly, imagination is highly dependent on our experience with external representations which, therefore, play a crucial role in thought and its communication. This idea that we learn and think on the basis of mental models which result from the internalization of external representations is especially relevant for instruction insofar as the construction of external representations provide us with

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the means to easily influence the learners’ construction of mental models intentional. I will refer to this point later in this article. Here, it should be emphasized that modeling basically involves the interactions between three types of systems: • internal conceptual systems of a model building person, • representational systems that function both as externalizations of the internal conceptual systems and as internalizations of external systems, and • external systems that are experienced in nature, or that are artifacts that were constructed by humans (cf. Lesh, 1998; Rumelhart et al., 1986). Accordingly, Kluwe and Haider (1990) have distinguished between the following basic types of semantic models that are of interest in this article: • Semantic models have their field of reference in a more or less complex system S of the physical world. • In order to explain a particular system S individuals develop distinctive internal representations that are called mental models of S, MM (S), and that represent the individuals’ distributed knowledge with regard to S. • On the basis of their mental models, scientists develop conceptual models CM (S) which represent the shared knowledge of a discipline with regard to the system to be explained. • Cognitive psychologists, for their part, develop psychological models of model building activities: PM [MM (S)]. Actually, this chapter is concerned to a large extent with the description of such psychological models of model building activities. • Finally, so-called design and instructional models DIM [CM (S)] are of special interest from an instructional point of view. They are instruction-oriented descriptions of the conceptual models of the system S that are used for the construction of interfaces (e.g., learning tasks, manuals and trainings) in order to guide the learners’ construction of mental models. The interplay between these different kinds of semantic models and the world to be modelled may be illustrated as in Figure 2. Kluwe and Haider (1990) have pointed out some important relationships between these kinds of models. For example, there is a strong relationship between mental models and conceptual models insofar as the shared knowl-


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FIGURE 2 Varieties of semantic models

edge of a discipline—expressed through conceptual models—presupposes the distributed knowledge of the individuals who constitute a scientific community of practice. I argue that conceptual models evolve from the learningdependent progression of the subjective mental models which scientists construct (cf. Norman, 1983). A second important relationship exists between MM (S) and the field of cognitive psychology in which explanatory models are constructed with regard to model building activities of learners. A third kind of relationship can be identified between the design and instructional models. We argue that these models are related to all other types of models. However, in the case of subject matter oriented learning there is a clear preference for teaching conceptual models in order to improve this kind of learning. Finally, there is a mutual relationship between DIM [CM (S)] and PM [MM (S)]. Kluwe and Haider (1990) have pointed out that in the literature the distinction between these different types of models is often not clear insofar as several psychological approaches (e.g. di Sessa, 1986; Williams et al., 1983; Young, 1983) are actually concerned with the notion of design and instruc-

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FIGURE 3 Relationships between different types of semantic models.

tional models. This leads to the next section of this article, concerning the instructional implications of model-building activities of learners.

INSTRUCTION THAT HELPS TO CONSTRUCT MENTAL MODELS As I have mentioned in the introduction of this article, the question how we can influence model-building activities of learners has been at the core of various educational approaches for a long time. In addition, in the field of research on mental models we can find a strong pedagogical impetus from the very beginning (cf. Anzai & Yokoyama, 1984; Mayer, 1989; Norman, 1983; Seel, 1986). Johnson-Laird (1989) distinguished between three different sources for constructing mental models: • The learner’s ability to construct models in an inductive manner, either from a set of basic components of world knowledge or from analogous


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models that the learner already possesses; • everyday observations of the outside world, and • other people’s explanations. This differentiation corresponds, to a large extent, with several paradigms of model-centered instruction: (a) Self-organized discovery and exploratory learning, (b) externally guided discovery learning (for example in the form of “learning by design,” cf. Kolodner et al., i.pr.), and (c) receptive learning oriented toward an expert’s behavior or a teacher’s explanation. According to Carlson (1991) instruction can be designed to involve the learner in an inquiry process in which facts are gathered from data sources, similarities and differences among facts noted, and concepts developed. In this process, the instructional program serves as a facilitator of learning for students who are working to develop their own answers to questions. On the other hand, instructional programs can present concepts with clear definition followed by clear examples. A designed conceptual model may be presented ahead of the learning tasks in order to direct the learner’s comprehension of the learning material. Clearly, there might exist environments that can initiate a form of learning based on free exploration by invention, but in instructional contexts (especially in schools) we regularly operate with wellprepared and designed learning environments that constrain the student’s learning processes to various extents. Johnson-Laird (1989) has expressed the central point of instructional guidance for model-centered learning as follows: Although mental models may differ markedly in their content, there is no evidence to suggest that they differ in representational format or in the processes that construct and manipulate them. What is at issue is how such models develop as an individual progresses from novice to expert, and whether there is any pedagogical advantage in providing people with models of tasks they are trying to learn. (Johnson-Laird, 1989, p.489) This paradigm of model-centered instruction concerns the learningdependent progression of mental models, defined (in accordance with Snow,

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1990) as a specific kind of transition between preconceptions (i.e. the initial states of the learning process) and causal explanations (i.e. the desired end states of learning). I have illustrated this paradigm of instructionally guided model-centered learning as follows (cf. Seel, Al-Diban & Blumschein, 2000).

FIGURE 4 The mental model as created through an instructionally designed conceptual model.

In contrast with this paradigm, several authors (such as Johnson-Laird, 1989; Penner, Lehrer & Schauble, 1996; Stewart et al., 1992) have emphasized the role of self-organized discovery learning for the construction of effective mental models. In accordance with this paradigm the learner has to search continuously for information in the given learning environment in order to complete or stabilize an initial mental model which corresponds to an “a priori understanding” of the material to be learned. All current existing instructionally guided exploratory models for discovery learning were designed with a specific endpoint in mind. The goal is to create microworlds in which objects follow specific sets of rules. One example is a microworld in which balls fall in accordance with Newton’s laws of motion (cf. White, 1993). Students explore this model by developing hypotheses and then varying input parameters to investigate how well their conjectures align with the model. In math education the defining characteristic of this kind of exploratory learning is that students explore conventional mathematical symbolizations in experientially real settings. The instructional intent is usually well defined and typically involves the students’ development of the mathematical understanding necessary for the mature use of symbolizations (cf. the MathCars of Kaput, 1994). This author suggested that one might facilitate students’ learning by supporting their efforts to explore the physi-


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cal linkages between the mathematical symbolizations and their own experiences, and to generate new hypotheses. Moreover, he argued that “as the model develops […] the mental model based in the mathematical representations comes to relate more directly to conceptualizations of the setting” (Kaput, 1994, p. 390). However, with regard to settings of self-guided discovery learning, Doerr (1996) stated students themselves develop expressive models to explain phenomena using a variety of (software) tools. Here, students invent models on their own that express their developing interpretations of the phenomena in question. Doerr determined that this model-building approach begins with students’ informal understandings and progressively builds on it. Self-guided learning occurs as a multi-step process of model-building and revision (Penner, 2001). In terms of model theory, this process can be conceived as a procedure called “fleshing out” (JohnsonLaird, 1983, p 452) that continuously examines whether a model can be replaced with an alternative model or not. I have defined this as a Reductio ad absurdum that is at the core of mental modeling in general (Seel, 1991). However, self-guided discovery learning is very ambitious insofar as the learners must have previously achieved adequate problem-solving and metacognitive skills to guide their learning process. Therefore, for novice students it can be argued that self-organized discovery learning is closely associated with learning by trial-and-error but not by insight. Incidentally, Briggs (1990) demonstrated in a case-study that an instructional strategy aiming at discovery learning may dramatically increase the probability that faulty initial mental models may be stabilized. Consequently, a substantial conceptual change does not take place, and relatively stable intermediate states of causal understanding often precede the instructionally intended conceptual mastery (Galili, Bendall & Goldberg, 1993). In sum, as a matter of fact self-organized learning aiming at the creation of mental models can be rather pretentious. It is a process which even an expert might sweat over sometimes. Regardless of the choice of one of the aforementioned paradigms of model-centered instruction, I agree with Gibbons (2002) on the fact that instructional designers have to create effective learning environments and materials as well as a variety of time and space structures to influence model-centered learning. However, “the events of instruction, which are the structures we design, serve human learning processes under the ultimate control of the individual. Instruction, therefore, does not cause learning but supports learning intentions to which the learner commits. [...] Some of these processes (such as the initial processing of visual or auditory informa-

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tion) are involuntary, but many of them (focusing attention, finding and selecting associations, etc.) are completely voluntary.” (Gibbons, 2002, p.3) If we intend to initiate model-centered learning we have to take into consideration the preconceptions with which learners enter into a given learning environment and their motivation to engage in learning. Furthermore, we also have to take into consideration the quality of the learning material and the information which must be understandable, coherent, plausible etc. in order to persuade the students to engage in the learning environment. Actually, the learners’ preconceptions and motivational states as well as the quality of the given learning materials strongly influence the patterns of participation and persuasion (cf. Dole & Sinatra, 1998), understood here as central factors of effective model-centered instruction. By combining these factors with the theoretical framework of model-based learning and instruction developed by Buckley and Boulter (1999), one may describe the interplay between modelcentered learning and instruction can be described as in Figure 5. The top of the diagram is concerned with model-based teaching. It focuses on the patterns of participation, persuasion and model-building which individuals follow in the classroom to construct their understanding of some phenomenon. This is accomplished mainly through discourse with and about external representations, provided and guided by the teacher who facilitates negotiation among the discourse participants—including those not present such as the scientists who developed the conceptual models in the domain and the instructional designers who developed the materials and activities which are to facilitate of the learners’ understanding of the phenomenon. The bottom half of the diagram is concerned with model-based learning. It focuses on individuals’ construction of mental models of the phenomena under study. During the course of this process learners form an initial model of the phenomenon, either intententionally to meet some learning goal or spontaneously in response to some task. When the model is used successfully, it is reinforced and may eventually become a precompiled, stable model. If it turns out that the model is unsatisfactory, it may be revised or rejected in a progression of mental models. In the following section I will describe the state-of-the-art of related research on model-centered learning in the context of this theoretical framework.

RESEARCH ON MODEL-CENTERED INSTRUCTION In accordance with the foregoing argumentation I distinguish between


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FIGURE 5 The interplay between model-based learning and instruction

two basic settings or scenarios to influence the students’ construction of mental models through instructional intervention programs: • Scenario 1: Providing students with relevant information (e.g. presentation of a conceptual model) aiming at receptive model-centered learn-

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ing and • Scenario 2: Design-based modeling as employed in discovery learning. Research on scenario 1: Providing students with model-information When we consider the history of mental model research in the field of instruction we can observe a clear predominance of studies aiming at modeloriented learning explicitly directed by a teacher or an instructional program. Mayer (1989, p. 47) has expressed the pedagogical idea of this approach, commenting that “students given model-instruction may be more likely to build mental models of the systems they are studying and to use these models to generate creative solutions to transfer problems.” Accordingly, the learners are provided with a conceptual model (i.e. an external representation) constructed in accordance with instructional principles to illustrate the main components and relationships of a complex system with the help of graphical diagrams or object-based replica. Actually, many researchers are convinced of the effects of graphical diagrams or even “helpful video” on the construction of mental models, insofar as they consider these instructional media to be effective with regard to the creation of dynamic images that constitute the frame of reference for the construction of mental models (see, for example, Hegarty & Just, 1993; Schnotz & Kulhavy, 1994; Sharp et al., 1995). However, this presupposes that the learner is sensitive to characteristics of the learning environment (Anzai & Yokoyama, 1984), such as the availability of certain information at a given time, the way the information is structured and mediated, and the ease with which it can be found in the environment (cf. Seel, 2000). It has been argued that it is often easier for a beginning learner to assimilate an explanation (provided through a conceptual model) rather than to induce one individually. In this case, the conceptual model provided will be functionally incorporated in the thinking process, and related information can be progressively integrated in a more or less consistent manner to achieve substantial conceptual changes. Meanwhile, there are numerous studies which have demonstrated that the presentation of a conceptual model actually affects the construction of a task-related mental model depending on the stage in the learning process at which the conceptual model is presented. From my point of view, the seminal work of Mayer (1989) represents a milestone in this research. Mayer indicates that the presentation of modelrelevant information at the beginning of the learning process seems to increase both the quality of comprehension during the learning process and the quality of causal explanations at the end of the learning process.


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According to these findings, we presupposed in our own research that a conceptual model provided at the beginning of a lesson facilitates the construction of an adequate mental model for cognitively mastering the demands of the learning situation (cf. Seel, 1995; Seel & Dinter, 1995). However, the research on mental models in the 1980s has been criticized by several authors (such as Royer, Cisero & Carlo, 1993; Snow 1990) because it has been typically performed piece-meal, in small scale, specialized contexts. In order to overcome these shortcomings of experimental research, my research group looked for a more comprehensive instructional approach as a fundamental basis for initiating and directing model-oriented learning. Accordingly, our research in the past six years has centered around three main topics: (1) The investigation of the learning-dependent progression of mental models (more specifically of analogy models of dynamic systems of economics) in the course of a comprehensive instructional program; (2) how this progression can be guided by way of a particular instructional intervention, designed as a multimedia environment in accordance with principles of the Cognitive Apprenticeship approach, and (3) how to assess mental models and their learning-dependent progression as influenced by model-centered instruction. Actually, when we started in 1994 with the development of a multimedia environment aiming at an externally guided goal-oriented, and systematic influence upon the learners’ progression of mental models the Cognitive Apprenticeship approach of Collins et al. (1989) proved to be the only promising instructional strategy which corresponded with the idea of providing the students with model-instruction in the aforementioned sense. This immediately becomes clear when we consider the instructional methods of Cognitive Apprenticeship: Modeling, coaching, scaffolding, articulation, reflection, and exploration. Evidently, the instructional intervention of apprenticeship starts with the presentation of an expert’s conceptual model of the tasks to be accomplished, and then the students are coached and scaffolded to adapt this model for their own solutions (exploration) of the designed learning tasks. In the course of the 4M-project1 more than 400 students (secondary school, 17 years on average) accomplished the multimedia program ____________________________

From 1994 until 2001 we gratefully acknowledge financial support for this research from a grant provided by the German Research Assocation (Deutsche Forschungsgemeinschaft) with Grant-No. Se 399/4. 1

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Dynamic Systems of Economics, which was designed in accordance with the principles of Cognitive Apprenticeship. This project and its results have been described in several articles (e.g. Al-Diban & Seel, 1999; Seel et al., 2000). In five replication studies we investigated: • the effects of providing a conceptual model at the beginning of the learning process on the construction of a corresponding mental model; and • the long-term effectiveness of the multimedia learning program on both the acquired domain-specific knowledge and the stability of the initially constructed mental models. Over the project’s life it was possible to realize and evaluate the methods of the Cognitive Apprenticeship approach with the help of a step by step formative evaluation strategy. Parallel with this, we investigated the learning-dependent progression of mental models with the help of a specific diagnosis, causal diagrams, that confirmed central assumptions of the theory of mental models. In fact, causal models (for more details consult, Seel, 1999; 2001) proved to be suitable instruments for the assessment of a learner’s subjective assumptions about the causality of a dynamic system as well as for appropriate representations of the learner’s mental model of a dynamic system. On the whole, the results of our evaluation studies allow the conclusion that the Cognitive Apprenticeship approach can be considered an appropriate framework for the instructional design of environments aiming at modelcentered learning. So far the results correspond with observations and empirical results of other studies, such as those of Casey (1996), Chee (1995), and Lajoie and Lesgold (1989). This suggests that Cognitive Apprenticeship principles are suitable for the instructional design of learning environments in spite of the following reservations: • It proved to be very difficult to realize the methods of articulation and reflection in multimedia environments, and • the methods of scaffolding and exploration, which focus on the improvement of self-regulated learning, proved to be as less effective than expected. Numerous studies in the research field of conceptual change (cf. Dole & Sinatra, 1998) have indicated that students dynamically modify and restruc-


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ture their knowledge bases when externally provided information is judged to be more plausible and convincing. Accordingly, we especially investigated the permanence and stability of mental models generated after a student’s early exposure to a designed conceptual model. Thereby, we focused on two research questions: • Do the learners adapt the conceptual model designed by an expert they are provided with in the multimedia program and do they retain it in the course of the learning process? Therefore, are the learners’ causal diagrams similar to the conceptual models they are provided with? • Are there significant similarities between the causal diagrams constructed by the learners at several measurement points in the course of the multimedia program? In other words: Do the learners retain the causal diagrams they produced initially (defined here in terms of external representations of mental models) or do they vary depending on the changing demands of the learning tasks? Surprisingly, our investigations indicated that the subjects exhibited only a minor tendency to adopt the conceptual models they were provided with in the multimedia-program. Incidentally, they typically drew causal diagrams which indicated varying degrees of similarity to the provided conceptual models. Therefore, a conclusion from our research with far-reaching consequences for instruction is that mental models are not fixed structures of the mind, but are rather constructed when needed to master a learning situation with its specific demands. This contradicts the assumption that learners tend to adopt provided conceptual models when no relevant preconceptions are available in order to construct idiosyncratic mental models of the tasks they are trying to learn. Consequently, we cannot suppose a factual persistence of a mental model over time. Rather, it is more plausible to assume a situation-dependent reconstruction of previously generated mental models. As a consequence of the results of our investigations it could be concluded (1) that the learners constructed situation-bound problem solutions independently on according to the specific instructional strategies they were provided with (such as subsumption of learning tasks under a common schema vs. induction of a schema from analogous task examples); and

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(2) that an effective design of successful learning environments presupposes the provision of cognitive tools which facilitate and support an individual model-building and revision for problem solving. Research on scenario 2: Design-based modeling for exploratory learning For this scenario, the research on model-centered learning is not strongly embedded in the theory of mental models but rather integrated in the field of instructional investigations with an emphasis on the curriculum of different subjects, such as mathematics and science. Stewart et al. (1992) have delineated the central idea of these instructional approaches, commenting that “a science education should do more than instruct students with respect to the conclusions reached by scientists; it should also encourage students to develop insights about science as an intellectual activity.” (p. 318; see also Hestenes, 1987) Accordingly, advocates of this approach argue that “given that we wish to involve students in the practices of scientists, we focus primarily on model building.” (Penner et al., 1998, p. 430) Indeed in science, some of the most important goals of instruction are to help students develop powerful models so that they can make sense of their experiences involving light, gravity, electricity, and magnetism; it has also become evident that young students invent models of their own and that changing students’ ways of thinking must involve challenging and testing these models. The modelbuilding approach provides a significant challenge in understanding how to nurture, accommodate, and respond to the partial and incomplete models that students are likely to build with regard to phenomena of physics (see, for example, Clement, 1989; Vosniadou & Brewer, 1992, 1994). Interestingly, we can find a similar argumentation with regard to the learning of mathematics insofar as several authors, such as Doerr (1996), Gravemeijer (1999), Hodgson (1995), Lesh and Doerr (2000) and others, argue that mathematizing (e.g. quantifying, visualizing, or coordinating) is a particular form of modeling. It generally involves the use of specialized languages, symbols, graphs, pictures, concrete materials, and other notation systems for the development of mathematical descriptions and explanations. This obviously constitutes a heavy demand on learners’ representational capabilities. “The primary role of algebra at the school level is to develop confidence and facility in using variables and functions to model numerical patterns and quantitative relationships.” (National Council of Teachers of Mathematics, 1994) Accordingly, Lesh and Doerr (2000) as well as other


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authors discuss models that students should develop in attempts to produce mathematical descriptions or explanations of systems of the physical world. These authors argue that helping students to develop powerful models should be among the most important goals of science and mathematics instruction. In science and mathematics, where there is an emphasis on symbolic representations, it is often assumed that students do not (and cannot) develop appropriate symbol systems to make sense of systems in the external world that involve mathematical entities such as directed quantities (negatives), multivalued quantities (vectors), ratios of quantities, changing or accumulating quantities, or locations in space (coordinates). However, when confronted with the need to create meaningful models of experientially real situations, students can invent significant mathematical solutions on the basis of model constructions. Such “modeling is seldom a one-shot process; rather, model testing and evaluation are most often followed by model revision.” (Penner et al., 1998, p. 433). An analysis of the literature shows very good examples of this approach but unfortunately there is a substantial lack of empirical research including quantitative data which could be interpreted in accordance with the theoretical assumptions in the literature. This also holds true with regard to the currently prospering field of the Learning-byDesign approach, which focuses on the sampling of qualitative data (cf. Kafai & Ching, 2001). In view of this research situation we have recently started a long-term project which focuses on model-centered discovery learning (according to the theory of mental models) as guided through properly designed multimedia learning environments involving a particular tool to teach students analogical reasoning and the production of analogy models.2 At the moment, the research group is engaged in the construction and design of the learning environment for which we have defined several design features, such as the use of representational formats of multimedia technologies, context boundedness of the learning tasks, explications of the semantic depth structure, scaffolding, and networking by way of analogies between different domains. These design features are linked with several learning activities, such as the active construction of structural knowledge (as in Scandura’s Structural Learning Theory), the step by step development and refinement of a gener____________________________ 2 Again we are subsidized by a grant fromf the German Research Association (Deutsche Forschungsge meinschaft) with Grant-No. Se 399/8-1. The research group consists of Bettina Couné, Pablo Dummer, Katharina Schenk, and Susanne Steiner.

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al problem solving schema, cognitive experimenting (thought experiments), and conceptual networking. The first experimental study (in accordance with the idea of “enlarged design experiments,” Dummer, 2002) is planned for December 2002. As in the case of our former experiments in the aforementioned project, we hope to find quantitative data that confirm our theoretical assumptions about model building in the course of externally guided discovery learning. Thereby, we follow Scandura’s verdict that any theory of teaching and learning must include some way of finding out what students know at any phase of learning. And, “in addition, a fully adequate theory of teaching and learning must allow for the growth of knowledge over time as learners interact dynamically with a changing [...] environment.” (Scandura, 1988, p. 53)

RESUMÉ Model-based learning and instruction is a complex phenomenon which occurs not only in classrooms, but also in a variety of informal learning environments. It also occurs on many levels (individuals, groups of various size and composition, in diverse cultures). Nevertheless, the classroom is undoubtedly a prominent place for the improvement of model-based learning in various subject matter domains. Those who advocate model building and revision in science and mathematics consider modeling to be a specific kind of problem solving, and thus, they argue that modeling in the classroom would help to develop students’ problem-solving skills (cf. Hodgson, 1995). Moreover, Tanner and Jones (1994) believe that model building activities in the classroom improve students’ metacognitive competence. This is not the place for a detailed commentary on these beliefs but it is noteworthy to mention that some enthusiasts have a tendency to misplace the emphasis of discovery learning in science and mathematics by not paying sufficient attention to what it is that is being discovered. Therefore, Lesh and Doerr (2000) have pointed out that model building and revision in the classroom must correspond to the conceptual models as well as the main constructs of the scientific disciplines that underlie the curriculum in mathematics and science. Nevertheless, the “big idea” of those who advocate model building and revision in the math and science classroom is to provide students “with the skills they will need to accomplish this in the real world. This is the objective of ...modeling.” (Hodgson, 1995, p. 353) However, to do a good job we need a comprehensive and empirically valid theory of instructional design of


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model-centered learning in various instructional settings. To date, there have only been few attempts to develop a theory of instructional design for model-centered learning environments. One of them was developed by Gravemeijer et al. (2000) in close connection with Freudenthal’s (1973) comprehension of mathematics as an activity that involves solving problems, looking for problems, and organizing subject matter resulting from prior mathematizations or from reality. An important heuristic method for instructional design focuses on the role that emergent models play in individual students’ learning and in the collective mathematical development of the classroom community. It is possible for the designer to lay out a proposed developmental route for the classroom community in which students first model situations in an informal way (this is called a model of the situation) and then mathematize their informal modeling activity (this produces a model for reasoning). The transitions from a model of to a model for are generally consistent with Sfard’s (1991) historical analysis of the process of reification. Sfard argues that the history of mathematics is characterized by repeated processes of reification in which understandings that initially existed only in action were objectified, thus creating mathematical entities that were experienced as independent of activity. However, Lesh and Doerr (2000) have pointed out that models are interacting systems based in moe complex conceptual systems, and as such models cannot simply be handed to students in a meaningful form. This is the basis for the claim that models (constructs) must be constructed. But it is also the case that • construction can lead to a great many things (such as complex systems of low level facts and skills) that are not models for making sense of experiences) and • construction is not the only process that contributes to the development of models. For example, models evolve by being sorted out, refined, or reorganized at least as often as they evolve by being assembled (or constructed). Thus, some enthusiasts of “discovery learning” tend to overemphasize the process of discovery without paying much attention to what it is that is being discovered. Whereas some authors, such as Kafai and Ching (2001), focus on model-building activities of children acting as designers whereby they are not confronted with the shared conceptual models of experts I suppose that if instruction and learning focus on models and modeling, then it

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is absolutely critical to focus on models that correspond to the “big ideas” or main constructs and conceptual systems that underlie the curriculum in mathematics and science.

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Norbert M. Seel is Professor of Learning Research and Instructional Design and the Head of the Department of Educational Science of the Albert-Ludwigs-Universität of Freiburg, Germany. His areas of interest include basics and applied research in model-based learning and instruction, evaluation and psychometrics, instructional design and ISD.