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Asia-Pacific Forum on Science Learning and Teaching, Volume 8, Issue 2, Article 4 (Dec., 2007) Representations in problem solving in science: Directions for practice |
Internal representations constructed during problem solving: mental models
According to the cognitive psychologist Mayer (1992) the process of solving problems has two steps, problem representation and problem solution. For problem representation, a learner needs to transform a problem’s description to his or her internal mental representation in two stages: problem translation and integration. Problem translation extracts concepts from the textual description of the problem by using linguistic and semantic knowledge. Linguistic knowledge is used to comprehend the words’ meanings in the textual description, while semantic knowledge means factual knowledge in the world. Problem integration requires a learner to connect sentences in a problems’ description and produce a coherent representation. At this stage, schematic knowledge of problem classification is needed to integrate the pieces of information provided by the problem. Moreover, schematic knowledge allows a learner to determine the category of a problem. After the problem’s description is translated into the learner’s internal mental representation (mental model), it means that the learner has already comprehended the problem.
Pribul and Bodner (1987) concluded that the preliminary stages in the problem-solving process that involved disembedding the relevant information from the statement of the problem and restructuring or transforming the problem into one the individual understands are particularly important in determining the success or failure of the problem-solving process. Bodner and Domin (2000) suggest that an essential component of an individual’s problem solving behaviour is the construction of a mental representation (mental model) of the problem that can contain elements of more than one representation system. The first representation establishes a context for understanding the statement of the problem. In some cases, this representation contains enough information to both provide a context for the problem and to generate a solution to the problem. In other cases, additional representations may be needed. According to Slotta, Chi, and Joram (1995), problem solvers set up some initial representation based on key words in the problem statement. The information is often closely tied to real, familiar objects which in the case of the chemistry problems are images of laboratory apparatus or procedures. This representation is not linguistic but based on the individual’s experience with, and knowledge about, the world. Bodner and Domin (2000) also found that successful problem solvers construct significantly more representations while solving a problem than those who are not successful. Unsuccessful problem solvers seem to construct initial representations that active an inappropriate schema (also referred to as frames or scripts, relate to one’s knowledge about science) for the problem.
One of the most influential theories to be formulated in cognitive psychology in recent years is Johnson-Laird’s (1983; 2000) theory of mental models. The theory seeks to provide a general explanation of human thought; at its core is the assertion that humans represent the world they are interacting with through mental models. In order to understand a real-world phenomenon a person has to hold, what Johnson-Laird describes as, a working model of the phenomenon in his or her mind. Johnson-Laird has formulated his mental model definition in his attempt to explain the reasoning processes in tasks of syllogisms and language comprehension. The author proposes that reasoning about a problem is facilitated if a person utilises a mental model that represents the relevant information in an appropriate fashion for the problem to be solved.
This theory is based on three main assumptions (Johnson-Laird, 2000).
• Each mental model represents a possibility. Models can represent relationships among three-dimensional entities or abstract entities; they can be static or kinematic. They underlie visual images, though many components of models are not visualizable.
• A mental model is iconic, that is, its parts correspond to the parts of what represents, and its structure corresponds to the structure of the possibility. The iconic nature of the model yields a conclusion over and above the propositions used in constructing the model.
• Mental models represents what is true according to the premises, but by default not what is false.
Johnson-Laird’s mental model theory proposes a semantic, non-rule-based approach reasoning. According to mental model theory, human deduction depends on the construction and manipulation of analogical models in the mind. Model building and manipulation are processes that people carry out on line. Thus, models are not retrieved from long-term memory as rules or schemas are. To execute cognitive tasks, a person forms in working memory a mental representation, combining the information stored in long-term memory with the information on the task characteristics extracted by perceptual processes (Cañas, Antolí, & Quesada, 2001). Reasoning capacity limitations are explained within this theory as a consequence of the limitations in the human processing capacity. The limited capacity of working memory would restrict the number of possible models considered (Santamaría, García-Madruga, & Carretero, 1996). For this theory, the number of models is the main factor of difficulty in syllogistic reasoning. In fact, problems generating two or three mental models are more difficult than single-model problems (Johnson-Laird & Bara, 1984)
