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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 |
External representations to facilitate problem solving
Using external representations through symbols and objects to illustrate a learner’s knowledge and the structure of that knowledge can facilitate complex cognitive processing during problem-solving (Vekiri, 2002). Such external representations can help a learner elaborate the problem statement, transform its ambiguous status to an explicit condition, constrain unnecessary cognitive work, and create possible solutions (Scaife & Rogers, 1996). Larkin (1989) argued that an external representation supports human problem-solving by reducing the complexity of problem and its associated mental workload. Moreover, Bauer and Johnson-Laird (1993) showed that diagrams helped learners solve a problem more effectively and efficiently.
Learners have a limited working memory, and instructional representations should be designed with the goal of reducing unnecessary cognitive load. However, prior knowledge can determine the ease with which learners can perceive and interpret visual representations in working memory (Cook, 2006). Three issues developed from using multiple representations in problem solving: how students use multiple representations when solving problems, how different representational formats affect student performance in problem solving, and how the utilization of representational learning strategies can lead to substantial improvements in problem-solving.
Physics education literature indicates that using multiple representations is beneficial for student understanding of physics ideas and for problem solving (Dufresne, Gerace, & Leonard, 1997; Larkin, 1985; Van Heuvelen, 1991). These representations can include but are not limited to words, diagrams, equations, graphs, and sketches. However, there is less research on thought processes that students use while applying multiple representations in problem solving. The hypothesis of Rosengrant, Van Heuvelen and Etkina (2006) is that students are probably aware intuitively that they do not have the mental capacity to remember all the information in the problem statement, and thus use the representations to visualize an abstract problem situation. Their previous research (Rosengrant, Van Heuvelen, & Etkina, 2005) showed that students improve their chances of solving a problem correctly if they include concrete diagrammatic representations as part of the solving process.
Kohl and Finkelstein (2005) examined student performance on homework problems given in four different representational formats (mathematical, pictorial, graphical, and verbal), with problem statements as close to isomorphic as possible. They found that there were statistically significant performance differences between different representations of nearly isomorphic statements of problems. They also found that allowing students to choose which representational format they use improves student performance under some circumstances and degrades it on others. In another work (Kohl & Finkelstein, 2006a) reported that students who learnt physics using lots of representations were less affected by the specific representational format of the problem. Finally, these authors investigated in more detail how student problem-solving performance varies with representation (Kohl & Finkelstein, 2006b). They discovered that student strategy often varies with representation, and that students who show more strategy variation tend to perform more poorly. They also verified that student performance depends sensitively on the particular combination of representation, topic, and student prior knowledge.
Longo, Anderson and Wicht (2002) used knowledge representation and metacognitive learning strategies called visual thinking networking. In these strategies students constructed network diagrams which contained words and figural elements connected by lines and other representations of linkages to represent knowledge relationships. Earth science learning was improved in the area of problem solving for students who used visual thinking networking strategies. Chan and Black (2006) investigated what learners need for constructing mental models to understand and reason about systems and scientific phenomena which can be described in text, pictures, and animation. Their results corroborated that, for simple and moderately systems, students did not perform significantly different on learning activities. However, as the systems became more complicated, students who directly manipulated the animation outperformed those in text-only groups and texts-and-static-visuals groups on the outcome measures. Mayer’s (1999) research pinpointed some conditions under which multimedia learning can lead to substantial improvements in problem-solving transfer. Overall, students make better sense of a scientific explanation when they hold relevant visual and verbal representations in their working memory simultaneously. When multimedia messages are designed in ways that overload visual or verbal working memory, transfer performance is adversely affected.
