Asia-Pacific Forum on Science Learning and Teaching, Volume 8, Issue 2, Article 4 (Dec., 2007) Joan Josep SOLAZ-PORTOLÉS & Vicent Sanjosé LOPEZ Representations in problem solving in science: Directions for practice Previous Contents Next

Mental models, problem solving, and cognitive variables: Directions for practice

The construction of a mental model results from links made between the elements of the problem description and the underlying knowledge base (Heyworth, 1998). Expert performance seems to lie in the organization of the experts’ domain knowledge. Experts possess a large knowledge base that is organized into elaborate, integrated structures, whereas novices tend to possess less domain knowledge and a less coherent organization of it (Zajchowski & Martin, 1993). The way knowledge is organised allows optimised access to the long-term memory. The borders between long-term memory and working memory of experts become fluent so that the capacity of the working memory in comparison to a novices’ memory is considerably expanded (Ericsson & Kintsch, 1995). Humans chunk content pieces together such that very large amount of content are concurrently accessible. Experts make use of big chunks that were developed over those years which they became experts (Brooks & Shell, 2006).

According to Kempa’s studies (Kempa, 1991; Kempa and Nicholls, 1983) a direct connection emerges between cognitive structure (long-term memory structure) and problem-solving difficulties. These difficulties are usually attributable to one or more of the following factors.

• The absence of knowledge elements from a student’s memory structure.
• The existence, in the student’s memory structure, of wrong or inappropriate links and relationships between knowledge elements.
• The absence of essential links between knowledge elements in the student’s memory structure.
• The presence of false or irrelevant knowledge elements in the student’s memory structure.

The knowledge needed to solve problems in a complex domain is composed of many principles, examples, technical details, generalizations, heuristics, and other pieces of relevant information (Stevens & Palacio-Cayetano, 2003). The development of a knowledge base is important both in terms of its extent and its structural organisation. To be useful, students need to be able to access and apply this knowledge, but the knowledge must be there in the first place. Any claim that is not so, or that knowledge can always be found from others sources when it is needed, is naive (Dawson, 1993).

Shavelson, Ruiz-Primo and Wiley (2005) present a conceptual framework for characterizing science goals and student achievement that includes declarative knowledge (knowing that, domain-specific content: facts, definitions and descriptions), procedural knowledge (knowing how, production rules/sequences), schematic knowledge (knowing why, principles/schemes) and strategic knowledge (knowing when, where and how our knowledge applies, strategies/domain-specific heuristics). For each combination of knowledge type and characteristic (extent-how much?; structure –how it is organized?; and others), Li and Shavelson (2001) have begun to identify assessment methods. However, while we can conceptually distinguish knowledge types, in practice they are difficult to distinguish and assessment methods do not line up perfectly with knowledge types and characteristics.

Ferguson-Hessler and de Jong (1990) distinguished four major types of knowledge for the content of an adequate knowledge base with regard to its importance for problem solving.

• Situational knowledge is knowledge about situations as they typically appear in a particular domain. Knowledge of problem situations enables the solver to sift relevant features out of the problem statement.
• Declarative knowledge, also called conceptual knowledge, is static knowledge about facts and principles that apply within a certain domain.
• Procedural knowledge is a type of knowledge that contains actions or manipulations that are valid within a domain. Procedural knowledge exists alongside declarative knowledge in the memory of problem solvers.
• Strategic knowledge helps the student to organize the problem-solving process by showing the student which stages he should go through in order to reach a solution.

Working memory capacity plays an important role in many different types of problem solving (Welsh, Satterlee-Cartmell, & Stine, 1999). The ability to maintain information in a highly activated state via controlled attention may be important for integrating information from successive problem-solving steps, including the construction and manipulation of mental models. Working memory capacity may also be involved in a number of well-documented problem solving “difficulties” (Solaz-Portolés & Sanjosé, 2007c). Studies on the association between limited working memory capacity and information load in problem-solving provided support for the positive relationship between working memory and science achievement. Because working memory capacity limits the amount of information which can be concurrently processed, performance on science problem-solving tasks is expected to drop when the information load exceeds students’ working memory capacity (Johnstone & El-Banna, 1986). Opdenacker, Fierens, Brabant, Sevenants, and Slootamekers (1990) study reported that students gradually decreased their chemistry problem-solving performances when the amount of information to be processed exceed their working memory capacity. This phenomena is also consistent with Sweller’s (1994) cognitive overload theory, which posits that learning processes will be negatively affected if the cognitive load exceeds the limit of working memory capacity.

In science, mental capacity (M-space) is associated with students’ ability to deal with problem-solving (Níaz, 1987; Tsaparlis, Kousathana & Níaz, 1998). Gathercole (2004) found a strong relationship between working memory capacity and science achievement: the correlation coefficients between working memory measure and science achievement ranged from 0.32 to 0.5. Danili and Reid (2004) found that students with high and low working memory capacity differed significantly in their performance on chemistry tests. Tsaparlis (2005) examined the correlation between working memory capacity and performance on chemistry problem-solving and the correlations ranged between 0.28 and 0.74.

From Anderson’s cognitive perspective, the components of science knowledge required to solve problems can be broadly grouped into factual (declarative), reasoning (procedural), and regulatory (metacognitive) knowledge/skills, and all play complementary roles (Anderson, 1980). According to O’Neil and Schacter (1999), to be a successful problem solver, one must know something (content knowledge), possess intellectual tricks (problem-solving strategies), be able to plan and monitor one’s progress towards solving the problem (metacognition), and be motivated to perform. Mayer (1998) examined the role of cognitive, metacognitive and motivational skills in problem solving, and concluded that all three kinds of skills are required for successful problem solving in academic settings.

Artz and Armour-Thomas (1992) suggest the importance of metacognitive processes in mathematical problem solving in a small-group setting. A continuous interplay of cognitive and metacognitive behaviours appears to be necessary for successful problem solving and maximum student involvement. Similarly, Teong (2003) demonstrated how explicit metacognitive training influences the mathematical word-problem solving. Results from his study revealed that experimental students outperformed control students on ability to solve word-problems. Experimental students developed the ability to ascertain when to make metacognitive decisions, and elicit better regulated metacognitive decisions than control students. Longo, Anderson and Wicht (2002) used an experimental design to test the efficacy of a new generation of knowledge representation and metacognitive learning strategies called visual thinking networking (VTN). In these strategies, students constructed network diagrams that contained words and figural elements connected by lines and other representations of linkages to represent knowledge relationships. Students who used the VTN strategies had a significantly higher mean gain score on the problem solving criterion test items than students who used the writing strategy for learning science (students used other strategies of learning including writing assignments). To get an overview of the characteristics of good and innovative problem-solving teaching strategies, Taconis, Fergusson-Hessler and Broekkamp (2001) performed an analysis of a number of articles published between 1985 and 1995 in high-standard international journals, describing experimental research into the effectiveness of a wide variety of teaching strategies for science problem solving. As for learning conditions, both providing the learners with guidelines and criteria they can use in judging their own problem-solving process and products, and providing immediate feedback were found to be important prerequisites for the acquisition of problem-solving skills. Abdullah (2006) indicated that there are only a few studies looking specifically into the role of metacognitive skills in physics despite the fact these skills appear to be relevant in problem solving. This researcher has investigated the patterns of physics problem-solving through the lens of metacognition.

Based on the overview on problem solving presented here, a number of instructional measures that will assist teachers are suggested below.

• A conceptual understanding of the topic must be obtained before students are given problems to solve, rather than trying to get this understanding by means of problem solving. A valuable science education will integrate the process of acquiring and applying conceptual knowledge. One technique that can be used by teachers to help students organise their understanding of a topic is concept mapping (Pendley, Bretz, & Novak, 1994). The introduction of a concept map can often assist students to understand the concepts and the relationships between them (Novak & Gowin, 1984).
• Instructional texts are dominated by declarative knowledge whereas procedural and situational knowledge is more implicit and has to be extracted, often by deep processing. Stimulating specific, deep study processes (e.g., explicating, relating, and confronting) might encourage students to change their learning habits (Ferguson-Hessler & de Jong, 1990).
• Traditional methods and instructional strategies of teaching science (lectures by the teacher, follow-the-recipe laboratory activities, exercise-solving recitation sessions, and examinations oriented toward algorithmic or lower-order cognitive skills) are not compatible with attaining conceptual learning and higher-order cognitive skills (Zoller et al., 1995). A major purpose of science education should be to develop instructional practices for developing scientific reasoning skills such as laboratory work, inquiry-based science, computer simulations, quantitative data analysis, constructing explanations, and critical thinking and decision-making capacity. Improvement in reasoning skills has been shown to occur as a result of prolonged instruction and can lead to long-term gains in science achievement (Shayer & Adey, 1993). This study indicates that duration and intensity of exposure to reasoning situations are important factors for development of reasoning skills and that more individually targeted interventions may enrich/personalize the process.
• Encouraging an understanding of problems, rather than giving numerical procedures which may be memorized and used without understanding (Neto & Valente, 1997). This can be achieved using text-based or diagrammatic stimuli that require a knowledge of underlying concepts or basic theories of science. Qualitative discussions could be carried out while problems are solved on the chalkboard and also by getting students to work together while solving problems with students being asked to derive general procedures rather than mathematical solutions.
• Provide students with diverse, continual and prolonged problem-solving experiences. Associated with all problems are three variables: the data provided, the method to be used and the goal to be reached (Johnstone, 1993). Once students have derived and understood procedures for basic problems (recall of algorithms), they should be given plenty of practice to the other problem types, for example, problems unfamiliar to the student that require, for their solution, more than conceptual knowledge application, analysis, and synthesis capabilities, as well as making connections and evaluative thinking on the part of the solver. Give practice of similar problem solving strategies across multiple contexts to encourage generalization.
• Offer strategies in metacognition, such as teaching the existence of functional knowledge types and the role of problem schemata. Use problem-solving heuristics and metacognitive activities (Lorenzo, 2006). Explain the role of metacognitive skills in the steps in problem-solving. Metacognitive skills can be found in the steps of planning, reflecting (monitoring progress), checking (verifying results), and interpreting problem-solving (Abdullah, 2006).
• Alloway (2006) suggests that the learning progress of students with poor working memory skills can be improved dramatically by reducing working memory demands in the classroom. She recommends a number of ways to minimise the memory-related failures in learning activities: by using the instructions that are as brief and simple as possible, by reducing the linguistic complexity of sentences, by breaking down the tasks into separate steps, by providing memory support, by developing in the students effective strategies for coping with situations in which they experience working memory failures, etc.
• It is useful for the teacher to understand that the M-demand (mental demand) of an item (problem) can be changed without changing its logical structure. This can facilitate student success by decreasing the amount of information required for processing and, avoiding working memory overload (Níaz, 1987). Johnstone, Hogg, and Ziane (1993) suggest physics problems can be presented in a way that reduces the noise input of the processing system, and consequently allows greater success for all students, particularly field-dependent students (students with worse ability to disembed information in a variety of complex and potentially misleading instructional context). This means words, combined with a diagram, can reduce memory overload.
• Sweller, van Merrienboer, and Paas (1998) argued that students only had to maintain the problem state and any problem-solving step for that state when solving goal free problems, thus reduced cognitive load.