A new approach: Computer-assisted problem-solving systems

Most researchers working on problem solving (Dewey, 1910; Newell & Simon, 1972 etc.) agree that a problem occurs only when someone is confronted with a difficulty for which an immediate answer is not available. However, difficulty is not an intrinsic characteristic of a problem because it depends on the solver’s knowledge and experience (Garrett, 1986; Gil-Perez et al., 1990). So, a problem might be a genuine problem for one individual, but might not be for another. In short, problem solving refers to the effort needed in achieving a goal or finding a solution when no automatic solution is available.

One of the fundamental achievements of education is to enable students to use their knowledge in problem solving (Reif et al., 1976; McDermott, 1991; Heller et al., 1992). Therefore, many researchers find that their students do not solve problems at the necessary level of proficiency (Van Heuvelen, 1991; Reif, 1995; Redish et al., 2006). To help improve the teaching and learning of physics problem solving, studies began in the 1970’s (McDermott & Redish, 1999).

Research on developing an effective general instruction for physics problem solving started at least 50 years ago (Garrett, 1986) and changed after the late 1970s with the works of Larkin & Reif (1979), Larkin et al. (1980), Chi et al. (1981), Larkin (1981), Heller & Reif (1984), Reif, (1995), Dufrense et al. (1997), Kozma & Russell (1997), Mestre (2001), Kozma (2003) and Kohl et al. (2007). Most of the research during this period aimed to identify the differences between experienced and inexperienced physics problem-solvers.

These studies show that the experienced problem solvers were individuals with important knowledge, experience and training in physics, and so the process of reaching a solution was both easy and automatic for them. In contrast, the inexperienced problem solvers had less knowledge, experience and training in physics, which means that they were facing real problems.

In physics problems, inexperienced problem solvers tend to spend little time representing the problem and quickly jump into quantitative expressions (Larkin, 1979). Instructors have found that inexperienced problem solvers carry out problem solving techniques that include haphazard formula-seeking and solution pattern matching (Mazur, 1997; Van Heuvelen, 1991). By contrast, experienced problem solvers solve problems by interjecting an another step of a qualitative analysis or a low-detail review of the problem before writing down equations (Larkin, 1979) This qualitative analysis used by experienced problem solvers, such as a verbal description or a picture, serves as a decision guide for planning and evaluating the solution (Larkin & Reif, 1979; Kohl & Finkelstein, 2008). Although this step takes extra time to complete, it facilitates the efficient completion of further solution steps and usually the experienced problem solver is able to successfully complete the problem in less time than an inexperienced problem solver.

Reif & Heller (1982) discussed this view of problem solvers by comparing and contrasting the problem solving abilities of inexperienced and experienced problem solvers. Their findings showed that the principal difference between the two was in how they organize and use their knowledge about solving a problem. Experienced problem solvers rapidly re-describe the problem and often use qualitative arguments to plan solutions before elaborating on them in greater mathematical detail. Inexperienced problem solvers rush into the solution by stringing together miscellaneous mathematical equations and quickly encounter difficulties. Inexperienced problem solvers do not necessarily have this knowledge structure, as their understanding consists of random facts and equations that have little conceptual meaning. This gap between experienced and inexperienced problem solvers has been well studied with an emphasis on classifying the differences between students and experienced problem solvers in an effort to discover how students can become more expert-like in their approach to problem solving (Larkin et al., 1980; Reif & Allen, 1992).

As well as differences in procedures, experienced and inexperienced problem solvers differ in their organization of knowledge about physics concepts. Larkin (1979) suggested that experienced problem solvers store physics principles in memory as chunks of information that are connected and can be usefully applied together, whereas inexperienced problem solvers must inefficiently access each principle or equation individually from memory. Because of this chunking of information, the cognitive load on an experienced problem solver’s short-term memory is lower, and they can devote more memory to the process of solving the problem (Sweller, 1988). For inexperienced problem solvers, accessing information in pieces places a higher cognitive load on short-term memory and can interfere with the problem solving process.

According to these findings, instead of researching the advantages of experienced problem solvers to produce a problem solving instruction, researchers can try to examine students’ difficulties by confronting real physics problems and showing methods to overcome these difficulties. By researching the characteristics of students’ problem solving patterns, a general instruction guideline can be produced to meet the various patterns of physics problem solving found among students. It may be that some inexperienced problem solvers have already had good physics problem solving skills that can serve as examples for other inexperienced problem solvers.

Most of the researchers examined general and specific problem solving strategies. The most notably general strategies are Polya’s (1945) and Dewey’s (1910) problem solving strategy steps. Dewey (1910) cited for his four steps (problem’s location and definition, suggestion of possible solution, development by reasoning the bearings of the solution and further observation and experiment leadings to its acceptance or rejection) problem solving strategy.

Polya (1945) is cited for his four steps problem solving strategy. The first step is Understanding the Problem, by identifying the unknown, the data and the condition, and then drawing a figure and introducing a suitable notation. The second step is Devising a Plan, in which the solver seeks a connection between the data and the unknown. If an immediate connection is not found, the solver considers related problems or problems that have already been solved, and uses this information to devise a plan to reach the unknown. In the third step, Carrying out the Plan, the steps outlined in part two are carried out, and each step is checked for correctness. In the final step Looking Back, the problem solution is examined, and arguments are checked.

Reif et al. (1976) tried to teach students a simple problem solving strategy consisting of the following four major steps: Description, which lists clearly the given and wanted information. Draw a diagram of the situation. The next step, Planning, selects the basic relations suitable for solving the problem and outline how they are to be used. The Implementation step performs the preceding plan by doing all necessary calculations. The final step is Checking, which ensures that each of the preceding steps was valid and that the final answer makes sense.

Over the past 40 years, several physics problem solving methods have used the logical problem solving model (Heller & Heller, 1995); teaching a simple problem solving strategy (Reif et al., 1976); the systematic modelling method (Savage & Williams, 1990); the didactic approach (Bagno & Eylon, 1997); the collaboration method (Harskamp & Ding, 2006); the computer-assisted instruction (Bolton & Ross, 1997; Pol, 2005) and the translating context-rich problem (Heller et al., 1992; Heller & Hollabaugh, 1992; Yerushalmi & Magen, 2006); the creativeness approaches in problem solving (Walsh et al., 2007; Bennett, 2008); and the epistemic games (Tuminaro & Redish, 2007) have all been produced by researchers to help students improve their problem solving.

The steps of the University of Minnesota problem solving strategy include Focus the Problem, which involves determining the question and sketching a picture, and selecting a qualitative approach. The next step, Describe the Physics, includes drawing a diagram, defining symbols, and stating quantitative relationships. The Plan a Solution step entails choosing a relationship that includes the target quantity, undergoing a cycle of choosing another relationship to eliminate unknowns and substituting to solve for the target. The step Execute the Plan involves simplifying an expression, and putting in numerical values for quantities if requested. The final step is Evaluate the Answer, which means evaluating the solution for reasonableness, and to check that it is properly stated (Heller & Heller, 1995).

Loucks (2007) introduced a method for solving university physics problems, particularly when algebra is involved, which is similar to Savage and Williams’ problem solving. For Loucks, the most important factor is to setup the problem, so that the solver can determine which equations are suitable. Once it is setup, the problem becomes simply a mathematical problem. Loucks recommended five steps to effectively solve physics problems with algebra; a) identify the type of problem (for example, concept, keyword or feature); b) sort by interval and/or object (e.g., list everything, draw diagram); c) find the equation and unknowns, try to relate the intervals; d) outline solution or make a chain of reaction; and e) do the mathematics.

Mayer (2008) asserted that effective practice in problem solving should be given in a structured way, but not in a step-by-step procedure. He concluded that problem-solving programs are most effective when they focus on problem solving not as a single intellectual ability, but as a collection of smaller component skills. He stressed that successful problem-solving training involves specific problem-solving skills, contextualized tasks that students are expected to perform in school, practice in the process of problem-solving, discussion of the problem-solving process, and teaching problem-solving before students have fully mastered content, knowledge of a domain. He also stressed that problem solving training should be provided in addition to developing domain-specific content knowledge. Students need to learn domain-specific problem-solving skills in order to become successful learners in physics.

Tóth & Sebestyén (2009) studied the importance of the cognitive variables to problem solving in chemistry. They assumed that the success of the problem solving is basically determined by three block variables containing six predictor variables:

1. Prior knowledge:

a) Specific knowledge: knowledge directly related to the problem.

b) Non-specific but relevant knowledge: knowledge related to the subject area of the problem.

2. Linkage:

a) Concept relatedness: relatedness between concepts involved in problem solving.

b) Idea association: linkage between the information retrieved from the existing knowledge structure and the external cues.

3. Problem recognition skill:

a) Problem translating skill: the capacity to comprehend, analyzes, interpret and define a given problem.

b) Prior problem solving experience: the prior experience in solving the similar problems.

Based on empirical research, they found that the significance of the above variables depends on the topics and level of the chemistry problems; however, these differences in topics and levels have little effect on the importance of these variables on problem-solving performance.

Kowalski et al. (2009) examined the review of problem solving strategies. Their study was a modification of well-established steps used to teach increased competency in problem-solving strategies in engineering courses. They combined the problem solving strategy steps with three steps (identifying of the fundamental principle, solving and checking).

In this research a combination of problem solving strategies and a computer based learning tool is performed (Integrated Problem Solving Strategy steps (IPSS)) to increase the benefits of the current LON-CAPA education system.