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General methods for solving physics problems

Cognitive apprenticeship has been used as a framework to explore the affective side of undergraduate research experiences Sadler et al. Although cognitive apprenticeship is not useful for teaching rote knowledge, it is a robust and well-researched technique for teaching complex tasks in many disciplines.

The committee has characterized the strength of conclusions that can be drawn from this research as moderate because the body of research includes a review and a line of research with multiple studies that were conducted in multiple courses. Particularly in design, it is important to use authentic problems and to sequence experiences within various courses to support the learning of core concepts.

Solving physics problems how to solve physics problems

Strategies such as case analyses, model-eliciting activities,. However, these activities must be implemented correctly to be effective. Incorporating reflection and self-explanation prompts into instruction also has been shown to improve student problem solving Cheville, ; Cordray, Harris, and Klein, ; Litzinger et al. The strength of conclusions that can be drawn from biology research on problem solving is limited because the research base consists of a few studies that have been conducted in the context of single courses.

However, consistent with findings from physics and engineering, the results suggest that problem-solving skills can be enhanced through instruction. Invention activities are based on work that challenges students to solve problems that seem unrelated to current class material, which then helps students to construct a mental framework that promotes better understanding of the course content. Students in a first-year biology class who participated in an invention activity began working on problems much more quickly and generated more hypotheses many of which were plausible than students who did not participate in the invention activity Taylor et al.

As discussed in Chapter 6 , collaborative problem-solving activities are increasingly popular in physics, chemistry, and biology. Some recent work has been done to develop and validate tools for comparing collaborative and individual problem-solving strategies in large students biochemistry courses where students discuss ill-defined problems in small online groups Anderson et al. Both of these assessment tools allow students to regularly practice their problem-solving skills, and, perhaps more importantly, allow instructors the opportunity to provide targeted intervention, as appropriate, to groups.

Studies using these instruments are ongoing and have not yet been published. Problem-solving skills in the geosciences are commonly taught in the context of problem-based learning Macdonald et al. With instructional strategies and activities that are influenced by Bransford, Vye, and Bateman and Kolb , problem-based learning in the geosciences often involves ill-defined problems that have applications to society, such as environmental issues, public policy, geology and human health, natural hazards, and Earth resources see Ishikawa et al.

The products of these learning activities typically are measured against professional norms of geoscience research projects, such as geologic maps and written reports Carlson, ; Connor, ; de Wet et al. For the most part, the geoscience education literature describes these activities and does not examine their efficacy. However, Ault made a notable early effort to formulate a research agenda on problem solving for Earth science education, laying out the difficulties that confront students.

In addition, as discussed in Chapter 6 , technologies such as GPS tracking devices are being used to monitor student navigation and yield insight into problem-solving skills Riggs, Balliet, and Lieder, ; Riggs, Lieder, and Balliet, That research reported an optimum amount of relocation and backtracking in field geology: too much retracing indicates confusion, and too little reoccupation of key areas appears to accompany a failure to recognize important geologic features.

Early research in physics emphasized expert-novice differences in various aspects of the solution process, whereas chemistry education research and later research in physics has examined the. Most of the research in engineering has addressed instructional strategies, particularly around authentic problems; instruction is also an important area of inquiry for physics.

In most disciplines, considerably less research exists on problems that are more characteristic of what scientists and engineers encounter in their professional lives. Students novices have difficulty with all aspects of problem solving and approach well-defined problem solving in ways that are consistently and identifiably different from those of experts.

Specifically, experts often preferentially focus on creating a representation of the problem at the outset. In addition, experts and undergraduate students represent problems in very different ways, with experts attending to the underlying principles required for solution and students focusing on superficial features such as the particular objects mentioned in the problems. These differences have important implications for problem solving success and, in turn, instruction. Nonetheless, some research shows that students often do not persist in using effective strategies over the long term.

Problem solving has been a significant focus of DBER in many disciplines, and DBER has generated important insights into the nature of the problem-solving process, differences between experts and novices, and strategies for improving problem solving. However, some areas remain ripe for exploration. For example, little DBER has investigated individual and.

A better understanding of similarities and differences in problem solving among subpopulations of students is needed, along with careful studies investigating the effects of various individual differences spatial skills, working memory capacity, logical thinking ability and their implications for instruction. In all disciplines, DBER scholars have a pressing need for measurement tools that will assess student problem-solving skills for large numbers of students in an authentic classroom setting.

Some of these tools have been developed in physics Docktor and Heller, , and in chemistry Cooper et al. Many research papers offer implications for teaching, but relatively few actually investigate the effect of an intervention designed to improve problem solving in some context most of these studies come from physics, chemistry, and engineering. A productive approach might be to identify trajectories that can lead to greater problem-solving expertise Lajoie, Further research on attributes that might characterize trajectories toward problem-solving competence could include data on interpersonal interactions when discussing problems, and the use of methodologies such as eye tracking Smith, Mestre, and Ross, Systematic explorations also are needed of the effects of changing problem features e.

In addition, strategies should be developed for effectively reducing working memory load while still highlighting important aspects of problem solving. Sweller and colleagues Owen and Sweller, ; Sweller and Levine, ; Sweller, Mawer, and Ward, in psychology have shown that one effective way to accomplish this goal is to have students engage in open-ended problem solving rather than attempt to reach a particular goal e. As discussed, the open-ended approach reduces the number of variables and problem conditions that students must keep in their working memory.

This research has used problems in kinematics, geometry, and trigonometry, which suggests that the technique may be widely applicable to the science and engineering domains that are the purview of this report. Real-world problems are often considerably different from the types of problems students typically solve in the laboratory or class, because they are ill-defined, messy, and knowledge intensive Novick and Bassok, Most DBER on problem solving addresses well-defined problems. Substantial work remains to be done to understand how students approach less well-defined problems and how to improve their ability to tackle these problems.

Although well-defined numerical problems are typical in traditional science and engineering courses, most practicing scientists and engineers typically solve conceptual problems, such as deducing structure with spectroscopic tools and designing experiments or approaches to target molecules. The consideration of well-defined versus ill-defined problems naturally leads to the distinction between problem solving and problem finding or problem discovery. Before professionals engage in problem solving, they must confront the critical initial step of choosing which problem s to solve. Not all problems are equally worthy of extended effort, and not all are equally likely to result in significant insights or breakthroughs.

For scientists and engineers, therefore, problem finding is crucial.

Three Tips for Solving Physics Problems

In most educational situations, however, students are simply provided problems by their teachers. Instructors and discipline-based education researchers may under-emphasize the importance of problem finding because, traditionally at least, it is not a task in which students are expected to engage. In biology and the geosciences, rich opportunities exist to conduct research on ill-defined or open-ended problems. As physics education research and chemistry education research have done, this work can readily extend the more general research on the development of problem-solving skills in cognitive science.

In the geosciences, it would be productive to build on emerging research on cognitive apprenticeship and related work on metacognition in which geoscientists reveal their thought processes in a mentoring capacity to students Manduca and Kastens, ; Petcovic and Libarkin, In addition, abstract spatial representations can actually modify, and in some cases simplify, the nature of a task Larkin and Simon, For example, people can usually estimate proportions more easily from a pie chart than from a table of numeric data.

In addition to interpreting representations produced by experts, students can construct their own representations to enhance learning and engagement Ainsworth, Prain, and Tytler, This suite of skills has been termed representational competence Hegarty, Developing representational competence requires the ability to mentally manipulate two- and three-dimensional objects, a skill that is called visuospatial thinking or spatial ability.

Given the importance of spatial representations and thinking processes in science, it seems logical that spatial ability is correlated with participation in science generally Shea, Lubinski, and Benbow, ; Wai, Lubinski, and Benbow, ; Webb, Lubinski, and Benbow, However, as the following discussion illustrates, evidence from DBER on the role of spatial ability is mixed.

Spatial thinking and the use of representations are important areas of inquiry for DBER because representational competence is so vital to acquiring expertise within a discipline.


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For example, the visualization and representation of the unseen molecular level is central to a robust understanding of chemistry. Chemistry students must learn how to create novel, discipline-specific representations, how to translate those representations into the more familiar equation format, and how and when to apply each representational format for solving problems. As another example, the ability to visualize a three-dimensional image from a two-dimensional graphical representation,.

In the science and engineering disciplines, the represented world might be a problem to be solved or a device to be designed. These elements could be any of the following:. Rules for mapping elements of one world to those of the other world, or a set of conventions for constructing a particular type of representation Hegarty, Carpenter, and Just, , which students must learn if they are to successfully use appropriate representations to solve problems and reason about scientific phenomena.

Processes that operate on the representing world. One set of processes uses the mapping rules to create the representation. Other processes then extract information from the representation to reason about the represented world. DBER on representations and spatial ability is particularly valuable in understanding the many disciplinary differences that pertain to thinking visually and understanding visual representations.

For example, in some disciplines e. Mental animation ability may be more important in disciplines for which motion is a central concern e. Disciplines may also differ in the extent to which they use graphical versus mathematical representations as the means of conveying critical insights. In a comparison of representations in scientific papers across several scientific fields, authors of geoscience and chemistry papers were found to use the most figures whereas authors of physics papers inclined more toward equations and psychology authors toward tables Kastens and Manduca, Biology is increasingly coming to rely on mathematical representations, especially to interpret large genomic databases.


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  6. In chemistry, spatial and mathematical representations are both important. Different science and engineering disciplines also may differ in the extent to which they call upon large-scale versus small-scale spatial ability Hegarty et al.

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    The two kinds of spatial information may be processed separately by the human visual system Previc, Hegarty et al. It should be noted, however, that tools for assessing small-scale spatial abilities are far more advanced than those for assessing large-scale spatial abilities Hegarty, This section discusses DBER on how students develop, use, and interpret representations, and the role of spatial thinking in visualization and mental model formation.

    A critical theme in this research is the importance of general cognitive and perceptual factors for understanding and reasoning with representations in science and engineering, as well as features related to the diagrams themselves. Because the breadth of cognitive science research in this area reflects the cross-disciplinary importance of representations, much of this research has used materials and tasks from various science disciplines. Many of the disciplinary differences just described are reflected in the focus of DBER.

    In physics and chemistry, the research base on spatial ability and the use of representations is strong because multiple studies exist—many of relatively large scale—with high convergence of findings. As characterized by Docktor and Mestre , p.

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    Some studies investigate the representations students construct during problem solving and how they use those representations Heller and Reif, ; Larkin, ; Rosengrant, Etkina, and Van Heuvelen, ; Van Heuvelen and Zou, , whereas other studies explore the facility with which students or experts can translate across multiple representations Kohl and Finkelstein, ; Meltzer, Still other studies in physics focus on student difficulties with particular representations. More than studies exist on spatial thinking and representations in chemistry, including books Gilbert and Treagust, and reviews Taber, These studies examine difficulties translating between representations Gilbert and Treagust, ; Johnstone, , the role of spatial ability in visualization and mental model formation Abraham, Varghese, and Tang, ; Bodner and McMillan, ; Pribyl and Bodner, ; Stieff, , and the influence of animated and static visualizations on conceptual understanding Abraham, Varghese, and Tang, ; Aldahmash and Abraham, ; Sanger and Bader, Spatial ability and the use of representations are emerging areas of study in engineering Sorby, , biology Dirks, and the geosciences Piburn, van der Hoeven Kraft, and Pacheco, In engineering, much of this research addresses instructional approaches to improve spatial ability; these approaches typically are grounded in constructivist theories of learning Gerson et al.

    Most of the biology studies investigate the role of different representations in improving understanding, promoting conceptual change, and stimulating interest in biology. Many are grounded in constructivism and dual-coding theory. In the geosciences, research in this area has concentrated on the relationship between spatial ability and success in the geosciences Liben, Kastens, and Christensen, and on instructional strategies to improve spatial ability Piburn et al.