Discipline-Based Education Research Understanding and Improving Learning in Undergraduate Science and Engineering (2012) / Chapter Skim
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5 Problem Solving, Spatial Thinking, and the Use of Representations in Science and Engineering
5 Problem Solving, Spatial Thinking, and the Use of Representations in Science and Engineering
Pages 75-118
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From page 75... ...
The discussion of each topic in this chapter begins with an introduction of that topic and its importance to undergraduate science and engineering education. Following these introductions, we provide an overview that summarizes the focus of DBER on the topic, the theoretical frames in which DBER is grounded, and the typical methods used.
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From page 76... ...
This discussion of problem solving is structured around important findings from DBER that are consistent with prominent themes from the cognitive science literature, namely problem representation and the nature of the solution process. In the cases for which the findings apply to only a small number of problem domains or disciplines, their broader applicability to problem solving within the disciplines of interest here is an open question.
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From page 77... ...
This general pattern of consistent results across disparate types of problems lends support to the committee's view that findings from cognitive science research on problem solving may be applicable in undergraduate science and engineering domains in which they have not yet been investigated. After all, humans have a single cognitive system, with specific operating parameters and constraints, that underlies their learning and problem solving regardless of the problem or discipline under investigation (Simon, 1978)
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From page 78... ...
A significant body of research on problem solving also exists in cognitive science, and that research overlaps considerably with DBER. Cognitive science research corroborates some DBER findings, can help to explain or extend others, serves as the theoretical basis for some studies, and provides potential building blocks for future DBER on problem solving (Bassok and Novick, 2012)
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From page 79... ...
In the geosciences, one emerging line of research draws on the cognitive science field of naturalistic decision making (Klein et al., 1993; Marshall, 1995) to investigate student problem solving in the field setting using global positioning satellites.
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. Similarly, a major focus of cognitive science research on problem solving has been to compare the performance of novices (usually, although not always, college students)
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. Students' working backward strategy (referred to as a means-ends analysis in the cognitive science literature)
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Novices, 2 Thissection draws heavily on a review of physics education research that the committee commissioned for this study (Docktor and Mestre, 2011)
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From page 83... ...
However, similar to findings from physics and cognitive science, research on problem solving in stoichiometry and equilibrium indicates that students are sometimes able to solve a problem using algorithmic/algebraic strategies or analogous problems, with only a superficial understanding of the underlying concept (Camacho and Good, 1989; Chandrasegaran et al., 2009; Gabel and Bunce, 1994; Tingle and Good, 1990)
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From page 84... ...
One source of cognitive science evidence for this claim is that isomorphic problems (problems that have the same underlying structure) may lead people to construct very different representations of their 3 This section draws heavily from a review of the literature that the committee commissioned for this study (Svinicki, 2011)
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From page 85... ...
. A second source of evidence comes from a large number of studies, in cognitive science and DBER, showing that (relative)
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From page 86... ...
Physics education research has found that whereas experts categorize physics problems according to the major concepts or principles that can be applied to solve them (e.g., Newton's second law) , novices rely much more on the surface attributes of the problems -- such as the specific objects mentioned (e.g., pulleys versus inclined planes versus springs)
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From page 87... ...
Smith (1992) found that undergraduate biology students grouped classical genetics problems based on superficial features (e.g., whether the problem concerned humans or fruit flies, how the question was worded)
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. Other research on individual differences has examined the relationship between spatial thinking, or the ability to mentally manipulate two- and three-dimensional figures, and problem solving in chemistry.
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. Instructional Practices to Improve Problem Solving Across all disciplines, instructional strategies to improve students' conceptual understanding, problem solving, and overall academic performance
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, • elucidating different problem types (Mestre, 2002; Van Heuvelen, 1995; Van Heuvelen and Maloney, 1999) , • providing example solutions (Chi et al., 1989; Ward and Sweller, 1990)
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. Engineering Engineering education effectively has incorporated key elements of cognitive science into problem-solving and design4 experiences for engineering courses and curricula, and into the research about effects on learning (e.g., 4 "Design" has distinct meanings across engineering sub-disciplines.
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From page 92... ...
92 DISCIPLINE-BASED EDUCATION RESEARCH BOX 5-1 Cognitive Apprenticeship A chemistry postdoctoral researcher shows an undergraduate how the gas chromatograph/mass spectrometer needs to be calibrated; a young astronomer watches her mentor give a research talk at a confer ence; an engineering student uses a computer-aided design program for the first time and follows step-by-step instructions prepared by his professor. In each of these cases, skills -- and often cultural norms -- are passed down from an expert to a novice.
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From page 93... ...
However, consistent with findings from physics and engineering, the results suggest that problem-solving skills can be enhanced through instruction. One quasiexperimental study examined the use of "invention activities" as a way to improve biology problem-solving strategies (Taylor et al., 2010)
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. With instructional strategies and activities that are influenced by Bransford, Vye, and Bateman (2002)
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These differences have important implications for problem solving success and, in turn, instruction. • As cognitive science research has shown more broadly, insufficient spatial skills and working memory capacity may impede perfor mance on some forms of problem solving.
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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.
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From page 97... ...
. THE USE OF REPRESENTATIONS AND SPATIAL THINKING IN PROMOTING CONCEPTUAL UNDERSTANDING AND PROBLEM SOLVING Visual/spatial, mathematical, logical, and verbal representations are central to human thinking, as well as to learning and instruction in virtually
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From page 98... ...
. Developing representational competence requires the ability to mentally manipulate two- and three-dimensional objects, a skill that is called visuospatial thinking or spatial ability.
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From page 99... ...
For example, in some disciplines (e.g., geology, anatomy) , penetrative thinking, or the ability to represent and reason about the hidden internal structure of a multilayered three-dimensional object, is critically important (Hegarty, 2011; see "The Role of Spatial Ability in Visualization and Mental Model Formation" in
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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., 2010)
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. This section discusses DBER on how students develop, use, and interpret representations, and the role of spatial thinking in visualization and mental model formation.
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, the role of spatial ability in visualization and mental model formation (Abraham, Varghese, and Tang, 2010; Bodner and McMillan, 1986; Pribyl and Bodner, 1987; Stieff, 2011) , and the influence of animated and static visualizations on conceptual understanding (Abraham, Varghese, and Tang, 2010; Aldahmash and Abraham, 2009; Sanger and Bader, 2001)
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More specifically, research in cognitive science has shown that across disciplines, students have (a) a preference for representations that have a high degree of visual similarity to their referents; (b)
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-- shows that learning via more R than one representation can help to build understanding (Van Heuvelen and Zou, 2001; see Box 5-4 for an example)
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105 PROBLEM SOLVING, SPATIAL THINKING, AND REPRESENTATIONS BOX 5-4 Visualization/Representation in Physics The common free-body diagram helps students move from a physical view of concrete objects to the more abstract idea of vector forces. This is a major component of a multirepresentational teaching methodology developed by Alan Van Heuvelen (1991)
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From page 106... ...
Johnstone noted that to teach chemistry is to help students explore the dyads of the triangle: the relationship be tween symbols and their corresponding features in particles of molecules and atoms, the connections between the particles and the properties that can be seen and smelled with the human senses, and the language of symbols used to represent elements and compounds. Macroscopic 2Na(s)
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From page 107... ...
The principle of good continuation states that a continuous line is perceived as a single entity. Good continuation has been shown to interfere with college students' understanding of the hierarchical structure of cladograms (diagrammatic depictions of descent)
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108 DISCIPLINE-BASED EDUCATION RESEARCH BOX 5-6 Visualization/Representation in Biology Cladograms, or diagrams that depict evolutionary relationships among a set of taxa, are typically depicted in either a tree or ladder format. Trees are much more common in the evolutionary biology lit erature, while ladders are slightly more common in high school and college biology textbooks (Catley and Novick, 2008; Novick and Catley, 2007)
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. The Role of Spatial Ability in Visualization and Mental Model Formation In many science and engineering disciplines, spatial thinking is a vital component of expertise in the discipline.
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110 DISCIPLINE-BASED EDUCATION RESEARCH BOX 5-7 Visualization/Representation in the Geosciences In a study of visual penetrative ability, high school students were asked to sketch a specific plan view or profile slice through a three dimensional volume, using information about the outside of the volume in the form of a block diagram (Kali and Orion, 1996; see the figures in this box)
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. The Geosciences The relationship between spatial ability and understanding of geoscience concepts are of great interest to geoscience education researchers
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Instructional Strategies and Tools to Improve Students' Spatial Ability and Use of Representations Given the difficulties students have with spatial thinking and the use of representations, improving these skills is an important part of moving
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From page 113... ...
Here we discuss these bodies of research as they relate to improving the use of diagrammatic displays, enhancing students' spatial ability, and identifying the role of animations in these tasks. Improving the Comprehension of Diagrammatic Displays In addition to being important tools of discipline, diagrammatic d isplays -- e.g., general-purpose abstract diagrams such as hierarchies and matrices, domain-specific diagrams such as free body diagrams in physics or a drawing of the components of a cell in biology, and graphs of data -- are important tools in instruction.
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From page 114... ...
The Gestalt psychologists identified many other perceptual features that have psychological importance, including two that have particular implications for DBER. The first is good continuation, which states that a continuous line is interpreted as a single entity (discussed in the biology education research section on the role of visualization and spatial ability)
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From page 115... ...
In the longitudinal studies, first-year engineering majors of low spatial ability (as measured by the PSVT:R) who took a specially designed, multimedia training course improved their spatial skills, earned higher grades, and persisted in the university at greater rates than students of similar spatial ability who did not take the course.
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Thus, these technologies may require greater spatial ability and other aspects of representational competence for their successful use. It is not a foregone conclusion, therefore, that all animations will necessarily be beneficial for learning.
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Directions for Future Research on Spatial Thinking and the Use of Representations DBER and cognitive science have yielded many useful insights into how students use mathematical and graphical representations, but important gaps remain. For example, the research community, instructors, and those who develop representations would benefit from a deeper understanding of students' use of representations as tools to enhance their learning, and studies along these lines should leverage what is already known about the basic cognitive and perceptual processes that students use to comprehend graphical representations.
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From page 118... ...
Representations vary within and across disciplines. As one example, the nature of the representations used in geoscience education varies enormously on multiple important dimensions, including the use of spatial representations to represent nonspatial data (Dutrow, 2007; Kastens, 2009, 2010; Libarkin and Brick, 2002)
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