My primary research areas are situated at the core of contemporary research on problem solving and reasoning. Broadly speaking, my research is focused on examining the strategies, processes, and representations that college (and more recently high school) students use to reason and solve problems. On the one hand, I am interested in skilled problem solving, including its relation to less skilled problem solving, so my work often considers individual differences. On the other hand, I am also interested in general principles of, or constraints on, cognition that are related to reasoning and problem solving.
I have studied problem solving and reasoning in a variety of content domains, which were chosen because they are good ones for studying issues of representation, solution strategies, and expertise: (a) students' knowledge of spatial diagrams (matrices, networks, and hierarchies) and their use of these abstract representations for solving problems involving analytical reasoning, (b) students' understanding of cladograms, a type of hierarchical diagram that is the most important tool that contemporary scientists use to reason about evolutionary relationships among taxa, (c) the induction of causal relations and the effect of causal knowledge on subsequent reasoning, (d) analogical (i.e., procedural) transfer in the solution of mathematical word problems, (e) the nature of insight solutions and expertise-related differences in anagram solution, (f) the role of diagrams in facilitating the execution of instructions for object assembly (in particular, folding origami objects), and (g) a comparison of visual and textual representations for computer programming. Across these areas, my research has addressed the issue of how knowledge of a problem's underlying structure affects reasoning and problem solving. The different aspects of my research program, as well as the different content domains in which they are situated, fit together nicely as pieces in the larger puzzle of trying to understand human problem solving and reasoning.
The paragraphs below provide a short description of each of the four broad areas in which I have done research over the course of my career. Hot buttons after the paragraphs lead to more detailed descriptions of some of this research. Or you may go directly to the more detailed descriptions by clicking on the buttons below. A list of recent publications from all of the different research areas is available from the link here.
| Macroevolution Diagrams | Other Diagrams | Anagram Solution | Causal Reasoning | Procedural Transfer |
Macroevolution diagrams. In my main line of research, I am interested in college and high school students' understanding of and ability to reason from cladograms, a type of hierarchical branching diagram used in biology to depict evolutionary relationships among taxa. This IES-funded research, conducted in collaboration with Kefyn Catley, a biologist and science educator at Western Carolina University, is multifaceted. Our work compares the performance of three groups of students -- college students with stronger and weaker backgrounds in biology and high school students -- in order to determine the learning that results from instruction in (primarily organismal) biology, as well as the gaps in that learning. One project is investigating students' ability to reason from cladograms, a skill often referred to as tree thinking. A second project is investigating students' ability to translate between alternative, isomorphic formats for drawing cladograms. A critical aspect of both of these projects is to determine the cognitive processing and perceptual factors that affect students' comprehension and reasoning. A third project is examining students' understanding of evolutionary diagrams that are not cladograms. We are using the results of this experimental research to design tree-thinking curricula at both the college and high school levels.
Other diagrammatic research. I am also particularly interested in college students' knowledge and use of three spatial diagram representations -- matrices, networks (i.e., path diagrams), and hierarchies (i.e., trees) -- that are important tools for thinking both in everyday situations and in formal domains. This research has provided critical information concerning (a) the problem structures for which each type of diagrammatic representation is best suited (i.e., the applicability conditions for each of the representations), (b) the nature and content of students' knowledge about these representations, as well as their use of this knowledge in situations involving problem solving and analytical reasoning, and (c) the conventions for constructing the three spatial diagrams and the consequences for problem solving of adhering to versus violating these conventions (in collaboration with Sean M. Hurley, for his dissertation).
In a project conducted in collaboration with Doug Morse, a psychology graduate student, I investigated the role of iconic diagrams in facilitating the execution of a set of procedural instructions. In a second project, Kirsten Whitley (computer science graduate student), Doug Fisher, and I examined the effectiveness of the visual representation in LabVIEW, a visual programming language (Whitley, Novick, & Fisher, 2006)
.In collaboration with Jim Sherman, at Indiana University, I investigated the processes underlying anagram solution, particularly by highly skilled solvers. Our research bears on the nature of both insight problem solving and expertise. According to the Gestalt psychologists, problem solutions that pop into mind suddenly with no awareness of the process by which they were generated are objectively as well as subjectively sudden. Thus, such pop-out solutions are qualitatively different from search solutions, which are built up incrementally. In one project, we tested this claim in the domain of anagram solution. Contrary to the Gestalt hypothesis, but consistent with some recent research on insight problem solving, we found that both pop-out and search solutions to anagrams depend on the gradual accumulation of partial information. Nevertheless, some aspects of our results suggest that there may in fact be a qualitative difference between these two types of solutions.
In a second anagram project, we tested two predictions concerning the sensitivity of experts and novices to superficial and structural information during on-line problem solving: (a) Superficial features have a greater effect on problem difficulty for novices, whereas (b) underlying structural features have a greater effect on problem difficulty for experts. Although many studies have found that experts and novices differ with respect to the types of features on which they focus their attention during off-line tasks, there has been little investigation of the ramifications of these off-line differences for on-line problem solving. The results of two experiments supported our predictions.
The results from both of our anagram projects are consistent with the hypothesis that fast pop-out solutions to anagrams result from parallel processing of the multiple constraints on the rearranged order of the letters, whereas slower search solutions result from a serial hypothesis-testing procedure. Because pop-out solutions are much more common among highly skilled solvers, our results suggest that parallel processing of solution constraints may be a key characteristic underlying expertise.
As early as the age of 3, children form hypotheses about the causes of events happening in their world. This concern with understanding causes persists throughout people's lives, because it is one way people impose structure on what would otherwise be an endless stream of unconnected elemental events. Our attributions of the causes of events have important implications for how we behave in the world. To take a simple example, you would react quite differently toward a colleague who failed to show up for an important meeting with you depending on whether you attributed the cause to the person being irresponsible or swamped with work or very ill. Patricia Cheng, at UCLA, and I investigated how adults induce the causes of events from information concerning the presence versus absence of one or more potential causal factors and the effect. Our most recent work focused on the induction of conjunctive causes, that is, causes consisting of the combination (i.e., joint presence) of two causal factors. For example, hard work per se typically does not produce success; it must be combined with talent. A core principle underlying our research is that human causal inference is normative, once the appropriate norm has been identified.
There are (at least) two reasons why psychologists believe it is important to study transfer. First, the use of specific examples to help guide current solution attempts is ubiquitous. Students' attempts to understand and solve a current problem often mimic characteristics of an earlier problem-solving episode. Unfortunately, students' attempts to apply knowledge learned in one concrete situation to another concrete situation are prone to errors. Attempts to remediate these difficulties, and to improve problem-solving instruction (e.g., in math and science) in general, will require an in-depth understanding of the types of knowledge students might transfer across problems, as well as the processes involved in transferring that knowledge. A second reason for studying transfer stems from its relation to expertise. Research across several different content domains indicates that abstract schemas representing classes of structurally-related problems are important components underlying (though not the sole cause of) experts' superior performance. Successful transfer of a solution procedure from an example problem to a structurally-related test problem may contribute to the acquisition of expertise by facilitating induction of domain-relevant schemas. My early research was in the domain of procedural transfer. Like many other researchers in this area, I used mathematical word problems as my stimuli because that is a domain in which students are known to rely on example problems to guide their problem solving. Within this domain, my research examined the processes that underly procedural transfer (especially the adaptation process), as well as individual-differences factors that affect the success with which these processes are executed.
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