Research Interests and Career Objectives
Origins
The goal of the research in which I am engaged is to help me to satisfy a longstanding curiosity about what sorts of things either help or hinder children's learning and transfer of problem solving skill.
I began graduate studies at the University of Pittsburgh in 1989 in order to become involved in the research in learning and instruction being done at the Learning Research and Development Center (LRDC). In order to work at LRDC I accepted an offer to study with Dr. Jonathan Schooler, even though he was studying the relationship between verbalization and non-verbal processes, which was somewhat indirectly related to my interests.
The research with which I began my work with Dr. Schooler originally focused on the negative effects of verbally describing a face on the non-verbal process of recognizing the face, a phenomenon that he named Verbal Overshadowing. It evolved, however, into considering the positive, as well as the negative, effects of verbalization. After completing my Master's thesis in the area of verbalization and face recognition, I was free to turn my research efforts toward my original goal.
I began doing experimental research in how college students form abstract representations of algebra problems and use those representations for transfer. During this time I was also working as a teacher at a private elementary school teaching 5th and 6th grade math. This offered me the perfect opportunity to gain hands on experience teaching algebra problem solving to younger children.
I reviewed the literature on how people use rules and examples to learn problem solving tasks, and conducted several studies on that issue. Initially, I used an abstract logical task, the Wason card selection task, before turning to algebra problems, a research domain that would have more direct relevance for education. Using the Wason card selection task, I found that focusing on the mapping between abstract rules and concrete examples improved peoples' performance on this logic task, but not their understanding. Further studies with algebra problems initially suggested that verbally explaining the mapping between an abstract representation and a concrete example improved some kinds of transfer and helped to overcome incorrect preconceived ideas about the task. A further study, however, showed that the process of comparing examples, even when the comparison process is non-verbal, can facilitate not only transferring a solution procedure, but also inferring principles useful for deriving variations of the procedure.
In 1996, while finishing my dissertation, I accepted a temporary teaching position at Slippery Rock University, and I continued to examine the effects of analogical mapping on problem solving transfer. Specifically, I began examining whether the beneficial effects of comparing example problems required that the examples have different, rather than the same solution procedures. In 1998 I accepted my first tenure track position at Union College in Kentucky where I finished that project. It showed that comparing problems with the same solution procedure may be sufficient to produce the previously observed beneficial effects of problem comparison. However, the differences between conditions were small, and need to be replicated and examined further before a confident conclusion can be reached.
While I was in Kentucky I sought a position at a larger University that would afford more ample resources for extending my research. Throughout this time I continued my interest in the verbal overshadowing effect and published a paper in Applied Cognitive Psychology on the individual difference characteristics that make people more or less susceptible to verbal overshadowing.
In 2000 I accepted the position I now hold here at Kutztown University. I am now conducting research along several fronts. Most of my research continues to be in the area of analogical reasoning and problem solving. However, it also includes following up on questions related to verbal overshadowing. Furthermore, there is a new area involving the emotion of disgust. Among the projects on analogical reasoning and problem solving are (a) examining people's ability to recognize a useful analogy for an algebra word problem, (b) examining the problem solving strategies people use before, during, and after comparing examples, and (c) developing more efficient methods for gathering data on people's mental representations of algebra word problems. Regarding verbal overshadowing, I am examining the effects of shifting people's cognitive processing strategy towards either global or local processing on face recognition. The new research on disgust is examining gender differences in how disgust versus fear motivates hostility.
One useful way to understand people's mental representations of algebra word problems might be to examine whether or not they can recognize what kind of a problem is a good analogy for another. An initial study has shown that comparing problems that form a good analogy for one another results in successful transfer at least to relatively easy test problems. A second study initiated in Fall 2005, and ongoing as of Fall 2007, is examining people's ability to recognize such a useful analogy, as well as factors that may affect the extent of their usefulness.
In the initial study, the results of which were presented at EPA in Spring 2005, subjects received worked examples as training problems for an upcoming test. The experimental subjects received problems that formed a good analogy, whereas control subjects did not. Specifically, in the experimental condition subjects compared a training problem that formed a good analogy for the upcoming test problems to another training problem that was also a good analogy for the test problems, and therefore was also a good analogy to the first training problem. In the control condition, they compared the training problem that was a good analogy for the test problems to another training problem that was irrelevant. That is, it was not a good analogy for the test problems, and therefore was also not a good analogy to the first training problem. The subjects' task was to write down anything they could see that was similar in the way that the two training problems were solved.
The test problems were all analogically similar to the first training example (and to both training examples for the experimental subjects) at the deep level of a general principle underlying the solution procedures for all of the problems. However, some of the test problems were easier in that they were also analogically similar at a shallower level of the particular set of solution procedure steps needed to find the particular problem element that was the unknown for those problems. Other test problems were more difficult in that they had a different problem element as the unknown. Therefore, they required a different set of solution procedure steps.
The result of this initial study was that the experimental subjects were superior at solving at least the easier test problems, although not the others. This confirms that the second training example used in the experimental condition was, as hypothesized, a useful analogy.
As of Fall 2007, the follow up study is examining how good people are at recognizing the useful analogy identified in the first study. Some of my earlier research had shown that people are easily misled into thinking that one algebra word problem forms a good analogy to a second one that it is not actually analogically similar to if merely the surface features of the first problem are similar to the second one. In this second study, subjects will be asked to chose which of two potential second training examples would be the most useful analogy to a first one. Some subjects will chose between a completely irrelevant problem and the one that was previously identified as being useful for transfer. Other subjects will chose between the irrelevant problem and one that merely appears on the surface to be similar. The hypothesis is that the latter subjects will chose the mere appearance problem over the irrelevant problem significantly more than the former subjects will chose the true analogy over the irrelevant problem.
In addition, those same subjects will then participate in a training phase of the study similar to the initial study described above. The purpose of this phase will be to determine whether comparing the true analogy rather than the mere appearance problem will result in the same benefit for transfer seen in the earlier study, even for the subjects who did not recognize its usefulness.It will improve upon the design of the initial study in that it will have a pretest, posttest design. In addition, it will also examine factors that may affect the extent of the true analogy's usefulness. The subjects in both the true analogy and the mere appearance conditions will be subdivided into half who compare the training examples in one way and half who compare then in another way. One half, called the free comparison subjects, will compare the training examples in the same way as was done in the earlier study. That is, they will just write down what they see as the similarities in the way in which the training examples are solved. The other half, called the match features subjects, will compare in a manner that has been shown in another previous study (the second of my two dissertation studies) to be beneficial for transfer even to the more difficult test problems.
In one study, presented at the American Psychological Society's annual meeting in 1999, I analyzed the beneficial and detrimental strategies used by subjects in the first of my two dissertation studies. It showed that comparing the solution procedures of algebra word problems improves people's ability to successfully use a newly generated procedure even though it also leads to a tendency to incorrectly apply an old procedure to a new problem. I obtained a grant to fund a project to examine whether the same evidence appears in the second dissertation study.
That project has now been completed. In the second study, comparing the solutions procedures not only improved people's ability to successfully use a newly generated procedure, but it also reduced the the tendency to incorrectly apply the old procedure to a new problem. A paper describing that study is now in preparation for submission to The Journal of Educational Psychology. The successful publication of that paper is intended to support my application for a follow up grant to support my ongoing research on analogical reasoning and problem solving.
During my first two years at Kutztown University I also conducted some studies with undergraduates in which we tried to develop methods of investigating the changes that occur in people's mental representations of algebra word problems as a result of comparing problems or making similarity judgments. Some of these studies have suggested that whether people's approach to the task is goal oriented or not may influence our ability to find the evidence we need in order to understand the changes in their representations. One such study by two of my undergraduate volunteer research assistants, Jeannie Heitzer and Angel Rogalinski, was presented at the Kutztown University Undergraduate Research Symposium, April 24, 2002.
I am also continuing to pursue research in verbal overshadowing. A recent study by Macrae and Lewis and by Tim Perfect examined the effect of processing orientation on face recognition. These researchers showed participants a videotape of a bank robbery. Then they shifted the participants to either global processing (considering a whole stimulus) or to local processing (focusing on individual parts). Control subjects did not have their processing orientation shifted. Then all the participants tried to identify the bank robber in a line-up. This study showed how such a processing orientation shift affected people's ability to make a correct line-up identification of the perpetrator.
When people try to make a real line-up identification, it is important that they can correctly identify the perpetrator if he is present. But in real line-up identification situations witnesses sometimes make a false-positive identification. That is, they incorrectly identify someone in the line-up who looks like the perpetrator when in fact the real perpetrator is not present. Therefore, it is important to know whether processing orientation could affect the likelihood of such false-positive identifications.
In a study that was begun in the spring semester of 2002, and ended in 2005, all the subjects were shown the same bank robbery video that was used by Macrae and Lewis. Then some subjects were shifted to local processing, some were shifted to global processing, and some were controls. All the participants tried to make line-up identifications, but they did not know whether the perpetrator was present or absent. The performance of these participants was intended to tell us whether or not a processing orientation shift affects false-positive identifications. However, that study not only failed to show that the processing shift affected false-positive identifications, it also failed to replicate the original effect on correct identifications.
In discussing this failure to replicate with Tim Perfect, I found that other researchers have failed to replicate this effect as well, although Tim himself and some others have succeeded in demonstrating it several times. At Tim's suggestion, as of Fall 2006, I am now conducting a "live interaction" version of the study. In this version, subjects try to recognize a live confederate of the experiment, rather than a photo or a videotape.
There are many possible directions for future research on people's mental representations of algebra word problems. Specifically, future research is needed to determine more precisely what kinds of information people use as the basis for the comparisons that they make and how their mental representations of the problems change as a result. Other important questions include what the role of verbalization is in the comparison process, whether children spontaneously develop problem comparison strategies, and what might foster the development of comparison strategies useful for transfer.
In the future, I would like to work with students of various ages because the hands on experience is so informative. For example, I have found that elementary school math textbooks typically teach problem solving techniques in which "deciding on a strategy" is a first step. The research on problem solving in cognitive psychology, however, emphasizes that such a first step requires the ability to represent a problem in a way that experts, but not novices, are equipped to do. Therefore, how people acquire the ability to represent problems in abstract ways that are useful for transfer is an important question for both theories of problem solving and for educational applications. I would like to explore what kinds of learning activities facilitate the development of the skill of representing a problem at different levels of abstraction and being able to move fluently between them. My intuition is that such a skill may be an important general learning skill which is useful for transfer and that it might be teachable. Therefore, it will be especially important to conduct experiments examining these questions not only in the laboratory, but also in actual classrooms.