Studying the meaning of giftedness: inspiration from the field of cognitive psychology.

How do we categorize our world so as to better understand and process the information streaming towards us? On a basic cognitive level, one must generalize and categorize new information so that one can better process it. The same concept applies to the identification of academically gifted students. We must identify academically gifted students so we can better serve them. However, there is one group of gifted students who are not being identified and therefore not served. The current education system in the United States often fails to identify academically gifted students who are not of the majority culture (Ford, 1998; Ford, Harris, Tyson, & Trotman, 2002; Stormont, Stebbins, & Holliday, 2001; U. S. Department of Education, 1993). This includes culturally diverse students, economically disadvantaged children, the differently abled, English Language Learners (ELL) and racial minorities.

Even though the vast majority of states have developed written policies that call for recognition, identification, and service for all gifted students including underrepresented gifted students (Coleman & Gallagher, 1995), the issue of underrepresentation persists. Despite efforts to create alternative strategies to identify students from diverse backgrounds, there remains a disproportionately small minority representation in programs for the academically gifted. Perhaps the policies recommended by the states to ameliorate the underrepresentation of students from diverse backgrounds in gifted programs are not being implemented. Perhaps they are being implemented inappropriately, or maybe they are being implemented, but are not working. Regardless, this is a significant issue in the field of education of the gifted.

There are myriad reasons for the underrepresentation of minority students, many of which are social and contextual (i.e., poverty, less supportive home lives) that cannot be adequately addressed by the school system (Donovan & Cross, 2002). However, one area that has a potential negative effect and thus deserves our attention is possible biases in the referral process (Donovan & Cross). Standardized tests and teacher nomination remain the most frequently used identification tools in American school systems (Coleman & Gallagher, 1995) despite suggestions from researchers that alternative methods such as dynamic assessment and portfolios be used (Hadaway & Marek-Schroer, 1992; Johnsen & Ryser, 1997; Kanevsky, 2000). Teacher nomination is often the gateway to even being considered for testing and subsequent inclusion in a program for the gifted. These teacher nominations may be limited because the teacher does not recognize gifted students who deviate from stereotypical traits associated with giftedness (Ford, 1998; Ford, Harris, Tyson, & Trotman, 2002). There are also possible negative expectations towards minorities and ELL students and a need for awareness of culturally valued behaviors that may differ from the mainstream (Bernal, 2000; Hadaway & Marek-Schroer; Weber, 1999).

In order to understand and recognize giftedness in children in general, and in culturally diverse children in particular, one must first have a sense of what giftedness means. In extension, in order to facilitate inclusive beliefs about giftedness, one must understand the implicit beliefs that teachers hold. When people engage in thinking, reasoning and other intellectual pursuits, or evaluate the thinking, reasoning and intellectual activities of others, they generally do not consciously use explicit theories such as those of Sternberg (1985; 1986; 1995), Gardner (1983; 1996), or Renzulli (1978; 1986). Instead, their thoughts, judgments, and possibly actions are based on their personal implicit conceptions or theories of these constructs (Argyris & Schon, 1974; Bluer, 1972; Lira, Plucker, & Im, 2002).

There is a relationship between teachers' theories about their students and their classroom practices (Dirkx & Spurgin, 1992; Lynott & Woolfolk, 1994; McCarty, Abbott-Shim, & Lambert, 2001; Rando & Mendes, 1991; Richardson, Anders, Tidwell, & Lloyd, 1991). It is reasonable to assume that teachers' theories of giftedness have an influence on identification practices. Many researchers in gifted education recognize the importance of people's attitudes and theories in the endeavor to change identification procedures (Callahan, Tomlinson, Moon, Tomchin & Plucker, 1995; Ford, Harris, Tyson, & Trotman, 2002; Grantham, 2002). However, with the exception of a few studies (e.g., Steinberg, 1993; Sternberg & Zhang, 1995), little research has been conducted on different groups' personal or implicit theories of giftedness. Further, although several studies have looked at teachers' beliefs regarding which characteristics describe gifted children (Campbell & Verna, 1998; Fernandez, Gay, Lucky, & Gavilan, 1998; Guskin, Peng, & Simon, 1992; Hunsaker, 1994; Peterson & Margolin, 1997; Rohrer, 1995; Siegle & Powell, 2004; Singer, Houtz & Rosenfield, 1992), no research could be found that made a direct link between teachers' theories of giftedness and subsequent actions.

A theory about giftedness would include information about the following two factors. First, it would describe the underlying principles and reasoning regarding which relationships among the characteristics of giftedness are important. Second, a theory includes information about how students would vary in the manifestation of these characteristics (Medin, 1989; Murphy & Medin, 1985). In contrast, studies of beliefs about the characteristics of gifted students tend not to include information about underlying relationships among the perceived characteristics. Considering the potential influence of theories of giftedness on what occurs in the day-to-day classroom, it is interesting that this concept has been given so little direct attention in research. Clearly, this is an area that merits further exploration.

One avenue that can be pursued as part of a continued research focus on different theories of giftedness is an exploration of how fields outside of education can be used to inspire new ways of conceptualizing and studying giftedness. One field that has much to offer is cognitive psychology. The application of the theories and methods of cognitive psychology to the study of gifted children is not a new idea (for a review of the links between cognitive science and the study of gifted students see Shore, Rejskind & Kanevsky, 2003). Previous research has provided much insight into the thinking and reasoning of gifted children (Coleman & Shore, 1991; Kanevsky, 1990; Shavinina & Kholodnaja, 1996; Shore, 2000; Sternberg & Horvath, 1998). However, the theories and methods used to study cognition can also be used to study the thinking and reasoning of teachers as they conceptualize giftedness. An area of cognitive psychology that seems to be most relevant is research on how people form categories.

In cognitive psychology research, concepts are thought of as mental representations that are used to create categories (Medin, 1989). For example, we have a mental image of "cat" that allows us to sort out a category of things that we would call "cats." In the same way, we have a mental image of "gifted children" that helps us to recognize a group of people we describe as "gifted." Cognitive science researchers (i.e., Ahn, 1998; Medin; Murphy, 1993; Nosofsky, 1989; Palmeri, 1997) have sought to understand how people form these concepts and the structure and mechanisms that determine categories. Theories of categorization and concept acquisition have evolved over time from the classical view, to similarity-based views, to theory-based approaches.

Giftedness can be thought of as an educational and social category. By understanding how categorization occurs on a cognitive level, we may find better ways of understanding what giftedness means to others and how to operationalize it for research purposes. This article presents a review of the different theories of categorization and explores the empirical models used to study these theories with a focus on how these theories and methods relate to the study of giftedness.

Classical Theory

According to the classical view, a concept is made up of a set of defining features that are individually necessary and collectively sufficient for category membership. This sounds very much like the way that some local plans for the identification of gifted students are written. A certain ability score, plus a certain teacher rating score, plus a certain parent rating score equals "gifted." This kind of identification procedure does not reflect best practices in gifted identification (Ford, 1998; Maker, 1996; Passow & Frasier, 1996: Renzulli, 1999). Like the field of cognitive psychology, education has moved away from necessary and sufficient features.

The classical theory has several limitations. Medin (1989) summarizes these limitations as follows. First, many concepts do not have defining features. Giftedness is one such concept. As is evident from the wide range of theories about the nature of giftedness, there are no agreed-upon defining features. A second problem with the classical view is that there is a high correlation between how typical of the category a person judges an item to be and the number of features it has that are characteristic of the category (Rosch & Mervis, 1975). Thus, members of the category vary in how typical they are of the category. In terms of giftedness, some gifted students are easy to recognize because their abilities manifest in typical ways, such as through superior academic achievement. The classical view provides no explanation of why members of a category vary in their typicality: all examples of a concept should be equally good. As a result of these issues, the view that concepts are probabilistic was adopted. The probabilistic view is that concepts are not strictly defined, but are organized around features that are typical of group membership. The two main probabilistic views are the prototype and the exemplar theories.

Prototype-Based Theory

According to the prototype view, a concept represents the central tendency, or prototype, of the category. For categories with discrete values, the prototype may include the modal or characteristic features of its members. For example, people's concepts of cats may include such characteristic features as "four legs," "thick fur," "a tail," "warm-blooded," and "meows." Such features are characteristic but not defining of cats. Some cats, such as the Manx, have no tails. Another breed is virtually furless. Features also may be weighted according to their importance (such as their frequency within the category or power to discriminate category members from nonmembers). In the prototype view, a person would determine whether something or someone was a member of a category by mentally computing how similar it was to the prototype. Methodologically, the similarity is operationalized as the sum of the features that match those in the prototype. If the similarity exceeds a designated threshold, the object or person in question is classified into the category. The prototype view accounts for the typicality effects as a typical entity would be more similar to the prototype.

A parallel of this approach can be seen in the Frasier Core Attributes study. Frasier et al. (1995) examined the literature on characteristics/traits of gifted students from 1957 to 1995, using qualitative content analysis to determine common features or core attributes of giftedness. Literature pertaining to general characteristics of giftedness as well as more culturally specific articles was included. The researchers' goal was to find the core attributes of giftedness that would be inclusive of all gifted students regardless of culture. The identified characteristics were systematically analyzed, placed in groups, and sorted by the researchers until an agreed upon set of descriptors was derived. Twenty-one descriptors were identified. Descriptors for which it was difficult to define levels of performance, or that were related to specific cultural values were dropped. The remaining ten descriptors were determined to be the core attributes or prototypical characteristics of giftedness. These were motivation, communication skills, problem-solving ability, unusual interests, imagination/creativity, memory, inquiry, insight, reasoning, and humor.

One main criticism of the prototype approach is that a concept that consists of only a prototype does not include some important information about the category, such as the variability among the members, correlations among features, and the category size (Medin, 1989). These limitations of the prototype view can help to identify some of the weaknesses of conceptualizing giftedness as a prototype. A teacher may have in mind the prototypical characteristics of a gifted child, but this does not give him or her information about how different children may vary in the manifestation of these features, nor does one have a sense of the relationships among the characteristics or a sense of how many gifted children one would expect to encounter in a classroom.

Exemplar-Based Theory

According to the exemplar-based theory, concepts consist of individual representations of the examples of a category that the person has experienced. People determine whether something belongs to a category by mentally computing its similarity to retrieved examples of the category. The greater the similarity of the target to the retrieved exemplar, the more likely the person would classify it into that category. In addition to being able to account for typicality effects, the exemplar view also retains information about correlations between features, category size, and variability. In general, the exemplar view has been found to be more successful in predicting how people categorize than the prototype view (Medin, 1989).

There are several methodological models used to study exemplar-based theories that have relevance for the study of giftedness. A fundamental and influential theory is the context model (Medin & Schaffer, 1978) and its extension, the Generalized Context Model (GCM; Nosofsky, 1989). According to this theory, people make decisions about category membership by computing the similarity between new instances and known category exemplars stored in memory in the following way. The probability of thing A being part of category B is a result of the sum of the similarity of A to each retrieved exemplar of category B divided by the sum of the similarity of A to all retrieved exemplars of categories (both category A and other alternate possible categories). In educational terms, this would mean that the probability of a child being considered by a teacher as gifted is a result of the sum of the similarity of the child to the teacher's retrieved examples of gifted children divided by the sum of the similarity of the child to all examples of different kinds of learners.

In this model similarity also represents selective attention to (and forgetting or) features. For example, if the teacher believes that early reading ability is highly predictive of giftedness and reading difficulty is highly predictive of learning disability, then the teacher may focus attention on reading at the expense of other dimensions, such as spatial ability. Due to the multiplicative nature of the similarity measurement in this model, something or someone highly similar to one exemplar and low in similarity to a second exemplar will be easier to categorize than something or someone that has medium similarity to both exemplars ([s.sup.3] + s is greater than [s.sup.2] + [s.sup.2]).

Other models have built upon the Generalized Context Model. The exemplar-based Random Walk Model (Palmeri, 1997) seeks to explain how an exemplar is retrieved from memory. According to this model, attempting to classify a stimulus causes stored category exemplars to race against one another in order to be retrieved. When an exemplar wins the race and is thus retrieved, a counter takes a step in the direction of the exemplar's category. One aspect determining the time to complete the race is activation, which is a function of the similarity of the exemplar to the stimulus and the strength of the exemplar. The similarity is computed according to the GCM. Strength is a function of how frequently and recently an exemplar has been experienced. Activation increases with frequency of encountering the exemplar and similarity.

The mechanisms of the context models provide a useful way for conceptualizing several issues in gifted education. The multiplicative aspect of the similarity judgment in the GCM may help explain why students with dual exceptionalities are difficult to identify. A child will be easier to place if he or she is highly similar to one exemplar and low in similarity to a second exemplar of an educational category than if he or she has medium similarity to both exemplars of an educational category. For example, a student may exhibit characteristics that are similar both to gifted and learning disabled exemplars. Because of the effect of contrasting exemplars, this student would be more difficult to place than a student with gifted characteristics alone.

In the exemplar-based Random Walk Model the strength of the exemplar is a function of how frequently and recently the exemplar has been experienced. The consideration of frequency and recentness is significant for gifted identification because teachers may have had little experience with gifted students resulting in weak exemplars. Further, teachers may have even less experience with students who are both gifted and from diverse cultural or social backgrounds. A lack of experience with students from different backgrounds could result in a very weak exemplar for the culturally diverse gifted student. Teachers may have few examples to go by for gifted students in general and even fewer encounters with students who do not exhibit their abilities in a typical way. An emphasis on similarity and typicality may be helpful in research determining how to modify teacher perceptions.

One way to expose teachers to examples of diverse gifted students is through the use of the case method of instruction (CMI.) This instructional technique was developed by the Harvard Business School in the early 1950s as a method to promote application of the knowledge taught through traditional lecture (McWilliam, 1992). CMI has been suggested as a technique that has potential for application in teacher education as a way to bridge theory and practice (Elksnin, 2001; Frank Porter Graham Child Development Center, 2000; Putnam & Borko, 2000; Roth, 2000). As it is unlikely that teachers will have had sufficient experience with diverse gifted students as a result of their usual classroom experiences, cases can be developed to familiarize teachers with these students. As a result, the teachers may be able to better recognize these students in their classrooms.

Theory-Based Models

Both the prototype and exemplar views of categorization are based on determinations of similarity. However, similarity may not be the key factor when it comes to how people determine which features are relevant for categories. There has been a shift from the similarity-based models towards an emphasis on theories in categorization research (Medin, 1989; Murphy, 1993). Murphy and Medin (1985) discuss the insufficiency of the similarity approach by pointing out several issues. One issue is that the previous approaches do not provide constraints on what counts as a feature. Second, similarity itself may be more complex than described in the prototype and exemplar theories. It likely involves more than a simple computation over a set of fixed features. Instead it is a dynamic and context-specific process. The act of comparing a person to exemplars may change how people represent the concept. Third, most things have representations that are more complex than a set of dimensions. As a result, determining something or someone's similarity to a category is less straightforward than making comparisons to the category representation. There are obviously some features that are relevant and some that are not. However, the shift to the theory-based view of categorization does not mean that similarity-based approaches should be abandoned. The theory-based approach builds upon and reinterprets what is meant by similarity, giving it greater abstraction, depth, and complexity.

The theory-based view takes the position that a person's theory of the domain determines category coherence (Murphy & Medin, 1985). Theory-based approaches involve the study of underlying principles that determine which relationships between features are important. The overall principle is that the human mind seeks to create theories to explain sensory information and forms concepts based on its theories about how the world functions. According to the theory-based view, our beliefs and biases, which permeate our conceptual systems, affect almost all category-based inferences (Murphy & Medin). The features of the category are determined by their importance to the underlying principles (Murphy & Medin).

One focus of the research on the theory-based approach is on defining and explaining why different features are of greater importance within a theory of category membership. Wisniewski and Medin (1994) examined how prior knowledge influences categories. They found that when categories are meaningfully labeled, people bring intuitive theories to the learning context. People seem to attend to features that prior knowledge has indicated are relevant to the category. Thus, theories and data mutually influence each other.

The method that the researchers used to assess the effect of intuitive theories involved the use of two sets of drawings of people done by children. The drawings were designed so that they could be grouped by both superficial feature rules and a possible theory-based approach based on abstract features. In order to activate an intuitive theory, half the participants were told that one set of drawings was done by a meaningfully labeled group (creative children/noncreative children, high IQ/low IQ, or emotionally disturbed/well adjusted). The control participants were told that the drawings were done by children in Group 1 and children in Group 2. The participants were directed to find a rule that could be used to sort the drawings into the two groups. The theory group tended to use more abstract and hierarchical rules. The authors stated that the abstract features were probably activated by people's intuitive theories about the categories of children who drew the pictures.

This method may be modified to activate and assess people s theories about gifted children. In this application, the focus is less on how intuitive theories affect category learning and more on the use of the methodology to access theories. Participants can be given product samples and be asked to devise a rule that would categorize the samples into different categories. The choice of the category would depend on the aim of the study. One could use gifted/not gifted or one could look at different subsets of gifted students. For example, the researcher could inform the participants that the two groups of products were created by gifted students from low socioeconomic backgrounds and gifted students from affluent backgrounds. The rules that the participants suggest may provide information about their theories of how these two groups differ.

A framework for determining feature importance or centrality has arisen from the work of Ahn and her colleagues on the causal status effect. Ahn (1998) proposed that people weigh features that serve as the causes for other features more heavily than their effects. This is the causal status effect. Concepts organized around causal theories provide more predictive power than those organized around surface characteristics. In addition, the more causal a characteristic, the more difficult it is to imagine changing the feature without changing the conceptual representation. In other words, central features tend to be less mutable (Sloman & Ahn, 1999; Sloman, Love, & Ahn, 1998). Causal background knowledge affects the construction of new categories (Ahn, 1999; Ahn, Kim, Lassaline, & Dennis, 2000).

The methodologies used to study centrality and the causal status effect have interesting applications in the study of individual groups' theories of giftedness. Sloman et al. (1998) studied the characteristics of features that are part of people's theories including mutability, category centrality, diagnosticity, and salience. The mutability of features is a measure of the conceptual centrality of the feature in the person's theory. Conceptual centrality is how central the feature is to the mental concept itself. Mutability refers to people's willingness to transform a feature that is part of their concept of an object while retaining the belief that the object is represented by the concept. For example, a person's cognitive representation of "cat" may include the features "has thick fur" and "is warm-blooded." However, "has thick fur" is more mutable than "is warm blooded" (i.e., if the animal in question did not have thick fur it may still be considered a cat; however, if it was not warm-blooded then it would not be considered a cat.) Category centrality is a measure of how central the feature is to instances that make up the category. Diagnosticity is the degree to which the feature is predictive of other features. Salience is the perceptual intensity of the feature. Aspects of features were measured using questions relating to the different components of the dimension. Application of the questions used in the Sloman et al. study to research on giftedness is presented in Table 1.

These questions have potential application in studies seeking to understand different people's theories of giftedness. They have the benefit of eliciting information beyond a list of characteristics that people describe as important and better address questions regarding the relationships between the characteristics and the structure of the individuals' theories of giftedness. The use of these kinds of questions in surveys and interviews may greatly improve the depth and richness of the information gathered and may increase the validity of the information as a measure of people's personal theories of giftedness.

An application of this methodology in the study of the causal status effect that has potential for the study of individuals' theories of giftedness emerges from the Kim and Ahn (2002) study of theories of different mental illnesses. They sought to demonstrate that lay concepts of several mental illnesses could be predicted from participants' naive causal theories about those disorders. The participants were given a task in which they graphically organized features related to the mental illness and drew arrows indicating the causal relationships among the symptoms. They then assigned causal strengths to each relationship. In another experimental task, the participants rated the importance of symptoms in diagnosis.

Kim and Ahn (2002) hypothesized that each symptom is conceptually central to the extent that other symptoms depend on it. Using the data gathered through their experimental tasks the researchers determined which characteristics were causally central, peripheral, or isolated in participants' theories. The participants then rated the likelihood that a patient with either causally central, peripheral, or isolated characteristics had the disorder. This allowed the researchers to test whether participants use their theories when making judgments.

This operationalization of the causal status effect theory can be applied to the study of individuals' theories of giftedness. Participants' theories of giftedness can be directly measured, including the structure of the theory and the relationship between the features. More importantly, one can determine whether people use their personal theories of giftedness when making decisions. This methodology can be applied with teachers to study whether they use their own theories when nominating students for gifted programs. The theories of different groups of people can be compared, allowing one to assess differences in beliefs among people from different cultures. Further, one can assess whether people have different personal theories regarding gifted students from different cultural and socioeconomic groups.

Conclusion

An exploration of research outside the field of education allows for fresh and innovative approaches to educational research. The research being completed by cognitive psychologists can provide inspiration for research in education. A useful parallel can be drawn between theories of categorization from the field of cognitive psychology and the study of giftedness. The evolution of models of categorization mirrors in some ways the evolution of thinking about the meaning of giftedness as an educational construct. The classical view of categorization focuses on necessary and sufficient features but fails to account for the complexity of such categories as "giftedness" that do not have an agreed-upon set of characteristics (Media, 1989). Just like many of the naturally occurring categories, giftedness is too complex to be reduced to absolutes.

The next step in the evolution is the probabilistic theories such as the prototype and exemplar-based approaches (i.e., Media & Schaffer, 1978; Nosofsky, 1989; Palmeri, 1997). Although improving upon the classical view, these approaches also have drawbacks. The limitations of these approaches illuminate parallel issues in gifted identification. Conceptions based on prototypes lack information regarding diversity in how talent is manifested. Lack of experience with gifted children in general and diverse gifted children in particular may lead to weak exemplars that may hinder teacher nominations.

The complexity of the construct of giftedness may be best captured by the theory-based models (i.e., Ahn, 1998; Murphy & Medin, 1985; Sloman et al., 1998) that focus on underlying principles rather than similarity to exemplars and prototypes. These methods allow one to delve beneath surface characteristics to study not just stated beliefs but the nature of theory. An exploration of reasoning and categorization benefits gifted education because application of the knowledge gained from a study of categorization may help to address unanswered questions regarding teachers' theories of giftedness and the impact of those theories on teachers' actions.

A deep understanding of teachers' beliefs about giftedness is particularly important given the potential effect of teachers' beliefs on the kind of students they nominate for participation in gifted programming and the kinds of ability profiles they value in the classroom. Teacher nomination can be a gateway into further consideration and assessment. In light of the underrepresentation of students from diverse cultural backgrounds in programs for the gifted, it is important that this aspect of the identification process be thoroughly understood. Hopefully, this discussion of research on categorization will result in future research directions that will produce a better understanding of the meanings and manifestations of giftedness.

Table 1

Studying the Dimensions of Features

  Aspect of Features                        Question

      Mutability
(conceptual centrality)
       Surprise            "How surprised would you be to encounter
                           a gifted child who does not read well?"
   Ease of Imagining       "How easily can you imagine a gifted child
                           who does not read well?"
  Goodness of Example      "How good an example of a gifted child
                           would you consider a gifted child who does
                           not read well?"
Similarity to an Ideal     "How similar is a gifted child who does not
                           read well to an ideal gifted child?"

  Category Centrality
 Counterfactual Naming     "Would a child be considered gifted even if
                           he/she never read well?"
      Variability          "What percentage of gifted children are
                           exceptional readers?"

     Diagnosticity
     Cue Validity          "Of all students who read well, what per-
                           centage are gifted?"
  Inferential Potency      "What proportion of the characteristics of
                           gifted children would you predict are
                           present in a child if all you knew was that
                           the child reads well?"

       Salience
      Prominence           "How prominent in your conception of gift-
                           ed children is the characteristic of reading
                           well?"

Note: Modified from Sloman, Love, & Ahn (1998)

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Erin Morris Miller is a doctoral candidate at the University of Virginia in the Educational Psychology-Gifted program. Her research interests include thinking and reasoning processes, the cognitive and social development of gifted students, and exploring the meanings and manifestations of giftedness. E-mail: [e-mail]

Manuscript submitted January 5, 2004. Revision accepted June 17, 2004.