Creativity In Physics

Creativity Research Journal 2000–2001, Vol. 13, Nos. 3 & 4, 401–410

Copyright 2000–2001 by Lawrence Erlbaum Associates, Inc.

Creativity in Physics: Response Fluency and Task Specificity

I. N. Diakidoy and Creativity C. P. Constantinou in Physics

Irene-Anna N. Diakidoy and Constantinos P. Constantinou University of Cyprus

ABSTRACT: The purpose of this study was to explore creativity in the domain of physics and, specifically, its relation to fluency of responses (divergent thinking) and type of task. Fifty-four university students were pretested on their knowledge of relevant physics concepts. They then were asked to solve 3 ill-defined problems representing different types of tasks. The appropriate responses given to each problem were evaluated as to their number (fluency) and frequency (originality). Task-specific components were found to influence creativity independently and to moderate the effects of general factors such as fluency of responses. Efforts to predict and facilitate creativity in educational settings, therefore, also must take into account the way creativity is manifested within particular domains and the constraints that different types of tasks may impose. Creativity is a complex construct and, although it has not been well operationalized, the importance of identifying and facilitating it in educational settings has been widely recognized. The various creativity tests and training programs that have been developed over the past several decades (Barron, 1969; deBono, 1976; Torrance, 1966; Treffinger, 1995) provide testimony to an increasing interest in creativity. Nevertheless, there is a general concern that creative potential is not identified systematically or nurtured in the schools the way it should be (Baer, 1993; Barron, 1988; Hennessey & Amabile, 1987; Hocevar, 1981; Sternberg, 1996; Weisberg, 1988). The purpose of this study was to examine creativity and factors that may contribute to it in a specific academic domain, namely physics. Problem solving represents a dominant activity of experts as well as learners in the domain. This study examined creativity in the solutions or responses given to different physics problems and its relation to fluency, problem type, and conceptual knowledge.

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Creativity research has been directed at explaining and predicting a complex psychological phenomenon on the basis of evidence concerning factors that are found or hypothesized to be crucial. However, our knowledge about the basic components of creativity and the factors that affect its development and manifestation remain more or less fragmented. Creativity has been conceptualized as an ability or characteristic of the person (Barron, 1988; Taylor, 1988) or as a cognitive process (Boden, 1992; Johnson-Laird, 1988; Schank, 1988; Weisberg, 1986) influenced by thinking styles or personality traits (Richardson & Crichlow, 1995; Sternberg, 1988) and associated with divergent thinking (Clapham, 1997; Guilford, 1956; Torrance, 1988). The issue we raise, however, concerns the extent to which a generally decontextualized approach to the study of creativity has the potential of providing us with a unified account of the construct and the factors that influence it. Creativity does not occur out of context (Baer, 1993). The context of its occurrence may be represented by a particular situation, task, or problem in an academic domain or in everyday life. In this respect, most previous research can be said to be contextualized by virtue of the materials and the tasks employed. However, there is still a need for a thorough exploration of creativity, its development, and its manifestation within single identifiable domains. Such an We would like to thank D. Natsopoulos and H. Tsoukas for their insightful comments and support, C. Varnavas and C. Bandis for their help with materials and scoring, and E. Theodorou for her help with the data. We also want to thank the students in our courses for their enthusiastic participation and interest in the study. Manuscript received May 20, 1999; accepted December 1, 1999. Correspondence and requests for reprints should be sent to to Irene-Anna N. Diakidoy, Department of Education, University of Cyprus, P.O. Box 20537, Nicosia CY–1678 Cyprus. E-mail: eddiak@ ucy.ac.cy.

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approach potentially can lead to a more unified theoretical account of the construct in a specific domain, which then can be contrasted with theoretical accounts of creativity in other domains and contexts. The validity of such an approach is implicated by the definition given to creative outcomes. Creative outcomes are conceptualized to be both novel, as indicated by their low frequency of occurrence (Sternberg, 1988; Torrance, 1990), and appropriate, as indicated by judgments of correctness, usefulness, and quality (Amabile, 1990; Johnson-Laird, 1987; Sternberg, 1988; Weisberg, 1986). The criterion of appropriateness is closely linked with the domain and task in question, because they necessarily impose constraints on what outcomes can be considered appropriate. Knowledge of the concepts, constraints, and regularities of a domain must influence the generation, evaluation, and modification of responses within that domain (Johnson-Laird, 1987; Weisberg, 1986). Moreover, Boden (1992) argued that if creativity is thought to involve the breaking or bending of rules imposed by the domain, then knowledge of these rules is a prerequisite for creativity in the domain. At the task level, knowledge of relevant concepts and solution requirements contributes to the representation of the givens and to the problem’s solution (Johnson-Laird, 1988). That, in turn, most likely provides the basis for the generation of appropriate and potentially creative solutions. Previous research on creativity has focused mostly on creativity as a general ability or process (Hennessey & Amabile, 1988; Richardson & Crichlow, 1995; Sternberg, 1988; Taylor, 1988; Treffinger, 1995). This focus has guided psychometric work in the area—as indicated by the fact that items on widely used creativity tests are relatively domain independent (Barron, 1988; Torrance, 1966, 1990)—and has resulted in the expectation that individuals who score high on general creativity tests are more likely to exhibit high creative achievement in one chosen area, if not in several. However, this is not generally the case (Baer, 1993; Feldhusen, 1993; Hocevar, 1981; Nickerson, Perkins, & Smith, 1985), and concern about the tests’ modest predictive validities led Feldhusen (1994) to suggest that creative functioning in one domain may be unique and psychologically different from creative functioning in another domain. The general lack of attention to domain-specific components does not only limit our understanding of creativity, but also may have serious educational impli-

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cations. Creativity test scores may contribute to decisions about placement in gifted education programs (Feldhusen, 1994, 1995), and findings, such as the influence of divergent thinking on creativity in general, may shape instructional methods developed to facilitate it in the school setting (deBono, 1976; Treffinger, 1995). Facilitating creativity in school also must involve facilitating creativity in specific academic domains in addition to promoting general creativity. However, it is highly unlikely that tests and instructional methods designed to identify and increase general creativity levels will be equally effective when the objective is to identify and promote creativity in domains, such as mathematics and science, in which outcomes, creative or otherwise, depend on the availability of conceptual knowledge and problem-solving strategies. A prerequisite to understanding the extent to which creativity is domain specific involves the examination of creativity in particular, identifiable domains. This study represents a first attempt in this direction. In this study, university students were asked to solve three ill-defined physics problems, each representing a different problem type in the domain: explanation, prediction, or application. Open-ended tasks and ill-defined problems that allow multiple solutions are assumed to facilitate creativity to a greater extent than well-defined tasks and problems (Barron, 1988; Hennessey & Amabile, 1987; Sternberg, 1988; Torrance, 1988; Weisberg, 1986). Problem type was operationalized in terms of solution requirements. A problem that requires one to explain or find the causes of a physical phenomenon presents different constraints with respect to what kinds of solutions are appropriate in comparison to a problem that requires one to predict physical consequences or to apply a concept. According to our position, we hypothesized that creative performance within the domain would vary as a function of the type of problem encountered. Although it is generally accepted that creativity is virtually impossible in the absence of some relevant knowledge, it also has been claimed that too much knowledge can have a negative impact, preventing the individual from going beyond what is already known (Sternberg, 1988; Taylor, 1988). In this study, to prevent simple recall or direct application of knowledge—which has been found to hinder creativity (Weisberg, 1986)—the physics problems were unfamiliar to the participating students. However, the un-

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Creativity in Physics

derlying physics concepts were judged by the students’ physics instructors to be within the students’ capabilities. In addition, a conceptual knowledge pretest was administered to establish the extent to which the underlying concepts were familiar and to allow for the examination of the effects of prior knowledge on students’ responses. We expected knowledge of the relevant underlying concepts to support creativity in the domain. Guilford (1956) proposed that divergent thinking, as opposed to convergent thinking, is a basic component of creativity. This hypothesis has been confirmed by research that has required participants to provide multiple responses (Richardson & Crichlow, 1995; Torrance, 1988), and it has dominated creativity testing and training (Clapham, 1997; deBono, 1976; Hocevar, 1981; Torrance, 1966). In fact, Torrance’s (1966, 1990) work on creativity testing has relied on the premise that divergent thinking qualities—that is, the ability to produce a large number (fluency) of different (flexibility) ideas that are unusual (originality) and richly detailed (elaboration)—are indicators of creativity. However, the importance of divergent thinking was disputed by Weisberg (1986, 1988), who argued that the ability to generate a large number of responses does not ensure that any of them will qualify as creative or original. This study examined the contribution of divergent thinking as represented by the number of appropriate responses given to each physics problem. Appropriate responses were considered to be those that fell within the domain of physics and that did not appear to originate from fundamental misconceptions with respect to the underlying physics concepts. This operationalization of appropriateness and the nature of the problems utilized allowed us to obtain a range of responses from each participant and for each problem. In this study, creativity was operationalized as response originality. The responses to each problem were scored as to their total number, their acceptability or appropriateness as indicated by the constraints of the domain, and their originality as indicated by frequency of occurrence in the sample. This method of scoring follows the guidelines and procedures commonly utilized in creativity research (Vernon, 1971). However, Davis (1989) drew attention to the fact that originality scores that are based on the sum of the frequency weights assigned to responses (see Torrance, 1990) are a direct function of the number of responses

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given. As a result, there may be a confounding of the originality measures with the fluency measures, which in turn may magnify the influence of divergent thinking functions. Therefore, in this study, fluency and originality were separated by computing originality as the average of the frequency weights of the appropriate responses given by each participant to each problem. This departure from standard procedure may result in an underestimation of the strength of the relation between divergent thinking and originality. On the other hand, it also allows the examination of the contribution of divergent thinking to creativity without any confounding influences.

Method Participants The participants were 54 University of Cyprus students majoring in education. The majority of the students were women (n = 50) and in their 3rd year of study (n = 40). Their college performance was average or above, compared to the performance of all education majors. Their grade point average (GPA) ranged from 7.00 to 9.00, with a mean of 7.52 and a highest possible grade of 10.00. At the time of the study, 45 of the students had completed a university course in physical science as part of their program requirements. Their average grade in this course was 6.91.

Materials The target physics problems were selected from a pool of 40 ill-defined problems constructed by two experts, both of them university professors of physics. All of the problems on this list were classified into three problem types on the basis of their solution requirements. Some problems required that solvers explain possible mechanisms behind a phenomenon; some required that solvers predict what will happen given a physical situation or a sequence of events; and, finally, some problems required that solvers find ways of using an item or device. These problem types were judged independently by the two instructors of the physical science course as not being representative of the problems found in textbooks and course assign-

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ments. The instructors, who were familiar with the participating students, were subsequently asked to identify the problems that were most likely to be unfamiliar but appropriate for this particular student group. Only problems identified by both instructors as fulfilling the set criteria were considered, resulting finally in the selection of three problems, each representing a different problem type (see Table 1). The explanation problem required students to provide possible valid explanations for a natural phenomenon, the prediction problem provided the beginning of a science fiction story that the students had to complete, and the application problem required students to describe possible applications for a device having specific physical properties. The students who had completed the physical science course had spent only 1 week covering static electricity (application problem) and 1 week on concepts pertaining to materials (explanation problem). Concepts related to radioactivity and the social impact of nuclear energy (prediction problem) were mentioned only in passing and were not treated rigorously in that course. The prior knowledge test consisted of 12 true–false statements constructed by the instructors of the physical science course (Table 2). There were 4 statements for each target problem assessing knowledge of concepts related to the phenomenon or situation described by the problem. For example, Statement 3.1 (Table 2) tests whether one understands the difference between magnetization and electrical charging. Inability to make such a distinction possibly would influence how one represents the application problem and, subsequently, his or her choice of Table 1.

technological applications. To prevent familiarization with the situations described in the target problems, the test statements were designed to assess the relevant concepts in contexts different from those presented in the problems. In addition to the items assessing knowledge of target problem concepts, there were 12 more true–false statements assessing knowledge of physics concepts unrelated to the problems, which served as foils. Their purpose was to prevent subsequent familiarization with the target concepts.

Procedure The students were divided into two groups for study participation. The prior knowledge test was administered on 2 consecutive days, with one group of students taking the test on the 1st day and the other group taking the test on the 2nd day. Students were instructed to think carefully before answering each item and to do their best. The test took students about 30 min to complete it. Two weeks later, the students met again in their groups and were given the target physics problems to solve. They were instructed to think carefully about each problem and to try to provide as many appropriate responses as possible to all three of them. Some effort was made to create a relaxed atmosphere in which the students would feel that they could work at their own pace. The students were allowed to make notes on separate pieces of paper and to work on the problems in any order they wished. It took students about 1 hr to complete this part of the study.

Target Physics Problems Representing Different Problem Types

Target Problem

Problem Type

When I think of iron rusting, wood rotting, and rubber disintegrating, then I am led to believe that “any material that is taken from nature, with time strives to return to its natural form and environment.” Why might this be happening? When the spaceship Thrumfus landed on the reef known as Imia to the Greeks and as Kardak to the Turks, its crew did not know what to expect from this planet. After 60 years of travel at the speed of light, Captain Maximus from the Andromeda galaxy decided to land somewhere in order to generate the radioactive fuel required by thei spaceship. He first had to distill 3 tons of water which would be used as a cooling liquid for the nuclear reactor. With a process of nuclear fusion he would produce the necessary plutonium, and then, with a large explosion, he would push the spaceship thousands of kilometers away in a matter of a few hundredths of a second. Complete the story. An electrically charged piece of a particular plastic has the ability to remove dust particles from the air. Mention ways in which this material could be used. You could assume that the material has additional properties as long as you specify them.

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Explanation

Prediction

Application

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Creativity in Physics

Table 2. 1.1 1.2

1.3 1.4

2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4

Prior Knowledge Test Items

Many construction materials derive from nature and have undergone some processing. On our planet there exists a fine and fragile equilibrium. In the case of a permanent temperature change (an increase of 1°C for example on a permanent basis) we could have catastrophic changes. When a system is in a state of dynamic equilibrium then it has ceased to change. Dinosaurs may have become extinct on this planet as a result of darkness persisting for a few weeks and caused by a comet impacting the earth. The atomic bomb explosion at Hiroshima gave rise to fire and major destruction that affected millions of people. Distillation of wine will yield water. Coca-Cola is produced through water distillation. The speed of light is 300 million kilometers per second. When I rub a pen it becomes magnetized, and I can use it to raise small pieces of paper. Dust is made up of groups of molecules which are suspended in the air. A transparent material has a smooth surface. An electrically charged body has more electrons than protons.

it was relatively easy to discern which responses were physically valid and particularly feasible. This was not the case with the prediction problem (Table 1), which included social and cultural aspects. In this case, responses such as the possibility of a Greek–Turkish war, which were possible and valid given the political situation, were counted as separate responses but were not considered to be appropriate unless they included valid physical information. The interrater agreement was 96%. Finally, all of the responses given by the students to each problem were tabulated, and their frequency of occurrence in the sample was calculated. A response given by fewer than 3 students (5%) received a score of 3 and was considered to be highly original. A response given by fewer than 15 students (15%) received a score of 2. Responses given by fewer than 27 students (50%) in the sample received a score of 1, and those given by more than 28 students received a score of 0. This procedure yielded a sample frequency score for each response. Subsequently, the average of all the frequency scores received by each student for each problem was calculated to give the student’s originality score.

Scoring The prior knowledge test was scored according to the number of items that were answered correctly. The scores were corrected for guessing—by subtracting the total number of incorrect answers from the total number of correct answers (Nunnally, 1978)—and converted to a proportional scale to indicate proportion of items answered correctly by each student. The scoring of the responses given to the target physics problems followed a three-step procedure. First, two independent raters, one expert in physics and one familiar with the target problems, examined the responses and counted the number of different responses given by each student to each problem. Responses that were similar to or simply elaborations of previous responses were grouped together and counted as one response. This step yielded a total number of responses score for each student for each problem. The interrater agreement was 75%, and the differences were resolved in conference. Second, two independent raters, both experts in the domain of physics, assessed the correctness or appropriateness of each response given. This step yielded a number of valid responses score for each student and problem. On the explanation and application problems,

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Analysis The data were analyzed using hierarchical regression following the logic of mixed analysis of covariance. The main dependent variable was originality. GPA and physics grade were between-subject factors and were entered first. The grand mean of the students across problems subsequently was entered to remove any remaining variance associated with between-subject factors. Then, the within-subjects factors—prior knowledge, problem type, number of valid responses, and total number of responses—were entered, followed by their interactions. That problem type was a within-subjects factor resulted in obtaining three measures of originality, one for each problem type. The F ratio for each within-subjects factor was calculated by taking into account the increment in R2 attributed to that factor: R2 change (1 - R2 ) /[( N - k - S - 1) - 1]

where R2 = the variance accounted for by the model, N = the number of observations, k = the number of vari-

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ables in the model, and s = the number of participants. This formula yields a more conservative test for the within-subjects factors than the standard formula commonly used for the calculation of the F ratio for the between-subject factors (Kerlinger, 1986). A preliminary examination of the data indicated that the distributions of total number of responses and number of valid responses were positively skewed (skewness > 1). That was expected because the problems were unfamiliar, resulting in fewer high scores than low scores. Square root transformations normalized the data, and the transformed scores were employed in the analyses. Because of missing values on physics grade, the data of only 45 students were utilized in the regression analyses.

Results Descriptive statistics indicated that students performed differently in the three target problems (Table 3). The concepts related to the application problem were less familiar to this sample, and yet the students

Table 3. Types

overall gave more responses and more appropriate responses to this problem. The responses given to the prediction problem were more original than those given to either the explanation or the application problems. Table 4 shows the correlation coefficients among the variables of interest. It can be seen that total number of responses, number of valid responses, and originality were all highly and positively correlated with each other (p < .01). However, the correlation between total number of responses and originality was not significant (r = .04, p > .05) when number of valid responses was partialed out. In contrast, the correlation between number of valid responses and originality increased (r = .63, p < .01) after total number of responses was partialed out, indicating that the ability to come up with more than one appropriate response is positively related to the degree of originality. Physics grade was positively related only to GPA, as expected, but not to any other variables. It is interesting to note that prior knowledge was negatively related to the number of valid responses. Analysis within each problem indicated that the corre-

Means of Originality, Number of Valid Responses, Total Number of Responses, and Prior Knowledge in Problem

Problem Type Explanation Measures Originality Number of Valid Responses Total Number of Responses Prior Knowledge

Table 4.

Prediction

Application

M

SD

M

SD

M

SD

0.43 0.19 1.27 0.64

0.92 0.39 0.29 0.17

1.14 0.54 1.32 0.68

1.18 0.57 0.37 0.20

0.97 1.37 1.74 0.46

0.81 0.55 0.53 0.23

Intercorrelations Among Measures of Academic Achievement, Knowledge, and Creativity

Measures

1

2

3

4

5

6

1. 2. 3. 4. 5. 6.

—

.69* —

.21* .17 —

.15 .13 –.06 —

.09 .13 –.22* .67* —

.10 .11 .05 .71* .43* —

Grade Point Average Physics Grade Prior Knowledge Total Number of Responses Number of Valid Responses Originality

*p < .01.

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lation coefficients between prior knowledge and each of the creativity measures (originality, number of valid responses, and total number of responses) were nonsignificant in all problems (p > .05) but negative only in the prediction problem. Preliminary regression analyses indicated that the day the prior knowledge test was administered and nonlinear components did not have significant effects on any variables of interest and, therefore, were excluded from the main analysis. Table 5 presents the final regression model predicting originality score. It can be seen that the variance accounted for by GPA, physics grade, and prior knowledge was not significant. Table 6 presents the means of originality, number of valid responses, and total number of responses in two levels of prior knowledge. Even though there were no significant differences in originality scores and total number of responses across prior knowledge levels (p > .05), the difference in mean number of valid responses across prior knowledge levels was significant, F(1, 162) = 7.98, p < .01. Students who received high scores (above the mean) on the prior knowledge test did not give as many correct responses to the problems as students whose prior knowledge of the relevant concepts was low. The same trend was apparent with originality scores and total number of responses as well. It can be seen from Table 5 that problem type was a highly significant predictor of originality. Students gave the least original responses to the explanation problem and the most original responses to the prediction problem (Table 3). Even though the interaction of prior knowledge with problem type was not significant, it did approach significance (p = .07). Table 7 shows the means of originality within problem types and levels of prior knowledge. Students with relatively high knowledge of relevant concepts showed a tendency to give more original responses to the explanation and application problems. In contrast, students with low conceptual knowledge gave more original responses to the prediction problem (Table 7). Even though none of the mean differences within each problem reached significance (p > .05), it may be the case that a high level of knowledge hindered creativity in the prediction problem, whereas the opposite appears to be true for the other two problems. This negative influence of prior knowledge on the originality scores of responses to the prediction problem also may have masked the positive effects of this

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Table 5. Summary of Hierarchical Regression Analysis for Variables Predicting Originality Score Variable Grade Point Average Physics Grade Grand M Prior Knowledge Problem Type Number of Valid Responses Total Number of Responses Problem Type × Prior Knowledge Problem Type × Number of Valid Responses Prior Knowledge × Number of Valid Responses Model R2 Multiple R

B

R2 change

F to Enter

0.18 0.07 1.00 0.11 0.32 1.08

.0077 .0039 .4727 .0005 .0541 .1958

1.03 0.78 41.01** 0.27 28.53** 103.25**

0.35 0.48

.0132 .0058

6.97* 3.03

–0.81

.0984

51.87**

.0001

0.06

–.088

.8521 .9231

Note: N = 45. *p < .05. **p < .01.

Table 6. Means of Originality, Number of Valid Responses, and Total Number of Responses in Levels of Prior Knowledge Prior Knowledge Low Measures Originality Number of Valid Responses Total Number of Responses

High

M

SD

M

SD

0.87 0.85 1.47

0.95 0.67 0.52

0.82 0.54 1.41

0.98 0.69 0.45

Table 7. Means of Originality Within Problem Types and Levels of Prior Knowledge Prior Knowledge Low Problem Type Explanation Prediction Application

High

M

SD

M

SD

0.37 1.32 0.94

0.87 1.19 0.82

0.47 1.05 1.04

0.97 1.19 0.84

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variable on the originality of responses given to the other two problems. It can be seen from Table 5 that the number of valid responses that a student could give predicted the extent to which at least some of these responses were original. The interaction of this variable with problem type was also significant. Table 8 shows the means of originality within problem types and levels of number of valid responses. It is apparent that the ability to produce a large number of responses influences originality in the explanation and prediction problems to a greater extent than in the application problem. The total number of responses that students gave to the problems was also a significant predictor of originality (Table 5). However, because the partial correlation coefficient between this variable and originality, when controlling for number of valid responses, was not significant (r = .04, p > .05), the high positive correlation initially observed and part of the variance accounted for may be due to this third variable and its relation to the total number of responses.

Discussion The results of this study indicated that the number of appropriate responses that students could give to ill-defined physics problems (fluency) and the type of problem were the most significant predictors of response originality. The number of appropriate or valid responses that a student can give to a problem is essentially an index of divergent thinking, and, within the framework of psychometric research, it has always been assumed that divergent thinking ability is highly related to creativity (Guilford, 1956, 1970, 1971; Torrance, 1966, 1988). Consequently, it has been argued that ill-deTable 8. Means of Originality Within Problem Types and Levels of Number of Valid Responses Number of Valid Responses Low Problem Type Explanation Prediction Application

408

High

M

SD

M

SD

0.00 0.00 0.00

0.00 0.00 0.00

2.30 2.29 1.04

0.48 0.41 0.80

fined tasks and problems, which allow more than one appropriate response, are more conducive to creativity (Hennessey & Amabile, 1988). However, the highly significant interaction of this factor with problem type indicates that the extent to which divergent thinking contributes to creativity depends on the type of the ill-defined task encountered. In this study, a greater number of valid responses was given to the application problem, but the responses given to the prediction problem received higher originality scores than the responses given to any other problem. This finding also supports, in part, Weisberg’s (1986, 1988) claim that the ability to produce a large number of responses does not ensure that these responses will be highly creative. The students in our study responded differently to problems representing different types of tasks in the domain of physics. An examination of the data revealed that, whereas 57% of the students gave highly original responses (responses receiving frequency scores of 3) to at least one problem, only 7% gave original responses to all three problems. Because the problems were equivalent in terms of appropriateness and familiarity, these differences in performance can be attributed, at least in part, to the fact that the problems differed in their solution requirements and constraints. Even though this study was motivated by the theoretical position that creativity is in part domain specific (Feldhusen, 1994; Hocevar, 1981), it was not designed to address this issue directly. Nevertheless, these findings allow the extension of this position and its implications to the level of the task. Creative performance in connection with one type of task does not appear to ensure creative performance in other types of tasks. The extent to which creativity is task and domain specific has important theoretical and educational implications, and needs to be the subject of further research. If creativity varies in connection with tasks, and possibly in connection with domains as well, then the extent to which it represents a relatively stable characteristic or ability is questionable. These findings cast doubts on the appropriateness of employing general measures to identify and predict creative potential for research or educational purposes. Instead, a more valid approach might be the assessment of creativity through the use of a variety of appropriate and representative tasks within a domain of interest. Even though the problem types we have employed—explanation, prediction, and application—are highly representative of those frequently addressed in

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the domain of physics and science in general, they are not representative of those encountered in physics courses at the secondary and undergraduate levels. Typically, students are required to describe physical phenomena, calculate quantities, and conduct experiments that have been carefully prespecified as to their procedures and outcomes by instructors and textbook authors. These activities are designed to promote the acquisition of theories, concepts, and procedures in the domain. At the same, time they may foster the perception of knowledge acquisition as an end goal, thus rendering the knowledge acquired less flexible and applicable in novel situations. In that case, these activities are unlikely to promote creativity as exemplified by the extension of acquired knowledge and the creation of new knowledge (Johnson-Laird, 1987). It has been argued extensively that creativity depends on the availability of a large knowledge base (Amabile, 1990; Boden, 1992; Sternberg, 1988; Weisberg, 1986). Conceptual knowledge is considered to be a prerequisite to mentally representing the problem and guiding the generation and evaluation of solutions (Feldhusen, 1994; Johnson-Laird, 1988). Although these findings do not appear to support the preceding claim, they cannot be taken to confirm the opposite claim that too much knowledge may hinder creativity (Sternberg, 1988). The relation between prior conceptual knowledge and the creativity measures was weak but negative only with respect to the prediction problem. An examination of the response protocols indicated that at least half of the appropriate responses to the prediction problem were based on concepts of astronomy and space travel, and not on concepts of nuclear energy as we had originally hypothesized and assessed with the prior knowledge test. Therefore, the negative relation may be partly due to the fact that we evaluated a different knowledge base from the one actually accessed by our students. According to Schank (1988), the interpretation and the solution of a problem depend not only on prior conceptual knowledge, but also on the availability of relevant previous experiences in memory. The rules, or what Schank (1988) referred to as the explanation patterns, that were employed to deal with previous experiences are selectively accessed and modified to apply to a new problem. Amabile (1990) and Runco and Chand (1995) also argued that creativity is based on different kinds of domain-relevant knowledge, both declarative and procedural. Considering these claims, it becomes

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apparent that the prior knowledge test employed in this study was limited in terms of the extent and the depth to which it assessed potentially relevant knowledge. The test was not designed to evaluate procedural knowledge—that is, familiarity and strategy use with problems of this type. The possibility that the results concerning the knowledge factor may be attributable to the test is strengthened by a closer examination of the responses and the results concerning the explanation problem. Knowledge of the underlying concepts (entropy and dynamic equilibrium) was above average, and the response protocols indicated that this knowledge provided the basis for the responses given. Yet, only 11% of all the responses were judged to be appropriate, and only 3% received high originality scores. Clearly, the explanation problem presented a greater challenge to our students than either the prediction or the application problem. The task it represents is highly demanding, requiring the formulation of a theory to account for the physical phenomena described. Theory formulation requires not only in-depth and flexible knowledge of immediately related and more distant concepts, but also knowledge about the structure of theories and the processes that are involved in their construction. Even though this study did not examine this kind of knowledge, it can be expected to be low. The content, goals, and methods of teaching and testing at the secondary and undergraduate levels, at least in the context of science education, are characterized by more of an emphasis on the learning of phenomena and the laws that govern their behavior than on the epistemological construction of structured theories. Therefore, our students can be expected to know more about established theories and their applications than the processes that guide theory formulation. The results concerning the influence of academic achievement indexes, such as GPA and grade in a physical science course, parallel those concerning the influence of prior knowledge. This is not surprising if we consider that grades in different academic subjects are taken to reflect the knowledge acquired in the corresponding subject areas. These findings overall support the notion that creativity and academic achievement are not linked (Guilford, 1956; Sternberg, 1988; Taylor, 1988). However, prior knowledge represents a complex factor, and creativity appears to depend not so much on the simple availability of knowledge but on the ability to extend and go beyond the knowledge ac-

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I. N. Diakidoy and C. P. Constantinou

quired. Therefore, further research should examine more thoroughly the different kinds of knowledge and skills that may contribute to creativity in different domains and tasks. Such research has greater potential to provide a more solid basis for educational planning and practice.

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