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47 ABSTRACT INTRODUCTION JOHN SCHACTER YEOW MENG THUM DAVID ZIFKIN How Much Does Creative Teaching Enhance Elementary School Students’ Achievement? This study examined the relationship between creative teach- ing and elementary students’ achievement gains. Forty-eight upper elementary school teachers’ classroom instruction was observed and evaluated over the course of 8 different lessons throughout the year. For each teacher, during each lesson, both a creative teaching frequency score and a quality score were derived. These scores were then used as predictor variables in a structural equation model to determine the magnitude of the relationship between creative teaching and classroom achievement gains in reading, language, and mathematics. Our results demonstrated that (a) the majority of teachers do not implement any teaching strategies that foster student creativ- ity; (b) teachers who elicit student creativity turn out students that make substantial achievement gains; and (c) classrooms with high proportions of minority and low-performing students receive significantly less creative teaching. Over the past 50 years, researchers have consistently docu- mented that developing student creativity is not a priority of American teachers (Dacey & Lennon, 1998; Gowan, Khatena, & Torrance, 1981; Grigorenko & Sternberg, 1997; Nickerson, 1984; Torrance, 1976, 1995; Torrance & Safter, 1986). In fact, several scholars portend that American teachers suppress children’s ability to imagine and to defy the status quo (Gowan & Olson, 1979; Parkhurst, 1999). Instead of increasing student creativity, teachers appear to stifle it (Grigorenko & Sternberg, 1997; Torrance & Safter, 1986). As E. Paul Torrance’s (1995) longitudinal studies have shown, the more students attend school the less curious, more cautious, and less creative they become. Volume 40 Number 1 First Quarter 2006

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ABSTRACT

INTRODUCTION

J O H N S C H A C T E RY E O W M E N G T H U M

D A V I D Z I F K I N

How Much Does Creative TeachingEnhance Elementary SchoolStudents’ Achievement?

This study examined the relationship between creative teach-ing and elementary students’ achievement gains. Forty-eightupper elementary school teachers’ classroom instruction wasobserved and evaluated over the course of 8 different lessonsthroughout the year. For each teacher, during each lesson, botha creative teaching frequency score and a quality score werederived. These scores were then used as predictor variablesin a structural equation model to determine the magnitude ofthe relationship between creative teaching and classroomachievement gains in reading, language, and mathematics. Ourresults demonstrated that (a) the majority of teachers do notimplement any teaching strategies that foster student creativ-ity; (b) teachers who elicit student creativity turn out studentsthat make substantial achievement gains; and (c) classroomswith high proportions of minority and low-performing studentsreceive significantly less creative teaching.

Over the past 50 years, researchers have consistently docu-mented that developing student creativity is not a priority ofAmerican teachers (Dacey & Lennon, 1998; Gowan, Khatena,& Torrance, 1981; Grigorenko & Sternberg, 1997; Nickerson,1984; Torrance, 1976, 1995; Torrance & Safter, 1986). In fact,several scholars portend that American teachers suppresschildren’s ability to imagine and to defy the status quo (Gowan& Olson, 1979; Parkhurst, 1999). Instead of increasing studentcreativity, teachers appear to stifle it (Grigorenko & Sternberg,1997; Torrance & Safter, 1986). As E. Paul Torrance’s (1995)longitudinal studies have shown, the more students attend schoolthe less curious, more cautious, and less creative they become.

Volume 40 Number 1 First Quarter 2006

48

Creative Teaching

While the findings from research on teachers’ effects on stu-dent creativity have been generally negative, no studies, to theauthors’ knowledge, have examined the relationship betweencreative teaching and students’ subsequent achievement. Stu-dents taught by creative teachers may very well attend better,be more motivated, engage in more thinking and problem solv-ing, and simply enjoy class more. These factors may, in turn,contribute to gains in student learning.

Recently, a convergence of studies has identified teachersas the primary dynamic responsible for increased studentachievement (Haycock, 1998; Jordan, Mendro, & Weerasinghe,1997; Rivkin, Hanushek, & Kain, 2001; Sanders & Horn, 1995,1998; Schacter & Thum, 2004). However, the teaching behav-iors, dispositions, qualifications, and qualities that separateeffective teachers from ineffective ones remain unknown(Hanushek, 2002; Shulman, 1986). Though it is clearly evi-dent that teachers vary in terms of their productivity (e.g., theirclassroom achievement gains), few researchers have been ableto explain why. We argue that accounting for the variability inteacher productivity by relating productivity to creative teach-ing has the potential to increase all classrooms’ achievement,because all teachers can be informed of a set of skills and dis-positions that augment student learning.

To reiterate, the purpose of this study is to establish a rela-tionship between creative teaching behaviors and studentachievement. Doing so not only may turn out students wholearn more and can think and act creatively, but also mayinform teachers how to teach more effectively. To measurehow teachers instruct in ways that foster student creativity, wedeveloped a framework of creative teaching behaviors. Thesebehaviors were based on a confluence of factors that have beenfound to increase the likelihood of creative output (Amabile,1983, 1996; Csikszentmihalyi, 1996; Gardner, 1993; Guilford,1967, 1976; Nickerson, Perkins, & Smith, 1988; Perkins, 1981,1986; Runco, 1999; Simonton, 1988, 2000; Singer & Singer,1990; Sternberg, 1985, 1996; Torrance, 1967, 1976). Our frame-work posits that teachers can promote student creativity by(a) explicitly teaching creative thinking strategies, (b) provid-ing opportunities for choice and discovery, (c) encouragingintrinsic motivation, (d) establishing a learning environmentconducive to creativity, and (e) providing opportunities forimagination and fantasy.

To our knowledge, this is the first study that systematicallyobserved a sample of elementary school teachers’ classroom

Journal of Creative Behavior

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instruction with the intent to record the frequency, and the qual-ity of the opportunities they provided to develop their students’creativity. We then used these teaching process data to buildan explanatory model that attributed differences in studentachievement to the differences in the frequency and quality ofcreative teaching.

This study measured 48 third-grade through sixth-gradeteachers’ creative teaching behaviors and the impact of thesebehaviors on students’ reading, language, and mathematicsachievement. All 48 teachers were observed on eight differentoccasions throughout the course of the 2001-2002 academicyear. Classroom observations lasted the entirety of a lesson.In total, the 48 teachers were observed for approximately 437hours.

For each teacher, during each observed lesson, both a cre-ative teaching frequency score and a quality score were calcu-lated. These scores were averaged over 8 observations and thenused as predictor variables in an SEM model to determine therelationship between providing opportunities for student cre-ativity and student achievement gains.

Teachers. Participants were 48 teachers (15 third-grade, 16fourth grade, 10 fifth-grade, and 7 sixth-grade teachers) fromfour public elementary schools in Arizona. All observed teach-ers were fully certified, and had at least 3 years of public schoolclassroom teaching experience. The teacher sample consistedof 4 males and 44 females, with 40 reporting themselves asCaucasian, 1 African American, and 7 Hispanic. The meanteacher age was 41.

Students. Eight hundred sixteen students participated (264third graders, 272 fourth graders, 157 fifth graders, and 123sixth graders). Of the 816 students, testing records identified354 as Caucasian, 54 African American, 305 Hispanic, 62Native American, 19 Asian, and 22 students classified as Other.Three hundred eighty-eight students were male and 428were female.

Observations. Over the course of the 9-month study, eachteacher was observed eight different times. Four classroomobservations were conducted from October to December 2001,and four from February to May 2002. All observations lastedthe entire duration of the lesson. Observations ranged from 31minutes to 1 hour and 28 minutes. Total observation time for

METHOD

Participants

Procedures

50

Creative Teaching

each teacher ranged from 7 hours and 22 minutes to 11 hoursand 32 minutes.

To ensure fair sampling of teacher behaviors, each teacherwas observed at different times of the day. Three observationswere early morning (between 8:00 and 9:30 a.m.), 3 mid-morn-ing (between 9:30 a.m. and 12:00 p.m.), and 2 in the after-noon (between 1:00 and 3:15 p.m.). Two observations wereformally scheduled, with the reason for the visit being to learnmore about how different teachers teach. Six observations werenot scheduled or announced. The researchers further variedthe days that they visited classrooms to ensure that they saweach teacher teach on each day of the week.

Researcher training. Four graduate student researcherswere hired and trained in observation and data collection pro-cedures during the summer of the 2001. All researchers hiredfor the study had completed at least two graduate level coursesin qualitative research methods. Training consisted of two1-day sessions.

Training Session 1. The first training session taught thegraduate student researchers how to take ethnographic fieldnotes and use the study’s standardized chronology. The gradu-ate students watched two videotaped lessons (one fourth-gradereading, and one sixth-grade mathematics), and practiced us-ing the field note strategies by composing scripts for each tape.After each videotaped lesson, participants compared their fieldnotes and chronology to those of the lead author of the study.Strengths and weaknesses in each of the graduate student re-searchers’ field notes were discussed.

B. Training session 2. The second training session focusedon reviewing field notes immediately following the observation,then rating the teacher for creative frequency and quality us-ing the items in the creative teaching framework (described inthe Results section). Graduate student researchers watchedthree videotaped elementary teacher lessons (i.e., third-gradereading, fourth-grade social studies, and fifth-grade mathemat-ics), composed field notes for each lesson, and then used theirnotes to rate each teacher’s behaviors. The videotapes thatthe graduate student researchers watched and scored werepre-rated by the lead author of the study. Graduate studentresearcher ratings were compared to the ratings of the leadauthor of the study, and where scores deviated, discussionswere conducted.

Journal of Creative Behavior

51

C. Ongoing training. In addition to the summer trainingsessions, the lead author of the study reviewed two sets of fieldnotes that each graduate student researcher composed eachweek. Through weekly phone conferences and face-to-face vis-its, the lead author provided written and verbal feedback toeach graduate student researcher to make certain that thequality of the field notes continued to meet an acceptable stan-dard, and that the graduate students’ ratings were derived fromwhat they had documented.

Researcher teacher assignments. The four graduate stu-dent researchers conducted all teacher classroom observa-tions. Each graduate student was assigned 12 teachers toobserve. In addition, 8 teachers were randomly selected (2 fromeach of the four schools) to be observed and rated on the sameday during the same lesson by the 4 graduate student research-ers. Table 1 reports the Cronbach alpha interrater reliabilitiesfor creative teaching frequency and quality ratings.

Interrater reliability for creative teaching frequency and quality.

Creative Teaching Creative TeachingTeacher Frequency Quality

1 .91 .632 .94 .723 .90 .694 .88 .815 .89 .746 .96 .687 .85 .878 .92 .76

Creative Teaching Framework. The Creative TeachingFramework consisted of 19 items designed to evaluate howfrequently and at what quality classroom teachers providedopportunities for their students’ creativity. Five areas found inthe literature that increase the likelihood of creative output wereidentified and teaching behaviors that elicited these qualitieswere drafted. The areas were (a) explicitly teaching creativethinking strategies, (b) providing opportunities for choice anddiscovery, (c) encouraging intrinsic motivation, (d) establish-ing a learning environment conducive to creativity, and (e)

TABLE 1.

Measures

52

Creative Teaching

providing opportunities for imagination and fantasy (thebehaviors measured for each area are provided in Table 3).

A. Scoring: Creative teaching frequency. Based on analy-ses of each researcher’s field notes, frequency counts for eachof the 19 creative teaching behaviors (described in Table 3)were recorded after each lesson. For instance, item 1 states“The teacher leads students in activities that require them togenerate and record multiple ideas.” Every instance in a les-son where this occurred received 1 frequency point. Thus, ifthe lesson was a math lesson and the teacher had studentsproduce multiple equivalent fractions for ½, represent ½ threedifferent ways, and create different math problems that involved½, the teacher would receive 3 frequency points.

After each lesson, the frequencies for each behavior weresummed. Then, over the course of the eight observations, thefrequencies for each behavior were summed. Finally, the totalsummed frequency scores for each of the 19 behaviors werescaled from 1 to 5 based on the following coding scheme. If,over the course of eight observations, the total frequency countfor the behavior was 0, the teacher received a score of 1 forthat behavior. If the count was from 1 to 2, the teacher receiveda score of 2. Behaviors that occurred 3 or 4 times were scored3; behaviors that occurred 5 or 6 times received a score of 4,and behaviors that occurred 7 or more times were scored as 5.To calculate a single total eliciting creativity teaching frequencyscore for each teacher, we summed and then averaged thecoded frequencies for the 19 behaviors.

B. Scoring: Creative teaching quality. After each lesson,researchers reviewed the teaching behaviors that were presentand assigned each behavior a quality rating. If behaviorsoccurred in more than one lesson, an average quality ratingover all the lessons in which the behavior occurred was com-puted. For behaviors that occurred in only one lesson, the singlequality rating was used. A 3-point coding scheme was devel-oped to assess the quality of each of the 19 eliciting studentcreativity teacher behaviors. The quality was determined basedon two dimensions: (a) whether the behavior was a goal orsubgoal of the lesson, and (b) whether the behavior wasexplained and elaborated such that students incorporated itinto their work and thinking. For a creative teaching behaviorto be rated as high quality (i.e., a score of 3), it had to becommunicated to students, linked to the lesson’s purpose,explained, and expectations for performance had to be explicit

Journal of Creative Behavior

53

and demanding. A creative teaching behavior that was ratedas low quality (i.e., a score of 1) was not clearly communi-cated; it was not related to the lesson’s purpose; little explana-tion for how to carry out the behavior could be inferred; andexpectations for performance were vague. Finally, a creativeteaching behavior that was rated as moderate quality (i.e.,a score of 2) was somewhat aligned to the lesson’s purpose,there was some explanation for how to carry out the desiredbehavior, and expectations for performance were clear to themajority of students.

Teacher productivity. Teacher productivity was defined asa composite measure of each teacher’s classroom’s achieve-ment progress from a pretest to posttest scenario in which theStanford 9 Reading, Language, and Mathematics total scalescores served as the outcome measures. Teacher productivitywas calculated by employing a multivariate multilevel statisti-cal model that appropriately reflected the nesting structure ofclassroom data (see the Appendix, and Thum, 2003, for addi-tional detail). In this study, we utilized student-level data (816students’ combined Stanford 9 Reading, Language, and Math-ematics scale scores) from 48 teachers’ classrooms to pro-duce each teacher’s productivity estimate.

Classroom composition. With a heterogeneous mix of stu-dents within classrooms (e.g., race/ethnicity, initial achieve-ment, limited English proficiency, etc.), validation of a plausiblerelationship between teacher productivity and creative teach-ing behaviors required that we control for the influence of stu-dent and classroom intake characteristics that may potentiallyimpact progress. Though previous research employing multi-level multivariate statistical models (e.g., value-added assess-ment) has shown a lack of relationship between studentbackground variables and achievement gains, little researchhas explored how the proportion of students with differentintake characteristics within classrooms may impact progress.As controls for the current study, we therefore, employ severalmeasures of classroom composition, specifically the propor-tion of Hispanic students in the classroom (HISP), the propor-tion of students in the classroom designated as limited Englishproficient (LEP), and the proportion of students in the class-room who were performing at the “Below Basic” level in theprevious year, and who were not LEP or in special education(LowNPR).

54

Creative Teaching

Our preliminary analyses for classroom composition con-sidered a larger set of classroom measures, including the pro-portion of children classified as Gifted, proportion of males,proportion of children of African American descent, and chil-dren who received special education services. HISP, LEP, andLowNPR, however, were the three measures that carried suffi-ciently nonoverlapping information about a classroom’s com-position for our set of 48 teachers, and thus were the measurescontrolled for in the subsequent models we describe.

In Table 2, we present descriptive statistics and correlationsbetween variables for the 48 teachers and 816 students thatparticipated in our study.

Table 2 indicates that the students of teachers in our sample,on average, showed gains in mathematics and reading, butexperienced losses in language. Gains for Sanford 9 Reading,Mathematics, and Language scores tended to be moderatelyto highly correlated. Moreover, our descriptive data demon-strate that teachers provided very few opportunities for studentsto exercise their creativity. Virtually no creative teaching strat-egies were implemented by the teachers in our sample overthe course of 8 different lesson observations. Furthermore,

TABLE 2. Descriptive statistics: Teacher productivity, teacher creativity, andclassroom composition.

Teacher Classroom

n = 48Teacher Productivity Creativity Composition

LANG MATH READ CREAT CREAT HISP LEP LOWF Q NPR

Mean –6.21 8.73 10.08 1.39 1.42 3.15 2.23 2.19

Std. 8.51 10.86 6.65 0.33 0.41 1.31 1.67 1.37

1.00

0.59 1.00

0.70 0.74 1.00

Correlation 0.74 0.63 0.79 1.00

0.68 0.57 0.73 0.89 1.00

0.00 –0.01 0.03 –0.07 –0.08 1.00

–0.23 –0.13 –0.17 –0.40 –0.40 0.68 1.00

–0.36 –0.27 –0.40 –0.46 –0.42 0.26 0.45 1.00

RESULTSData

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when creative teaching strategies were employed, the qualityof the teaching was low.

Interestingly, both Creative Teaching Frequency and Qual-ity scores were highly correlated with Teacher Productivity inLanguage, Reading and Mathematics, suggesting a strongrelationship between teachers who provide opportunities forcreativity in their classrooms and student achievement gainsin these subjects. Finally, Creative Teaching Frequency andQuality scores were negatively related to LEP (–.40, –.40), andLowNPR (–.46, –.42) students.

In terms of Classroom Composition, teachers taught classeswith approximately 37% Hispanic students, 9% LEP students,and 9% students classified as LowNPR. These variables corre-lated modestly with each other. Note that both the proportionof LEP students and Hispanic students in classrooms did notcorrelate with Teacher Productivity. This provides some evi-dence that there is no relationship between these ClassroomComposition variables and student achievement gains. How-ever, the proportion of LowNPR students (e.g., students per-forming below basic in Reading, Language and Mathematics)is moderately correlated with Teacher Productivity (–.36,–.27,–.40 for Language, Mathematics, and Reading, respectively).1

Creative Teaching Frequency and Quality. Table 3 pre-sents descriptive statistics for each of the 19 Creative Teach-ing Frequency and Quality behaviors. To reiterate, if over thecourse of eight observations the total frequency count for thebehavior was 0, the teacher received a score of 1 for thatbehavior. If the count was from 1 to 2, the teacher received ascore of 2. Behaviors that occurred between 3 and 4 times werescored 3; behaviors that occurred 5 to 6 times received a scoreof 4, and behaviors that occurred 7 or more times were scoredas 5. Quality was rated on a 3-point scale with 3 indicatinghigh quality, 2 moderate quality, and 1 low quality.

An examination of the means reveals that teachers on aver-age did not implement any teaching behaviors that providedopportunities for their students to develop their creativity. More-over, when teachers did elicit student creativity, the quality ofthe teaching was poor.1 Logarithmic transformations made each of these variables more

symmetric, but our analyses suggested that they remained slightly right-skewed. As a result, one needs to be cautious when interpreting test of fitand standard error estimates. This is particularly a concern when weemploy methods that are based on the assumption of multivariatenormality of the outcomes.

56

Creative Teaching

TABLE 3. Descriptive statistics: Creative teaching frequency and quality.

n Freq. Freq. Quality QualityStd. Std.

Teaching Creative Thinking Strategies1. The teacher leads students in

activities that require them togenerate and record multiple ideas. 48 2.09 .88 1.60 .63

2. The teacher teaches students creativethinking strategies such as: divergentthinking, brainstorming, usinganalogies, redefining a problem,or synectics. 48 2.11 .56 1.38 .63

3. The teacher explicitly teachesmetacognitive strategies. 48 1.21 .42 1.34 .52

Opportunities for Choice and Discovery4. The teacher creates learning scenarios

where students can choose fromone of several activities. 48 1.22 .41 1.43 .64

5. The teacher creates activities wherestudents have to discover the answerby examining various modelsand ideas. 48 1.11 .33 1.37 .72

6. The teacher develops activities wherestudents have to create an originalartifact and present this artifact as apotential new solution to a problem. 48 1.08 .37 1.36 .59

Intrinsic Motivation7. The teacher focuses students’

attention by reinforcing theimportance of the task, and notextrinsic factors such as gradesand rewards. 48 1.25 .43 1.55 .70

8. The teacher recognizes, values, andreinforces creative thinking andcreative processes. 48 2.03 .78 1.36 .59

9. The teacher links rewards with thecreative process, not solely the result. 48 1.09 .21 1.32 .58

10. When using rewards, the teacheremphasizes the importance of thetask rather than completing thetask for the reward. 48 1.34 .46 1.53 .64

Journal of Creative Behavior

57

TABLE 3. (cont.) Descriptive statistics: Creative teaching frequency and quality.

n Freq. Freq. Quality QualityStd. Std.

Environment Conducive to Creativity

11. The teacher is supportive andencouraging of students’ non-conformist and unusual ideas. 48 1.22 .23 1.64 .74

12. The teacher is tolerant of ideas thatdo not lead to the correct answer. 48 2.03 .82 1.74 .86

13. The teacher encourages creativethinking and creativity in tasksthat do not necessarily requirecreativity. 48 1.15 .43 1.23 .47

14. The teacher develops anatmosphere focused on inquiry,curiosity, exploration, andself-directed learning. 48 1.37 .47 1.30 .57

15. The teacher supports andencourages risk-taking and makesstudents aware that they will notbe penalized for failing. 48 1.30 .55 1.09 .30

16. The teacher emphasizes a sense ofindependence and responsibilityfor learning. 48 2.10 .81 1.58 .63

Imagination and Fantasy

17. The teacher explains howimagination and fantasy can leadto changing existing ideas intooriginal creations. 48 1.19 .29 1.23 .47

18. The teacher creates activities thatengage students in usingimagination and fantasy. 48 1.30 .36 1.38 .63

19. The teacher creates learningexperiences where students applyimagination and fantasy to realworld situations and problems. 48 1.16 .27 1.34 .55

Note. Creative teaching frequency scaled from 1 to 5 with 5 indicating highfrequency.

Creative teaching quality scaled from 1 to 3 with 3 indicating highquality.

58

Creative Teaching

We report our analyses by beginning with a path diagramrepresented in Figure 1. Arrows indicate a direct effect fromone variable or latent construct to another.

Analyses

1 1

2 1 2

3 3

.

LANG

MATH

READ

λ ελ η ελ ε

= +

2 We have employed a weighted least squares criterion to gain robustnessfrom small departures from multivariate normality.

, TEACHER PRODUCTIVITY

LANG

MATH

READ

LOWNPR

LEP

HISP

, CLASSROOM COMPOSITION β31 β23

β21

λ6

λ5

λ4 λ3

λ2

λ1

ζ1

ζ2

ε2

ε1

ε3

δ1

δ2

δ3

η1

CREATIVE TEACHING

QUALITY FREQUENCY ν1 ν2

λ7 λ8

η2

η3

FIGURE 1. Model.

Teacher Productivity. We estimated a factor analysis modelfor Teacher Productivity based on our prior classroom produc-tivity estimates (See Appendix A, and Thum, 2003) for thethree subtests of the Stanford 9 Achievement Tests (e.g., Lan-guage, Mathematics, and Reading). To capture overall TeacherProductivity, 1η , we pose a single-factor measurement modelfor our classroom gain estimates with factor loadings 1λ forLanguage, 2λ for Mathematics, and 3λ for Reading.

(1.0)

Our exploratory results suggested that a model that weightseach measure equally (by constraining 1 2 3λ λ λ= = ) providedan adequate fit to the data under a weighted least-squares cri-terion2 ( 2

1χ = 2.66, p = 0.10; GFI = 0.97; CFI = 0.96; NNFI = 0.89),although the average residual is somewhat high (RMSEA= 0.17).

Classroom Composition. In a separate factor analysismodel, we estimated the Classroom Composition construct,

2η , using the log transformations of the proportions of (1)Hispanic (HISP) students (2) Limited English Proficient (LEP)students, and (3) students performing below basic (LowNPR)

Journal of Creative Behavior

59

in each teacher’s classroom with factor loadings 4λ , 5λ , and

6λ representing these variables respectively.

(2.0)

Our exploratory results suggested that a model whichweights these classroom composition variables differently inthat they have equal error variances gave a reasonable fit us-ing the weighted least-squares criterion ( 2

1χ = 3.05, p = 0.08;GFI = 0.98; CFI = 0.94; NNFI = 0.83). There is, however, someindication of large residuals (RMSEA = 0.21).

Creative Teaching. For the Creative Teaching construct weestimated, 3η , using the creative teaching frequency and qual-ity scores 7λ , 8λ , respectively.

(3.0)

Model. Our model builds on the factor models above.

(4.0)

We hypothesized that Creative Teaching, , would impactTeacher Productivity, 1η (by 31β ), far greater than ClassroomComposition, 2η (by 21β ). Thus, the critical relationship forour purposes here is the impact of Creative Teaching onTeacher Productivity. For our final model, we therefore simul-taneously estimated our measurement models for TeacherProductivity, Classroom Composition, and Creative Teaching,along with our path model.

Our final model provided a more than adequate fit to thedata ( 2

15χ = 17.96, p = 0.26; GFI = 0.98; CFI = 0.99; NNFI =0.98; RMSEA = 0.06).

Our results are summarized in Table 4.Turning to the estimates that are central to our analyses, it

appears that teachers who implement teaching behaviors thatelicit student creativity are highly productive, meaning theyturn out students that make very large and significant achieve-ment gains ( 31β = 27.34; s.e. = 0.04; t = 671.20). According

4 1

5 2 2

6 3

HISP

LEP

LowNPR

λ δλ η δλ δ

= +

7 13

8 2

CREATF

CREATQ

λ υη

λ υ

= +

3 23 2 1

1 21 2 31 3 2+

η β η ζη β η β η ζ

= ⋅ += ⋅ ⋅ +

Findings

60

Creative Teaching

the Kline (1988) the standardized estimate of 0.90 indicates avery large achievement effect. Our second finding providesevidence that classrooms with higher concentrations ofHispanic, Limited English Proficient, or low-performing stu-dents (e.g., Classroom Composition) tend to receive lessCreative Teaching ( 23β = –0.13; s.e. = 0.04; t = –3.64). Thestandardized estimate for this path coefficient is –0.66, again

TABLE 4. Results: Factor loadings, error variances, and path coefficients.

Variable Factor Loadings Error Variances

Est. s.e. t-value Est. s.e. t-value

Teacher Productivity, 1ηLanguage 1.26 0.32 3.98 30.09 5.47 5.50

Mathematics 1.40 0.33 4.23 48.48 9.17 5.29

Reading 0.89 0.21 4.20 4.92 1.70 2.88

Classroom Composition, 2η% Hispanic 0.67 0.06 10.49 0.42 0.10 4.05

% LEP 1.35 0.11 12.50 0.77 0.15 4.97

% LOWNPR 0.94 0.13 7.30 0.72 0.22 3.25

Creative Teaching, 3ηCREATF 1.17 0.28 4.13 0.00 0.00 1.37

CREATQ 1.81 0.43 4.19 0.02 0.01 3.80

Latent Regression Residuals

1ς 0.02 0.01 2.01

2ς 3.72 0.29 12.70

Regression Coefficients Raw Standardized

31β , Creative Teachingon Teacher Productivity 27.34 0.04 671.20 0.90

23β , Classroom Compositionon Creative Teaching –0.13 0.04 –3.64 –0.66

21β , Classroom Compositionon Teacher Productivity –0.37 0.52 –0.72 –0.06

Journal of Creative Behavior

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a large and highly significant effect. Finally, the coefficient forClassroom Composition on Teacher Productivity is minimal( 21β = –0.37; s.e. = 0.52; t = –0.72) with a standardized coeffi-cient of –0.06. Similar to our previous research (Schacter &Thum, 2004), Classroom Composition does not appear toinhibit teachers from producing student achievement gains.

Our results demonstrate that: (a) the majority of teachersdo not implement any teaching strategies that foster studentcreativity; (b) teachers who elicit student creativity turn outstudents that make substantial achievement gains; and (c)classrooms with high proportions of minority and low perform-ing students receive significantly less creative teaching. Theseresults are disturbing because the benefits of being creativeare well established. Creative people tend to be happier, achievemore, receive more awards; are more likely than their peers tomake patentable inventions, publish articles, develop success-ful businesses, attain leadership positions later in life; and arein great demand by businesses worldwide (Csikszentmihalyi,1996; Dacey & Lennon, 1998; Mumford & Simonton, 1997;Torrance, 1995; U.S. Department of Labor, 1991).

In light of the fact that psychologists have argued that allpeople have the potential to be creative, that creative abilitiesare found in nearly everyone, and that creativity can beenhanced (Csikszentmihalyi, 1996; Gardner, 1993; Guilford,1975; Sternberg, 1985; Ward, Saunders, & Dodds, 1999), it isdisheartening that only a handful of the teachers we studiedimplemented instructional strategies that encouraged studentcreativity. In over 400 hours of observation of 48 elementaryteachers we found that the average teacher implemented hardlyany teaching behaviors that increased student creativity. Onaverage, each of the creative teaching behaviors we assessedoccurred less than 1 time over the course of eight differentlessons that took place from October 2001 to May 2002.Furthermore, in the rare instances when a teacher did elicitstudent creativity, the teaching strategy was not aligned withthe lesson objective, was not explained or elaborated, and thepurpose was not made clear to students.

In the introduction of this study, we cited previous research-ers, including Dacey and Lennon (1998), who claimed that“teachers, their peers, and the educational system as a wholeall diminish children’s urge to express their creative possibili-ties” (p. 69). We argued, however, that this prior work was notbased on systematic observations of classroom instruction.

DISCUSSION

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Creative Teaching

We posited that, by looking in classrooms and analyzingteacher behaviors based on an inclusive confluence model ofcreativity, our results would shed a more positive light on howelementary school teachers enhance their students’ creativity.Unfortunately, a more encouraging conclusion did not materi-alize. In fact, the results of this study support Torrance andSafter’s (1986) conclusion that teachers are not equipped tomeet the needs of students in terms of creativity, because teach-ers do not appear to know how to initiate, conduct, or evaluatecreativity themselves.

The first limitation of this study is the sample size. Due tothe expensive nature of intensive classroom observations, wewere only able to study 48 teachers.

The second limitation of our research was in how often wesampled each teacher’s instruction. Teachers were observedthroughout the course of an academic year on eight differentoccasions. All teachers were evaluated on various days of theweek, at various times of day, during lessons on different aca-demic content, in both announced and unannounced visits,and at different times interspersed throughout the school year.These careful sampling conditions were established to ensurethat the teacher behaviors observed captured how teachersregularly taught. While careful attention was paid to the sam-pling plan, and eight hours of observation per teacher wereconducted, more observation time in classrooms to draw amore comprehensive picture of each teacher’s instructionalbehaviors would have been valuable.

The final limitation of this research was that we only usedstandardized test data to draw a relationship between creativeteaching and student achievement gains. Standards-basedassessments and performance assessments that more com-prehensively test problem solving, thinking, and deep contentknowledge, might have replicated or refuted the strength ofassociation between creative teaching and student achievement.

Given the stated limitations, the results of this study dem-onstrate that creative teaching substantially improves studentachievement. This finding runs counter to the way educatorshave responded to the standards and assessment movement.Many teachers have claimed that high-stakes accountabilityhas limited their capacity to teach creatively, because standardsand state assessments dictate what and how to teach. Themajority of teachers, therefore, feel that to increase studentachievement, they must focus exclusively on the tested stan-dards, and devote little to no time to subjects and teaching

Study Limitations

Implications forPractice

Journal of Creative Behavior

63

strategies that do not appear on the state assessment. As thedata from this article evince, this reasoning is flawed. Insteadof drawing a dichotomy between accountability and teachingcreatively, this study suggests that the two are complemen-tary. Our implications for practitioners are these: focus on thestandards, and expand your instructional strategy repertoireto include creative teaching techniques.

AMABILE, T. (1983). The social psychology of creativity. New York:Springer-Verlag.

AMABILE, T. (1996). Creativity in context. Boulder, CO: Westview Press.

CSIKSZENTMIHALYI, M. (1996). Creativity: Flow and the psychology ofdiscovery and invention. New York: Harper Collins.

DACEY, J. S., & LENNON, K. H. (1998). Understanding creativity: Theinterplay of biological, psychological, and social factors. SanFrancisco, CA: Jossey-Bass.

GARDNER, H. (1993). Multiple intelligences: The theory in practice. NewYork: Basic Books.

GOWAN, J. C., KHATENA, J., & TORRANCE, E. P. (1981). Creativity: Itseducational implications. Dubuque, IA: Kendall/Hunt.

GOWAN, J. C., & OLSON, M. (1979). The society, which maximizes creativity.Journal of Creative Behavior, 13, 194-210.

GRIGORENKO, E. L., & STERNBERG, R. J. (1997). Styles of thinking,abilities, and academic performance. Exceptional Children, 63, 295-312.

GUILFORD, J. P. (1967). The nature of human intelligence. New York:McGraw-Hill.

GUILFORD, J. P. (1975). Varieties of creative giftedness. Their measurementand development. Gifted Child Quarterly, 19, 107-121.

GUILFORD, J. P. (1976). Aptitude for creative thinking: One of many?Journal of Creative Behavior, 10, 165-169.

HALPERN, D. F. (2002). Thinking critically about creative thinking. In M.Runco (Ed.), Critical creative processes (pp. 189-207). Cresskill, NJ:Hampton Press.

HANUSHEK, E. A. (2002). Teacher quality. In L. T. Izumi & W. M. Evers (Eds.),Teacher quality (pp. 1-12). Palo Alto, CA: Hoover Press.

HAYCOCK, K. (1998). Good teaching matters: How well-qualified teacherscan close the gap. Washington, DC: Education Trust.

JORDAN, H., MENDRO, R., & WEERASINGHE, D. (1997). Teacher effectson longitudinal student achievement. Dallas, TX: Dallas IndependentSchool District.

MUMFORD, M. D., & SIMONTON, D. K. (1997). Creativity in the workplace:People, problems and structures. Journal of Creative Behavior,31, 1-6.

NICKERSON, R. S. (1984). Kinds of thinking taught in current programs.Educational Leadership, 42(1), 26-36.

REFERENCES

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NICKERSON, R. S., PERKINS, D. N., & SMITH, E. (1988). The teaching ofthinking. Mahwah, NJ: Lawrence Erlbaum Associates.

PARKHURST, H. B. (1999). Confusion, lack of consensus, and the definitionsof creativity as a construct. Journal of Creative Behavior, 33, 1-21.

PERKINS, D. N. (1981). The minds best work. Cambridge, MA: HarvardUniversity Press.

PERKINS, D. N. (1986). Knowledge as design. Hillsdale, NJ: LawrenceErlbaum Associates.

RIVKIN, E. A., HANUSHEK, E. A., & KAIN, J. F. (2001). Teachers, schools,and academic achievement. Washington DC: National Bureau ofEconomic Research.

RUNCO, M. A. (1999). A longitudinal study of exceptional giftedness andcreativity. Creativity Research Journal, 12, 161-164.

SANDERS, W. L., & HORN, S. P. (1995). Educational assessment reassessed:The usefulness of standardized and alternative measures of studentachievement as indicators for the assessment of educational outcomes.Educational Policy and Analysis Archives, 3(6). Retrieved June 7,2004, from http://epaa.asu.edu/epaa/v3n6.html

SANDERS, W. L., & HORN, S. P. (1998). Research f indings from theTennessee Value-Added Assessment System (TVAAS) database:Implications for educational evaluation and research. Journal ofPersonnel Evaluation in Education, 12, 247-256.

SCHACTER, J., CALIFANO, L., BOCK, J., & BENDOTTI, M. (2002). Qualityteachers: Defining and developing them. Instructional Leader,15, 1-12.

SCHACTER, J., & THUM, Y. M. (2004). Paying for high and low qualityteaching. Economics of Education Review, 23, 411-430.

SHULMAN, L. S. (1986). Paradigms and research programs in the study ofteaching: A contemporary perspective. In M. C. Wittrock (Ed.),Handbook of research on teaching (3rd ed., pp. 3-36.). New York:Macmillan.

SIMONTON, D. K. (1988). Scientific genius: A psychology of science.Cambridge: Cambridge University Press.

SIMONTON, D. K. (1998). Creativity, genius and talent development. RoeperReview, 20, 86-87.

SIMONTON, D. K. (2000). Creativity: Cognitive, person, developmental andsocial aspects. American Psychologist, 55, 151-158.

SINGER, D. G., & SINGER, J. L. (1990). The house of make-believe:Children’s play and the developing imagination. Cambridge: HarvardUniversity Press.

STERNBERG, R. J. (1985). Beyond IQ: A triarchic theory of humanintelligence. Cambridge: Cambridge University Press.

STERNBERG, R. J. (1996). Successful intelligence: How practical andcreative intelligence determine success in life. New York: Simon andSchuster.

THUM, Y. M. (2003). Measuring progress toward a goal: Estimating teachingproductivity using a multivariate multilevel model for value-addedanalysis. Sociological Methods & Research, 32, 208-252.

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65

TORRANCE, E. P. (1967). Education and the creative potential. Minne-apolis: University of Minnesota Press.

TORRANCE, E. P. (1976). Guiding creative talent. Melbourne, AU: KriegerPublishing.

TORRANCE, E. P. (1995). Why fly? A philosophy of creativity. Westport,CT: Ablex Publishing.

TORRANCE, E. P., & SAFTER, H. T. (1986). Are children becoming morecreative? Journal of Creative Behavior, 20, 1-13.

UNITED STATES DEPARTMENT OF LABOR. (1991). What work requiresof schools. Washington, DC: Author.

WARD, T. B., SAUNDERS, K. N., & DODDS, R. A. (1999). Creative cognitionin gifted adolescents. Roeper Review, 21, 260-266.

Corresponding author: John Schacter, Ph.D., Milken Family Foundation, 1250Fourth Street, Santa Monica, CA 90401, [email protected]

The authors would like to thank Lowell Milken, president and co-chairman ofthe Milken Family Foundation. Mr. Milken has been a force in developingand funding educational reforms aimed at attracting, retaining, and rewardinghigh-quality teachers. Thank you Lowell and the Milken Family Foundationfor supporting this research.

ACKNOWLEDGEMENTS

66

Creative Teaching

Appendix AThe teachers we observed extensively for evidence of creativeteaching were part of a larger group of elementary school teach-ers who participated in a previous teacher productivity mea-surement study (see Thum, 2003). Measures of these 48teachers’ productivity are drawn from that analysis. For com-pleteness, we provide in this appendix a summary of the data,procedures, and methods we used to measure teacher gains.Table A1 lists the outcomes and covariates for the set of Ari-zona elementary classrooms from grades 3, 4, 5, and 6 thatparticipated in our productivity study.

Outcomes and covariates.

Outcomes

LANGUAGE Language (Form SA/TA) Scale ScoreMATHEMATICS Mathematics Total Scale ScoreREADING Reading Total Scale Score

Student Covariates (dummy variables)

FEMALE gender, “1” for female and “0” for maleAFAM ethnicity, “1” for African American and “0”

otherwiseHISPANIC ethnicity, “1” for Hispanic and “0” otherwiseLEP Limited English Proficiency status, “1” for LEP

and “0” otherwiseGIFTED Gifted status, “1” if designated as “gifted” and

“0” otherwiseSPECED Special Education status, “1” for Special Ed.

and “0” otherwiseLOWNPR99 Low Prior Attainment if not a Special Education

student, “1” if the maximum National PercentileRank (NPR) for 1999 SAT 9 Language, Mathe-matics, or Reading is less than 30, “0” otherwise

Teacher/Classroom Factors

tAFAM Proportion of students who are African AmericanstHISPANIC Proportion of students who are HispanicstLEP Proportion of students who are designated as

Limited English Proficiency statustGIFTED Proportion of students who are designated as

“gifted”tSPECED Proportion of students who are designated as

Special EducationtLOWNPR99 Proportion of students who are LowNPR99

MEASURINGTEACHER

PRODUCTIVITY

TABLE A1.

Journal of Creative Behavior

67

The outcomes are from the Stanford Achievement Tests9th Edition (SAT 9) total scale scores for 2001 and 2002on three subjects (e.g., language, mathematics and reading).Our covariates represent the spectrum of factors typicallyemployed in the accountability and school-effectiveness litera-tures. Classrooms in our study had approximately 18 studentson average.

Thum (2003) argued that for a number of conceptual andtechnical reasons, estimating gains made by a student fromone year to the next with a growth model is the most appropri-ate approach to measure student learning. In particular, thismethodology is more defensible than systems that are basedon the raw gain score, or anchored on the residualized gain.Using the raw gain score may be conceptually congruent withthe notion of value-added, but it represents an inefficient useof data. Residualized gains are close to being arbitrary in thatadjustments are sensitive to the choice of covariates, andthey also depend on the particular group of students in theanalysis. In addition, the residualized gain score is statisticallyproblematic because the pre-test, usually the critical covariateemployed in the adjustment, is correlated with the residuals.Even with statistical refinements, the residualized gain scoreis conceptually awkward, giving at best a weak sense of anadjusted gain. A growth modeling approach, however, essen-tially removes the deficiencies of primitive raw gain scoreanalyses and it is free from the shortcomings of residualizedgain approaches. In this application, we take a fully multivariateapproach to reflect growth on a wider set of learning objectives.

Individual student test scores over time. Let ytijk be thetest score at time t = 1,2 for student i = 1,2,K, nj in classroomj = 1,2,K, J at time t = 2 on subject k = 1,2,3 for language,mathematics, and reading respectively,

(1.0)

Timetijk is “1” if the score is the pre-test, and “2” if it is the post-test. LANGtijk if the score is for the language test and is “0”otherwise; MATHtijk and READtijk are similar dummy variablesfor the mathematics and reading score components. Note thatwe assume that residual errors are correlated over time, withvar(ε1ijk) = σ 2

11, var(ε2 ijk) = σ 222, and cov(ε1ijk, ε2 ijk) = σ 12. With

more data, a less restricted error model can be used. Thevariance and covariances in this residual matrix, which may

Multilevelmultivariate growth

model for value-added analysis

ytijk = π0 ij + π1ij.(Timetijk –1).LANGtijk

+ π2ij.(Timetijk –1).MATHtijk

+ π3ij.(Timetijk –1).READtijk + εtijk .

68

Creative Teaching

conveniently be denoted by Σ, are also assumed be constantacross students in our study. Further justification of this model,and strategies for assessing the adequacy of the error assump-tions at this, and other levels, are documented in Thum (2003).

Distribution of individual student pre-test and gains inthe classroom. For each student random effect, p = 0,1,2,3,we explore the differences among the students i in classroomj in the pre-test average, π0 ij, the gains (π1ij, π2ij, π3ij) in lan-guage, mathematics, and reading in terms of our set studentcharacteristics:

(2.0)

In this between-student equation, β00 j is the adjusted classroompre-test mean and (β10 j, β20 j, β30 j) are the adjusted classroommean in gains for language, mathematics, and reading. For q> 0, βpqj measure the adjustments due to the indicated studentcharacteristics. The residuals (r0 ij, r1ij, r2ij, r3 ij) are assumed tobe correlated with var(rpij) = τ 2

pp and cov(rpij, rp'ij) = τ pp' forp=/ p'. The variance and covariances in this residual matrix, T,are assumed be constant across students in our study.Correlations among the performance factors between studentsare interesting in that one component of the student’s perfor-mance may be important for the increases or decreases ofanother. For example, τ01/(τ00

. τ11) suggests the extent thatthe average student pre-test may be important to making gainsin language.

Distribution of classroom-level pre-test and gains. Next,each of the between-classroom random effects (β00j, β10j, β20j,β30j) may depend on classroom-level characteristics. In ouranalysis, only the adjusted means, βp 0 j, are assumed to varybetween classrooms according to

(3.0)

but the average impact of student covariates, βpqj, are foundto not to vary between classrooms. Because we have in ourdata a mix of third to sixth-grade classrooms, we deploy dummy

πpij = βp0 j + βp1 j

.FEMALEij + βp2 j

. AFAMij

+ βp3j.HISPANIC

ij + βp4j.LEP

ij + βp5 j.LOWNPR99

ij

+ βp6 j.SPECED

ij + βp7j.GIFTED

ij + r pij.

βp 0j = γp00 + γp01. GRADE4j + γp02

.GRADE5j + γp03.GRADE6j

+ γp04. tLEPij + γp05

. tSPECEDij

+ γp06. tGIFTEDij + γp07

. tAFAM j

+ γp08. tHISPANICj + γp09

. tLOWNPR99j + υp0j,βpq j = γpq0, for all q =/ 0,

Journal of Creative Behavior

69

variables (GRADE4j, GRADE5j, GRADE6j) in order to distin-guish between the different grade-levels, with the result thatγ000 estimates the third-grade pre-test mean and (γ100, γ200, γ300)estimate third-grade average gains in language, mathematics,and reading respectively; each of which are adjusted for theimpact due to various aspects of classroom composition (seeabove). For example, γ101 estimates the difference betweenfourth- and third-grade pre-test classroom means on averagefor classrooms with no children (1) who are designated as lim-ited English proficient (γ104, tLEP), and (2) who are given spe-cial education (γ105, tSPECED), and (3) are gifted (γ106,tGIFTED), and (4) are of African-American (γ107, tAFAM), or(5) Hispanic descent (γ108, tHISPANIC), and (6) has performedpoorly in prior grade (γ109, tLOWNPR99).

Finally, we assume that the residuals (υ00j, υ10j, υ20j, υ30j,)are correlated, with var(υp0j) = ψpp, and cov(υp0j, (υp'0j) = ψpp'for p =/ p'. As with the covariances at the student level, correla-tions such as ψ01/ψ00

.ψ11) will provide an indication, for ex-ample, of the extent that language gains at the classroom levelare constrained by the average pre-test level of the students,after controlling for classroom composition. The between-class-room variances and covariances are elements of the matrix ψψψψψ.

Final Model. After weighing the results from several analy-ses, we found that the model for estimating student gains, thebetween-student equations in

πpij = βp0j + rpij , for all p, (4.0)

and the between-school equation

(5.0)

jointly provided a good fit to our data for the 2001-2002 analy-ses. See Thum (2003) for a detailed investigation regardingmodel selection and model comparison for our model.

β00 j = γ000 + γ001 × (GRADE4) + γ002 × (GRADE5) + γ003 × (GRADE6)

+ γ004× (tSPECED) + γ005 × (tGIFTED) + γ006 × (tHISPANIC)

+ γ007× (tLow NPR) + υ00 j,

β10j = γ100 + γ101 × (GRADE4) + γ102 × (GRADE5) + γ103 × (GRADE6)

+ γ104× (tLow NPR) + υ10 j,

β20 j = γ200 + γ201 × (GRADE4) + γ202 × (GRADE5) + γ003 × (GRADE6)

+ γ204× (tLow NPR) + υ20 j,

β30 j = γ300 + γ301 × (GRADE4) + γ302 × (GRADE5) + γ303 × (GRADE6)

+ γ304× (tLow NPR) + υ30 j,

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Creative Teaching

We note that as we have found in our previous studies(Schacter & Thum, 2004; Thum, 2003) that student-level char-acteristics do not predict student gains. Since these covariatesserve only to give us more accurate standard error estimatesof teacher productivity (in terms of classroom gains), we donot adjust our productivity estimates for differences in thesecovariates.

Model estimates. Table A2 shows the marginal posteriormeans and standard deviations for the 24 fixed-effects, γ, forthe 2001-2002 student assessments.

Table A3 shows the posterior means and standard devia-tions for the unique elements of the variance-covariancematrices ΣΣΣΣΣ, ΤΤΤΤΤ, ΨΨΨΨΨ.

Classroom Productivity Estimates. Finally, we produce inFigures A1 and A2 the scatterplot matrix of our estimates forclassroom pre-test average, and the average gain for the class-room. It appears that the average pre-test does not predictaverage gains.

Turning to subject-specific gains, we examine the scatterplotmatrix in Figure A2. The message seems clear that the amountof gains made in one subject is positively correlated to themagnitude of gains on other subjects.

RESULTS

TABLE A2. Fixed-effects estimates for 2001-2002.

Avg. Language Mathematics ReadingPre-test Gain Gain Gain

mean s.d. mean s.d. mean s.d. mean s.d.

Grade-Level Constants

Grade 3 617.5 2.18 0.95 1.47 7.83 1.93 9.43 1.39Grade 4 24.53 2.39 –5.22 1.8 6.2 2.45 4.21 1.74

Grade 5 41.41 2.64 –9.89 2.05 6.89 2.67 0.12 1.95Grade 6 46.44 2.85 –8.25 2.13 11.05 2.82 2.6 2.06

Classroom Characteristics

Special Ed. –45.2 7.19 n.s. n.s. n.s. n.s. n.s. n.s.Gifted 29.83 10.27 n.s. n.s. n.s. n.s. n.s. n.s.Hispanic –21.13 2.6 n.s. n.s. n.s. n.s. n.s. n.s.LowNPR –63.39 6.34 –15.53 4.39 –29.7 5.75 –13.1 4.22

Journal of Creative Behavior

71

TABLE A3. Standard deviations and correlations for random effects.

Between Time Pointsmean s. d.

Pre-test 1σ̂ 27.32 0.25

Pre-test with Post-test21

σ̂ 0.59 0.01

Post-test 2σ̂ 20.66 0.23

Between Students Between Teachers

Pre-test Avg. 0τ̂ 27.42 0.53 0ψ̂ 8.94 0.91

Pre-test Avg. with Language Gain10

τ̂ –0.28 0.0410

ψ̂ –0.81 0.06

Language Gain 1̂τ 11.21 0.60 1ψ̂ 7.64 0.64

Pre-test Avg. with Math Gain20

τ̂ 0.00 0.0520

ψ̂ –0.75 0.07

Language Gain with Math Gain21

τ̂ 0.86 0.0321

ψ̂ 0.81 0.05

Math Gain 2τ̂ 11.10 0.63 2ψ̂ 11.32 0.81

Pre-test Avg. with Reading Gain30

τ̂ –0.02 0.0630

ψ̂ –0.67 0.09

Language Gain with Reading Gain31

τ̂ 0.89 0.0331

ψ̂ 0.80 0.05

Math Gain with Reading Gain32

τ̂ 0.90 0.0332

ψ̂ 0.63 0.07

Reading Gain 3τ̂ 8.46 0.53 3ψ̂ 7.16 0.61

FIGURE A1. Gains by Classroom Pretest

FIGURE A2. Gains by Tests (Language, Reading, Math).

72

Creative Teaching

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