preservice early childhood teachers' sense of efficacy for integrating mathematics and science:...

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Preservice Early Childhood Teachers'Sense of Efficacy for IntegratingMathematics and Science: Impact of aMethods CourseMesut Saçkes a , Lucia M. Flevares b , Jennifer Gonya b & Kathy CabeTrundle ba Necatibey School of Education, Balıkesir University, Balıkesir,Turkeyb College of Education and Human Ecology, The Ohio StateUniversity, Columbus, Ohio, USAPublished online: 16 Nov 2012.

To cite this article: Mesut Saçkes , Lucia M. Flevares , Jennifer Gonya & Kathy Cabe Trundle (2012)Preservice Early Childhood Teachers' Sense of Efficacy for Integrating Mathematics and Science:Impact of a Methods Course, Journal of Early Childhood Teacher Education, 33:4, 349-364, DOI:10.1080/10901027.2012.732666

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Journal of Early Childhood Teacher Education, 33:349–364, 2012Copyright © National Association of Early Childhood Teacher EducatorsISSN: 1090-1027 print / 1745-5642 onlineDOI: 10.1080/10901027.2012.732666

Preservice Early Childhood Teachers’ Senseof Efficacy for Integrating Mathematics

and Science: Impact of a Methods Course

MESUT SAÇKES1, LUCIA M. FLEVARES2, JENNIFERGONYA2, AND KATHY CABE TRUNDLE2

1Necatibey School of Education, Balıkesir University, Balıkesir, Turkey2College of Education and Human Ecology, The Ohio State University,Columbus, Ohio, USA

The purpose of this study was to explore the impact of an integrated science andmathematics methods course on preservice early childhood teachers’ efficacy beliefsfor integrating these content areas. Thirty-four preservice teachers participated inthis study, which utilized a quasi-experimental design with two treatment groups.Participants in two cohorts were tested to assess their efficacy beliefs for teachingscience, mathematics, and integrated science and mathematics before and immedi-ately after instruction that lasted 8 weeks. Results indicated a statistically significantchange in preservice teachers’ efficacy beliefs scores from pre- to posttest measures.These results provide evidence that the methods course utilized in the present study waseffective in enhancing preservice teachers’ efficacy beliefs for integrating science andmathematics.

Introduction

Despite the importance of teaching science and mathematics in the early years (Clements& Sarama, 2004; French, 2004) and the current emphasis on integrating science and math-ematics (Beatty, 2005; Berlin & White, 1994), previous studies indicate that most earlychildhood teachers do not explicitly teach science and mathematics in their classrooms(Jarrett, 1999; Tu, 2006). In addition, they rarely attempt to integrate science and mathe-matics (Cady & Rearden, 2007; Douville, Pugalee, & Wallace, 2003; Koirala & Bowman,2003). Several factors influence the classroom practices of teachers, including the socialand physical structure of the school (Domingos, 1989), values (Bishop, 2008), epistemo-logical orientation (Pape & Woolfolk Hoy, 2002), teachers’ beliefs about students’ learning(Lee, 2006; Levitt, 2001) and teachers’ efficacy beliefs (Woolfolk Hoy, Davis, & Pape,2006). Among these factors, the beliefs teachers hold about how successfully they will beable to perform instructional activities seem to be particularly important.

Researchers have reported that many early childhood teachers have low confidencefor teaching science and mathematics due to their limited understanding of the scienceand mathematics concepts they are expected to teach (Garbett, 2003; Odgers, 2007; Pell &

Received 15 August 2011; accepted 23 January 2012.Address correspondence to Mesut Saçkes, Necatibey School of Education, Balıkesir University,

10100 Balıkesir, Turkey. E-mail: [email protected]

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350 M. Saçkes et al.

Jarvis, 2003). Along with these content knowledge concerns, early childhood teachers oftenstruggle with understanding effective instructional strategies for teaching mathematics andscience in early childhood classrooms (Bintas, 2008; Czerniak, & Chiarelott, 1990; Schoon& Boone, 1998). Lack of content knowledge and limited experience with integration havealso been identified as obstacles for the successful integration of mathematics and science(Koirala & Bowman, 2003).

Although the integration of mathematics and science at the elementary and middleschool levels has been advocated for a long time in the literature (Beatty, 2005; Berlin &Lee, 2005; Berlin & White, 1994; Tu, 2006), little effort has been made to prepare teachersin the practice of effective integration of mathematics and science (Furner & Kumar, 2007;Isaacs, Wagreich, & Gartzman, 1997; Jones, Lake, & Dagli, 2003). An increasing numberof studies have focused on teachers’ efficacy beliefs for teaching science and mathematicsand the nature of their instructional practices. However, studies that focus on preserviceand inservice teachers’ perceptions and practice of science and mathematics integrationare scarce (Cady & Rearden, 2007; Douville et al., 2003). Moreover, none of the previousresearch located for this study focused on teachers’ efficacy beliefs for integrating scienceand mathematics.

An increasing body of literature suggests that a well-designed methods course couldenhance preservice teachers’ efficacy belief for teaching science and mathematics. Thepurpose of this study was to examine the impact of an integrated science and mathemat-ics methods course on preservice early childhood teachers’ efficacy beliefs for integratingscience and mathematics in early childhood classrooms.

Teacher Self Efficacy Beliefs

Bandura’s (1977) seminal article introducing the construct of self-efficacy sparked greatinterest among researchers. As a result, a large body of research has been generated thatinvestigates the efficacy beliefs of individuals in several domains (Bandura, 1997). Teacherefficacy is one of these areas of study, and researchers have focused on this topic forover 20 years (Gibson & Dembo, 1984). Teacher efficacy is defined as “the teacher’sbelief in her or his ability to organize and execute the courses of action required to suc-cessfully accomplish a specific teaching task in a particular context” (Tschannen-Moran,Woolfolk Hoy, & Hoy, 1998, p. 233). Teachers make their efficacy judgements basedon an analysis of the difficulty of a teaching task and personal competence in executingthe teaching task. According to Bandura (1997), there are four major sources of teacherefficacy beliefs: enactive mastery experience (successful teaching experiences enhance effi-cacy beliefs), vicarious experience (observation of competent teaching practices increaseefficacy beliefs), verbal persuasion (specific feedback from a respected source regardingteaching performance increases efficacy beliefs), and physiological and affective states (amoderate level of affective arousal associated with teaching performance is perceived as anindicator of self-assurance).

Science Teaching Efficacy Beliefs

Prior research studies have identified a relationship between previous experience withlearning science and science teaching efficacy beliefs (Bleicher, 2004; Enochs & Riggs,1990). In general, preservice teachers who reported positive experiences with learning sci-ence tended to have higher science teaching efficacy beliefs than their peers who reportednegative learning experiences. Therefore, Huinker and Madison (1997) suggested providingpositive learning experiences as an important element of science methods courses.

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Efficacy for Integrating Mathematics and Science 351

Science content knowledge also emerged as an important factor that related to teach-ers’ efficacy beliefs (Bleicher, 2007; Schoon & Boone, 1998). Preservice teachers with highcontent knowledge and low misconceptions were reported to have higher science teach-ing efficacy beliefs. However, a high level of content knowledge alone does not seem toensure a high level of science teaching efficacy beliefs. Some studies provided evidencethat pedagogical content knowledge might play a more important role in the development ofscience teaching efficacy beliefs than science content knowledge (Morrell & Carroll, 2003).Studies suggest that not only the content but also the way the content of methods coursesis presented influence the development of science teaching efficacy beliefs. In addition,instructional strategies that are aligned with constructivist pedagogies appeared to be themost effective in enhancing science teaching efficacy beliefs (Jarrett, 1999; Settlage, 2000).

Researchers also have been interested in identifying the major sources of science teach-ing efficacy beliefs. Mastery experiences were found to be the most influential source ofscience teaching efficacy (Brand & Wilkins, 2007). However, some studies reported thatmastery experiences had little to no impact on preservice teachers’ science teaching effi-cacy beliefs (Yilmaz & Cavas, 2008). This inconsistency may be due to ceiling effects, asmany participants obtained high scores on the pretest in Yilmaz and Cavas’s study. In theabsence of enactive mastery experiences, students might develop science teaching efficacybeliefs by building content and pedagogy understanding and engaging in cognitive imag-ining (Palmer, 2006a). Recent studies showed that science methods courses that includeinquiry approaches, hands-on activities, and group investigations have a long-lasting impacton preservice teachers’ science teaching efficacy beliefs (Palmer, 2006b).

Mathematics Teaching Efficacy Beliefs

Studies that examined preservice teachers’ efficacy beliefs for teaching mathematics alsoidentified a relationship between previous learning experience and teaching efficacy beliefs.These studies reported that negative experiences with learning mathematics and mathemat-ics anxiety are associated with low mathematics teaching efficacy beliefs (Swars, 2005;Swars, Daane, & Giesen, 2006). Researchers found that mathematics methods courses thatincluded hands-on activities and inquiry-based strategies might be able to change preserviceteachers’ negative attitudes toward mathematics and enhance their mathematics teachingefficacy beliefs (Bintas, 2008; Cakiroglu, 2000). Prior experiences with mathematics learn-ing that negatively influence preservice teachers’ perceptions of mathematics and theirefficacy for teaching mathematics seem to be receptive to change through methods coursesthat offer positive experiences with learning mathematics.

Methods courses seem to be more effective in addressing preservice teachers’ mathe-matics teaching efficacy beliefs (Bintas, 2008; Cakiroglu, 2000) than in changing inserviceteachers’ efficacy beliefs (Ross & Bruce, 2007). Like the findings of studies in the scienceeducation literature, studies in mathematics education also identified mastery experiencesas the most important source of an individual’s mathematics teaching efficacy beliefs(Brand & Wilkins, 2007; Huinker & Madison, 1997). These findings suggest that inaddition to providing a positive mathematics learning experience through inquiry-basedstrategies, methods courses should also offer mastery experience opportunities.

Science and Mathematics Integration

Hurley’s (2001) meta-analysis of 31 integration studies conducted from the 1930s to the1990s indicated that integrating mathematics and science has a positive effect on stu-dents’ achievement in science and mathematics. Although there is empirical evidence to

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support integration practices, only a limited number of studies have examined preserviceand in-service teachers’ practices and perceptions of integration. These studies reportedthat preservice teachers tend to appreciate the idea of integration, but they rarely practiceit. Teachers also perceive integration as an exact matching of science and mathematics con-cepts (Koirala & Bowman, 2003). Teachers often have difficulty integrating mathematicsand science, and they tend to integrate mathematics and science subjects in a superfi-cial manner, without establishing conceptual connections between the subjects (Cady &Rearden, 2007; Douville et al., 2003). Teachers often use measurement and graphing asa primary means of mathematics and science integration, and they do not focus on dataanalysis, probability, spatial reasoning, number concepts, or algebra (Douville et al., 2003).A lack of or limited firsthand experience with integration and understanding of mathemati-cal and scientific concepts seem to be majosr reasons for poor integration practices (Cady &Rearden, 2007; Koirala & Bowman, 2003). Although many studies investigated the effectof methods courses on preservice teachers’ efficacy beliefs for teaching science and mathe-matics, the effect of methods courses on enhancing preservice teachers’ efficacy beliefs forintegrating science and mathematics has yet to be examined. Moreover, the relationshipsbetween the science teaching efficacy, mathematics teaching efficacy, and efficacy for inte-grating science and mathematics has also lacked investigation. The current study aimed toaddress this void in the literature.

Purpose of the Study

The major purpose of this study was to investigate the impact of an integrated scienceand mathematics methods course on preservice early childhood teachers’ efficacy beliefsfor integrating science and mathematics in early childhood classrooms. More specifically,answers to the following research questions were sought in the study:

� How do the participants’ efficacy beliefs for science teaching, mathematics teaching,and integrating mathematics and science relate?

� Is an integrated science and mathematics methods course effective for increasingparticipants’ self-efficacy scores from pre- to posttest assessments?

� What are the participants’ experiences and perceptions of integration before and afterthe integrated science and mathematics methods course?

Methodology

Design

This study utilized a quasi-experimental design with two treatment groups (Cook &Campbell, 1979). Participants in two cohorts were tested to assess their efficacy beliefs forteaching science, mathematics, and integrating science and mathematics before and imme-diately after instruction that lasted 8 weeks. Cohorts were randomly assigned into “sciencefirst” (SF) or “mathematics first” (MF) groups. During the first 4-week time block, partici-pants in the SF group received instruction in the science methods course during the morningsession. At the same time, participants in the MF group received instruction in the math-ematics methods course. For the second 4-week block the SF and MF groups switched.Both groups received additional instruction on integration during whole-group afternoonsessions that lasted throughout the entire 8 weeks. The duration and scheduling of thesecourses were constrained by the schedule of the teacher preparation program in which

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participants were enrolled. The integration course could only take place during the firstterm of methods courses; and other courses in the second term prevented the modificationof the preservice teachers’ schedule to include an integration course.

Participants

Participants of this study were preservice early childhood teachers enrolled in an inte-grated science and mathematics methods course, which was a part of an intensive Master’sin Education early childhood education prekindergarten to Grade 3 licensure and certi-fication program. The program’s stated goals include building future teachers’ contentknowledge and pedagogies while preparing them to meet the needs of diverse learners.The program has required integration in planning in the preservice teachers’ final capstoneproject, but this study was the students’ first experience with integration within methodscourses. All participants were female. Eighteen participants from the SF group and 16 par-ticipants from the MF group (n = 34 participants) completed all three instruments describedbelow.

Instruments

The Science Teaching Efficacy Belief Instrument (STEBI) was used to measure efficacy ofteaching science (Riggs & Enochs, 1990) and the Mathematics Teaching Efficacy BeliefInstrument (MTEBI) was employed to measure preservice teachers’ mathematics teachingefficacy beliefs (Enochs, Smith, & Huinker, 2000). An open-ended survey was used toreveal participants’ experience and perceptions of mathematics and science integration andtheir confidence in integrating mathematics and science.

Science Teaching Efficacy Belief Instrument. The STEBI instrument consisted of25 items on a 5-point Likert scale and included two factors: personal science teachingefficacy (an example item: “I know the steps necessary to teach science concepts effec-tively”) and science teaching outcome expectancy (an example item: “When a student doesbetter than usual in science, it is often because the teacher exerted a little extra effort”). Theauthors also adapted STEBI to assess preservice teachers’ efficacy for teaching science andcreated a parallel instrument called STEBI-B (an example item: “I will typically be able toanswer students’ science questions”) (Enochs & Riggs, 1990). Recently the factor structureof STEBI-B was reexamined and two outcome expectancy items that had low loadings weremodified (Bleicher, 2004). In the current study, a 13-item personal science teaching efficacysubscale of the modified version of STEBI-B was used to measure participants’ efficacybelief for teaching science. The instrument was reported to have a high reliability coeffi-cient, 0.87 (Bleicher, 2004). The reliability coefficient for the present study was also 0.87.

Mathematics Teaching Efficacy Belief Instrument. Items of the MTEBI (Enochs et al.,2000) were created by modifying the items of STEBI-B. The MTEBI consisted of 21 itemsand included two subscales: personal mathematics teaching efficacy (an example item: “Iunderstand mathematics concepts well enough to be effective in teaching early childhoodmathematics”) and mathematics teaching outcome expectancy (an example item: “Whena student does better than usual in mathematics, it is often because the teacher exerted alittle extra effort”). In the present study, a 13-item personal mathematics teaching efficacysubscale of the MTEBI was used to assess participants’ efficacy beliefs for teaching mathe-matics. Previous studies reported high reliability coefficient for MTEBI, 0.88 (Enochs et al.,2000). The reliability analysis produced an alpha coefficient of 0.85 in this study.

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Open-ended survey. A survey consisting of three questions was designed specificallyfor this study. The questions aimed to reveal participants’ experience of mathematics andscience integration (first question), to identify their perceptions of the benefits of integratingmathematics and science (second question), and to assess participants’ confidence in inte-grating mathematics and science (third question). The first two questions were qualitativelyanalyzed to describe participants’ experience and perceptions of integration. Responses tothe third question were scored using a 5-point Likert-type scale and used in a statisticalanalysis as a part of the outcome measure. Two researchers independently scored partic-ipants’ pre- and postresponses to the third question. Interrater reliability was calculatedusing a two-way mixed model with consistency procedure. The intraclass coefficient was0.80 for the pretest and 0.84 for the posttest indicating high interrater agreement betweenthe coders.

Instructional Intervention

The instructional intervention utilized in this study was specifically designed to enhancepreservice early childhood teachers’ pedagogical content knowledge of science, mathe-matics, and integration of the two content areas. This novel methods course aimed toprovide preservice teachers with firsthand, hands-on experiences in identifying connec-tions between science and mathematics concepts and integrating science and mathematicscurricula. The instruction emphasized child development knowledge, developmentallyappropriate learning experiences, and standards-based content, processes, and skills. Oneof the researchers taught the science methods, another the mathematics methods, and theycotaught the integration component. Students earned six credit hours, three from eachcourse, within the quarter term. The two orders of classes were necessitated by schedulingconstraints within the licensure program, but we also wondered if the order of courses mightaffect the degree to which the preservice teachers emphasized mathematics or science, bygiving primacy to the content experienced first.

Science methods course. The science methods course utilized discovery- and inquiry-based pedagogical approaches to help preservice teachers understand how to appropriatelyengage children in learning science concepts and processes. The instructor emphasizedways to investigate scientific questions, collect and analyze real data, and draw conclusionswithin the early childhood classroom setting. Methodologies were standards-based anddesigned to allow core content to emerge through the investigations. Students learned howto conduct hands-on experiments with young learners in order to help children understandthe phenomena and the scientific process. Experiments included motion (ramps), physicalproperties of matter (bubbles and soil), and energy (light and shadows).

Mathematics methods course. The mathematics course took a problem-based approachwith a focus on pedagogical content knowledge to facilitate effective mathematics teaching.The four sessions of mathematics instruction focused on understanding the building blockconcepts of early number, algebra, geometry, and measurement. Activities modeled howto create hands-on learning opportunities for young learners to understand fundamentalmathematical concepts, including quantitative and geometric-spatial ideas.

Integration. The integrated mathematics–science afternoon sessions facilitated thepreservice teachers’ experiences with inquiry processes and took a project-based approach,learning through work on two group projects, which focused on weather (earth science)and birds (life science). The first class meeting focused on using long-term projects to meet

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standards, using field drawings, and beginning to formulate questions for inquiry. Sessionsthen centered on refining inquiry questions, designing data collection, recording and rep-resenting field observations, understanding principles for good graphical representation,relating scientific inquiry and mathematical problem solving in early childhood classrooms,and connecting early childhood mathematics and science through measurement and dataanalysis. The integrated instruction sessions aimed at modeling how to engage children inthe inquiry process through their work on their long-term projects. As children would inearly childhood classrooms, the projects created the opportunity for the preservice teachersto conduct careful observations, record meaningful data, find patterns and relationships,develop their own investigations, and discover the world around them. The course syl-labus noted this discovery- and project-based approach: “Long term projects capitalize onchildren’s innate ability to use the world around them as an opportunity for discovery.”

The course and projects were designed to increase preservice teachers’ knowledge,familiarity and comfort with integrating science and mathematics in early childhood andusing a project-based, inquiry approach to early childhood mathematics and science learn-ing. The instructors included opportunities for reflection on preservice teachers’ developinglearning and understanding on principles underlying the integrated mathematics–scienceprojects, and the project-based approach allowed both instructors to work closely with thegroups and facilitated peer learning. The preservice teachers self-selected into groups ofthree or four students, and they worked together in those groups to complete the projectsdescribed below.

The bird project. The bird project centered around authentic inquiry regarding lifein our environment. The staff set up five bird feeders at a campus green space so thatall groups had the same habitat to observe. Groups conducted at least four observations,created observational drawings, collected artifacts, and used scientific logs and journalsto address the inquiry questions they generated about the birds (e.g., How many birdsvisited the feeders during the observation period? Which types of birds were observed?How did the birds interact with each other?). Based on their observations of the birds andtheir habitat, the groups were to satisfy three requirements: an integrated planning wheel,a bird “playground” blueprint, and a final oral presentation. For the integrated planningwheel, students needed to use the planning wheel model described by Conezio and French(2002), in which a concept is at the center and an integrated unit of activities and resourcesis planned across the curriculum. Students planned relevant experiences and selected aninquiry project that could span multiple days and incorporate areas such as outdoor playand gross motor activities (e.g., exploring how birds move), language arts (selecting birdbooks and planning circle time reading them), arts and expression (studying colors of birdsand drawing birds to explore their body shapes), and other areas of a typical preschool cur-riculum. The preservice teachers discussed and gave rationales for activities and resourcesas part of their inquiry process in the bird unit.

The bird “playground” blueprint required creating a habitat for birds based on obser-vations of behavior. The assignment required that the blueprints also convey the spatialrelations of elements as an exercise in mapmaking for early childhood. The final presen-tation required that the students show, through their field observations, integrated planningwheel, and blueprint, evidence of the scientific processes of data gathering, analysis, com-munication of results, and incorporation of mathematical principles and processes forlearning.

The weather project. For the weather project, the groups formulated a scientific ques-tion regarding weather that was appropriate for prekindergarten or kindergarten. They then

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collected the necessary data and analyzed it in a manner appropriate for pre-K/K children.Finally, they prepared graphical representations and other visual aids such as a paperdoll-style bear whose outfits corresponded to different weather conditions to demonstrate theinquiry process they had conducted and would conduct with young learners. Presentationcriteria included appropriateness for pre-K/K learners, demonstration of well-conducteddata collection and analyses, incorporation of multiple mathematical concepts, demonstra-tion of connections between concepts, use of terminology appropriate for young learnersand clear and appropriate graphical displays. Groups focused on weather elements such astemperature change, cloudiness of the sky, and observed precipitation.

Data Analysis

An inductive approach was used to identify themes and patterns in participants’ responsesto the first two open-ended survey items. Data analysis included organizing the data andsearching for patterns in participants’ responses to describe their perceptions of scienceand mathematics integration (Trundle, Atwood, & Christopher, 2002).

For this study, the sense of efficacy beliefs for integrating science and mathematics wasdefined as the linear combination of participants’ efficacy beliefs for science teaching, theirefficacy beliefs for mathematics teaching, and their confidence for integrating science andmathematics as measured by the third item of the open-ended survey. A doubly multivariateanalysis of variance was used to assess whether there was a difference between participantsin the SF (science first) group and participants in the MF (mathematics first) group in theamount of change in their scores of three outcome measures from pre- to posttest measures.A doubly multivariate analysis of variance, which is also called mixed MANOVA, is a mul-tivariate statistical technique that is often used when there is a between-groups independentvariable (in our case, science first and mathematics first), a repeated-measures independentvariable (time: pretest and posttest) and two or more dependent variables (Leech, Barret, &Morgan, 2005). The test includes the following assumptions: independence, linearity, mul-tivariate normality, and homogeneity of variance/covariance. The assumptions of the testwere inspected using graphical methods (residual plots and matrix scatter plots) and formaltests (Levene’s test and Box’s M test), and no violation of the assumptions was detected.All data analyses were two-sided and an alpha level of 0.05 was used to declare statisticalsignificance. The Bonferroni adjustment was utilized for the univariate tests to control theType I error rate. Statistical analyses were conducted using SPSS version 17.0.

Results

Descriptive Statistics

Participants’ scores from pre- and postefficacy assessments were used to calculate meansand standard deviations for each instructional group. There was no systematic differencebetween the SF and MF groups in their pre- and posttest scores. However, for both groups,posttest scores were substantially higher than the pretest scores. Table 1 presents the meansand standard deviations of efficacy scores for both groups.

Correlations Between Efficacy Scores

Correlations between pre- and posttest measures of dependent variables were calcu-lated using Pearson’s product-moments and Spearman’s formula. In both the pre- and

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Table 1Means and Standard Deviations of Efficacy Assessments

Pretest Posttest

Groups

Scienceteachingefficacy

Mathematicsteachingefficacy

Integrationefficacy

Scienceteachingefficacy

Mathematicsteachingefficacy

Integrationefficacy

Science firstMean 44.56 49.06 3.55 50.5 51.61 4.50SD 4.79 7.39 1.25 6.49 5.36 0.71n 18 18 18 18 18 18

Mathematics firstMean 44.69 48.63 3.31 48.13 49.81 4.44SD 4.64 6.94 1.14 6.30 5.96 .73n 16 16 16 16 16 16

posttest assessments, science teaching efficacy and mathematics teaching efficacy weresignificantly related. However, integration efficacy was not significantly related to scienceand mathematics teaching efficacy in the preassessment. Although correlations betweenthe integration efficacy, the science teaching efficacy and the mathematics teaching effi-cacy increased in the postassessment, the relationships did not reach statistical significance.Table 2 shows the correlation coefficients between the dependent variables.

Effectiveness of Instructional Intervention

The results of a doubly multivariate analysis indicated no significant multivariate effect forthe main effect of group (Hoteling’s T = .02, F3, 30 = .20, p = .90) and the interactionbetween group and time (Hoteling’s T = .08, F3, 30 = .81, p = .50). These results suggestthat groups were not significantly different on either dependent variable in both the pre-and the posttest measures. That is, sequence did not make any difference in participants’efficacy scores. However, there was a significant multivariate effect for the main effect oftime with a large effect size (Hoteling’s T = 1.53, F3, 30 = 15.25, p < .001, η2 = .60),indicating both groups’ posttest scores were significantly higher than the pretest scores.

Table 2Correlations Between Pre- and Postefficacy Assessments

Efficacy measures 1 2 3 4 5 6

1. Pretest science teaching efficacy —2. Pretest mathematics teaching efficacy .61∗ —3. Pretest integration efficacy .15 .04 —4. Posttest science teaching efficacy .53∗ .63∗ .32 —5. Posttest mathematics teaching efficacy .54∗ .84∗ .09 .77∗ —6. Posttest integration efficacy .08 −.05 .11 .31 .11 —

∗Statistically significant at the .01 level.

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Follow-up ANOVA tests indicated that the change from the pre- to the posttest was signif-icant for all three outcome measures: science teaching efficacy (F1,32 = 24.42, p < .001,η2 = .43), mathematics teaching efficacy (F1,32 = 8.13, p = .008, η2 = .20), and integrationefficacy (F1,32 = 20.47, p < .001, η2 = .39).

Participants’ Experience and Perceptions of Integration

An inductive process was used to identify themes and patterns that described the partici-pants’ perceptions of integration. Four key themes emerged from the pre- and postsurveydata: The ease of integration, the centrality of science, the means of integration, and thebenefits of integration.

The ease of integration. Many participants reported that integration is easy to accom-plish because science and mathematics are naturally related domains (25% of respondents).In the postsurvey, participants maintained their perceptions that integration is an easy taskbecause the two domains are related (29% of respondents).

The centrality of science. Participants tended to perceive mathematics as subordinateto science, stating that science activities involve doing mathematics (23% of respondents).They tended to maintain this view in the posttest by putting science in the center of integra-tion practices in their responses (29% of respondents), indicating that the scientific conceptswere the primary content and mathematics was a tool or instrument to find answers toscientific inquiries.

The means of integration. Participants mentioned mostly specific activities such asmeasurement (17% of respondents), recording observations (14% of respondents), dataanalysis (11% of respondents), and data representation (6% of respondents) as the waysof integrating science and mathematics. Few participants mentioned that integration is andshould happen around big ideas and skills that are common in both domains (9% of respon-dents). In the postsurvey data, representation (23% of respondents) and analysis (16% ofrespondents) were the most common ways of integration proposed by the participants.

The benefits of integration. When asked about integration, participants stated most fre-quently that integration helps children see the connection between science and mathematics(23% of respondents), and integration makes learning meaningful for young children (26%of respondents), allowing children to see the use of mathematics and science in their lives.Some participants believed that integration also makes mathematics learning a fun andinteresting activity for young children (9% of respondents).

Participants also reported that integration promotes deeper understanding of scienceand mathematics concepts (11% of respondents) and facilitates development of scienceprocess skills (17% of respondents). Many participants emphasized the limited time avail-able in preschool classroom for instructional activities and reported that integration can helpthem to save time and teach the concepts efficiently (23% of respondents). In the postsur-vey, an increased number of participants emphasized the recognition of connections (37%of respondents) and the construction of deeper understanding as benefits of integration(29% of respondents). Participants continued to emphasize time and ease of instructionalactivities as important benefits of integration (20% of respondents). They also reportedthat integration makes children’s learning meaningful (14% of respondents) and facilitatesthe development of science process skills (11% of respondents). Some participants, in thepostsurvey, stated that by promoting deeper understanding, integration facilitates children’slearning of more advanced concepts (9% of respondents).

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Qualitative discussion of projects. Overall, the projects were well done and showedgood planning for early childhood mathematics and science learning and the integration ofthe two. As is typically the case in a course, the projects varied in the depth, sophistica-tion, and pedagogical soundness of their designs, but every project incorporated the skillsand concepts at the core of early childhood mathematics and science learning, includingclassification, matching, sorting, counting, and quantitative and qualitative comparisons.

The bird projects. The students presented their bird “playground” blueprint maps andtheir integrated planning wheel of activities, accompanied by a written discussion of theirplans. The evaluation criteria included inquiry question appropriateness, soundness of datacollection methods and analyses, and clarity and appropriateness of information display.The presentation needed to especially demonstrate how scientific inquiry and mathemati-cal problem solving would be woven throughout the activities, such as through children’sliterature, learning centers and arts activities.

The groups created bird playground blueprints that incorporated their observations, forinstance, justifying the placement of feeders at certain heights or behind hedges to preventbirds from being easily startled; and the blueprints showed student understandings of scaleand spatial relations. One exemplary blueprint featured a clear layout with an accuratedepiction of the space and boundaries. The neatness of the design showed the shapes andangles of objects and the ground and pathways well. In addition, the presenters gave goodrationales for the individual elements (e.g., high wires going across, creating ways birdscan go back and forth) and for the placement of items primarily clustered in the center andfor the placement of items on the periphery of the playground.

Activities from the integrated planning wheel could accomplish more than one ped-agogical goal simultaneously. For example, some groups showed sorting activities withitems collected during their observations, such as feathers and seeds, and explained howthese activities could be used to draw children’s attention both to physical traits of theobserved birds (e.g., color and length of feathers) and also about their diet (e.g., varietyof seeds eaten, size of seeds eaten). Through this inquiry process, the preservice teachersfocused on doing and modeling the processes of sorting and classifying, fundamental ideasin both science and mathematics and essential to working with data. Even an act as simpleas counting the number of artifacts by type supports young children’s learning of funda-mental science and mathematics concepts such as the frequency of an item in a habitatand the number counting principles. The groups explicitly discussed scientific inquiry andmathematical learning processes (problem solving, connections, communication, represen-tation, and reasoning and proof) throughout their presentations, conveying how they wouldhelp young learners understand the phenomena under investigation.

The weather projects. Groups created inquiry questions such as: “How is the weatherdifferent from day to day?” and “What happens when the season changes?” Groups inte-grated multiple mathematical content areas by scripting questions about the quantitiesrepresented on the graph: number concepts (comparisons of “equal/same”, “most/more”and “least/less”), geometry and spatial concepts (shapes on graphs and spatial relationssuch as “next to” or “on top of” on the graphs), measurement and patterns, functions, andalgebra (aspects of time such as the pattern of days in the week, the functional relationshipof something).

The groups varied in the soundness of their inquiry questions and their use of datato answer them. The most effective projects used developmentally appropriate pictographsto represent weather conditions. What marked these pictograph activities as developmen-tally appropriate was the use of simple and easy-to-compare categories, an emphasis on

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sorting data and assigning data to categories, and introducing both qualitative and quan-titative change. Principles of measurement, a concept important in both mathematics andscience, figured prominently in the projects, with discussion and representations of mea-surement of temperature, formally or informally, and time, especially through calendars.One group’s inventive means for measuring cloud cover was a clear circular disk, dividedinto quadrants. The preservice teachers showed how they would use it with young learnersto decide on whether “all”, “most”, “half”, “some or a little”, or “none” of the sky wascovered in clouds. This introduced approximate quantities, qualitative categories, and theidea of relative amounts of cloud cover.

Weaknesses in a few of the projects included heavy emphasis on comparing two-digittemperatures for children still learning to count, problematic inquiry question formation(e.g., asking about change from season to season although the data collection was onlywithin one season), and data that might be too complex for young learners (e.g., comparingthe temperatures for their home location to temperatures at a location on another continentand then putting all the data on a single graph).

Discussion

The present study investigated the effectiveness of an integrated science and mathematicsmethods course on preservice early childhood teachers’ efficacy beliefs for integrating sci-ence and mathematics in early childhood classrooms. The findings of the study providedevidence that the methods course utilized in the present study was effective at enhancingpreservice teachers’ efficacy beliefs for integrating science and mathematics.

The results demonstrated that there was no statistically significant difference betweenthe SF (science first) and the MF (mathematics first) groups in the study. These findingssuggest that the order in which the content was taught did not make any difference inthe amount of change in preservice teachers’ efficacy beliefs scores from pre- to posttestmeasures. Thus, teacher educators can use either order in their implementation of such amethods course with preservice teachers who have similar characteristics.

Correlation coefficients between the efficacy scores suggest that integrating mathematicsand science might require a different set of skills than teaching mathematics and scienceas separate domains. These results imply that having a high efficacy for science teachingand high efficacy for mathematics teaching does not necessarily mean having high efficacybeliefs for integrating both domains. An alternative explanation is plausible for these results.The efficacy for integration was measured with a single item in this study. This might be thereason efficacy for integration and efficacy for teaching mathematics and science was notsignificantly related in the present study. An instrument with multiple items might revealsuch a relationship if it truly exists. Future studies should focus on developing such aninstrument to measure teachers’ efficacy beliefs for integrating science and mathematics.

Four themes were identified to describe participants’ perceptions of integration. First,preservice teachers often perceived mathematics and science integration as an easy taskbecause they are naturally related domains. Second, many participants perceived scienceto be at the center of integration practices, with mathematics and other content areas sub-ordinate to science. Third, measurement, recording observations, data analysis, and datarepresentation were seen by the preservice teachers as the most common ways of integratingscience and mathematics. Finally, participants mostly focused on the mechanics of inte-gration practices rather than the underlying conceptual basis of curriculum integration.The most common perceived benefits of integration were time and ease of instructionalactivities. These results seem to be consistent with the literature that teachers’ perceptions

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of integration are often at superficial levels (Cady & Rearden, 2007; Douville et al., 2003;Koirala & Bowman, 2003). Although the participants may have articulated their integra-tion at only a superficial level, we believe that the design of the activities in the coursesmay have planted the seeds of deeper understanding of integration for these novice teach-ers. The activities also helped participants understand and become more comfortable withconcepts such as the basic mathematics they used in more applied and meaningful waysthan they themselves may have experienced as young children.

To meet the goals of the two projects in the integration course, the preservice teacherparticipants needed to, themselves, engage in inquiry. Their inquiry questions about birdsand weather led them to conduct investigations into scientific phenomena and study thesephenomena through scientific and mathematical lenses and demonstrate how their inquirieswould allow children to experience the connections between the two subjects. Althoughour research project leaves us with questions about how to best foster student teachers’understanding of mathematics–science integration, we believe strongly that our partici-pants came to understand integration by integrating. The inquiry, project-based instructionfacilitated the participants’ integration of mathematics and science content and processes.We acknowledge that our data are limited to the preservice teachers’ work in the methodscourses and not in their preschool placements. Future study of methods experiences withintegration should be yoked to data from preschool placements to document the translationfrom planning integrated units to implementing them.

To identify the unique contributions of integrating methods course experiences, afuture investigation could use a control group methodology, with a group receiving stand-alone methods, alongside the methods integration instructional intervention. However, weacknowledge the practical and pedagogical concerns of creating different instructionalexperiences within a program, particularly teacher education programs that often use cohortmodels.

Future instructional interventions also can explore means of supporting participants’metacognition regarding integration practices. Much research has documented the role ofmetacognition in helping learners, in this case future teachers, reflect on their understand-ing and potential gaps in that understanding (Hennessey, 2003; Lin, Schwartz, & Hatano,2005). Future instructional interventions can explicitly incorporate metacognitive reflectionabout integration processes and goals. Such reflection may help the preservice teach-ers recognize existing integration and potential integration opportunities within children’smathematics and science learning experiences. Above, we suggested that a future investiga-tion should include examining the preservice teachers’ implementation of their integratedunits. In addition to providing an opportunity to observe the execution of their plannedintegration, this provides a chance to engage them in metacognition about their instruc-tional decisions. Such metacognition could facilitate their reflecting on and evaluating theirplans for integration in the classroom and revisions for future integrated instruction, whilesimultaneously providing a catalyst for deepening their understanding of integration.

Additionally, future investigations may benefit from alternative methods of tapping andmeasuring participants’ understandings. For example, participants could be asked to ana-lyze classroom episodes for how integration was or could be facilitated. Preservice teachers,who are still relative novices at integration, may be better able to speak to how it can beachieved and what its benefits may be if prompted by exemplars or contextualized scenar-ios. Follow-up data collections during student teaching, and beyond, can document if noviceteachers both understand and appreciate integration, whether they attempt to implement anintegrated learning experience, and how they respond to any challenges to implementingan integrated learning experience for children.

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The present study focused on a neglected area in teacher education. Although integrat-ing science and mathematics has been advocated for a long time in the literature (Berlin& White, 1994; Furner & Kumar, 2007; Jones et al., 2003), most studies in this area wereconducted with middle and high school teachers (Czerniak, Weber, Sandmann, & Ahern,1999). None of the studies we reviewed investigated preservice or inservice teachers’ effi-cacy beliefs for integrating science and mathematics. There is no instrument to measureefficacy beliefs for integrating science and mathematics, which is a clear indicator of theneed for further studies in teachers’ efficacy beliefs for integration practices. Given thegrowing emphasis placed on science and mathematics integration in early childhood class-rooms, future research should be conducted to investigate preservice and inservice teachers’perceptions and practices of science and mathematics integration. Such studies may informthe practice of teacher educators as they design and implement method courses to developand improve teachers’ curriculum integration practices.

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