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Correlations between kindergarten teachers’ attitudestoward mathematics and teaching practiceJoohi Lee aa College of Education , University of Texas‐Arlington , Curriculum and Instruction‐EC 4, Box19227, 701 S. College St., Arlington, TX, 76019–0027, USA Phone: +1 817 272 2264 E-mail:Published online: 25 Apr 2008.

To cite this article: Joohi Lee (2005) Correlations between kindergarten teachers’ attitudes toward mathematics andteaching practice, Journal of Early Childhood Teacher Education, 25:2, 173-184, DOI: 10.1080/1090102050250210

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ELSEVIER Journal of Early Childhood Teacher Education 25 (2005) 173-184

Journa y

ChildhoodTeacher

Education

Correlations between kindergarten teachers' attitudestoward mathematics and teaching practice

Joohi Lee*Curriculum and Instruction-EC 4, College of Education, University of Texas-Arlington, Box 19227,

701 S. College St., Arlington, TX 76019-0027. USA

Accepted 1 July 2004

Abstract

This study examined correlations between teachers' attitudes toward mathematics/teaching mathematics and thepractice of developmentally appropriate mathematics. This study tested two independent variables: (1) kindergartenteachers' attitudes toward mathematics; and (2) kindergarten teachers' attitudes toward teaching mathematics; andtheir relationships with the practice of developmentally appropriate mathematics.

The researcher designed a survey questionnaire by cross-referencing several instruments and the review ofrelated literature. A sample of 200 kindergarten teachers was randomly selected from the Indiana Department ofEducation website directory. Of the 200 kindergarten teachers, 81 teachers participated in this study by returningthe survey questionnaire to the researcher via the postal service, e-mailing, or posting the response over theInternet.

Each independent variable was tested to determine the level of its statistical significance by using multiple linearstepwise regression procedures. The results of this study revealed that kindergarten teachers' attitudes towardteaching mathematics were found to be a significant variable correlating with the practice of developmentallyappropriate mathematics, but kindergarten teachers' attitudes toward mathematics were not a significant variable.© 2005 Elsevier Inc. All rights reserved.

Keywords: Teaching mathematics; Attitudes toward mathematics; Developmentally appropriate mathematics

In order for children to perform well in math-ematics, they must begin exposure to high qualitymathematics education in the early years. Children inthe United States have long been known to show adistinct disadvantage related to mathematic prowess.Many believe that this can be remedied by focusingattention on the early childhood years and ways inwhich young children learn math. This study analyzedwhether kindergarten teachers' attitudes toward math-ematics and attitudes toward teaching mathematicswere effective predictors for the practice of develop-mentally appropriate mathematics.

* Tel.:+1 817 272 2264.E-mail address: Joohilee@uta.edu.

1. Mathematic competence

The National Association for the Education ofYoung Children (NAEYC) and the National Councilfor Teachers of Mathematics (NCTM) produced ajoint statement in 2002 that reflected United States(U.S.) students' poor performance in mathematics."Since the 1970s, a series of assessments of U.S.students' performances has revealed an overalllevel of mathematical proficiency well below whatis desired and needed" (NAEYC & NCTM, 2002,p. 1). Indeed, American students' poor performance inmathematics has been reported in several national andinternational documents, e.g., the report of the Inter-national Association for the Evaluation of Educational

1090-1027/$ - see front matter © 2005 Elsevier Inc. All rights reserved.

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Achievement, the report of the National Commissionon Excellence in Education (NCEE), and the resultof the Second International Mathematics Study(SIMS).

Awareness of the mathematic deficiencies foundin these studies has led policymakers to seriously con-sider the quality of American education. In 1983, theU.S. Secretary of Education released a report entitled ANation at Risk: The Imperative for Education Reform(NCEE, 1983). It reflected concerns about Americaneducation among educators, businessmen, and pol-icymakers. They believed that it was essential thatstudents show competency in mathematics to competein today's global economic environment. However,they argued, schools were not appropriately preparingstudents to compete in the global world (Romberg,1999).

A variety of attempts to improve the quality ofmathematics education appeared to have had littleinfluence on students' achievements in mathematics.The Third International Mathematics and ScienceStudy (TIMSS), conducted from 1994 through 1995,again showed that the overall means of Americanfourth, eighth, and twelfth grade math scores werebelow the international mean (Berryman, 2002).However, when examined individually, it was foundthat the mean scores of fourth graders ranked higherthan the international mean in both mathematics andscience, even though the mean scores of eighth andtwelfth graders ranked below the international mean(Berryman, 2002). According to the National Centerfor Education Statistics (NCES, 2003), the nationalaverage scores of mathematics of fourth and eighthgraders increased each year in 1990, 1992, 1996,and 2000. NCES (2003) reported that the averagescores of twelfth graders increased between 1990 and1996, but declined between 1996 and 2000. However,The College Board (2002) released a positive reporton students' SAT scores in mathematics. Accordingto the College Board (2000), the average mathe-matics score has continuously increased for the last10 years.

Regardless of some positive reports on Americanstudents' mathematics outcomes, U.S. educatorsstill have concerns about the lack of follow-throughon improvement plans in considering the qualityof teaching mathematics. There have been sev-eral mathematics education reforms designed toimprove the quality of mathematics education,some of which addressed mathematics educationfor very young children. The importance of earlymathematics education has been publicized sinceNCTM (2000) included mathematics standards forpre-kindergarten age children for the first time inits publication, Principles and Standards for SchoolMathematics.

2. Young children and developmentallyappropriate mathematics education

Children come to school with considerableinformal mathematics knowledge. However, theyoften have difficulty transforming their informalknowledge to formal knowledge (Heddens, 1986).Connecting the gap between children's informalmathematics knowledge and formal mathematicsknowledge is critical in early childhood mathematicseducation (NCTM, 2000). To implement appropriatemathematics education for young children, NCTM(2000) recommends teachers cautiously and con-tinuously assess children's mathematics knowledgethrough both informal and formal assessment. Sincechildren's dispositions for mathematics developfrom early experiences (NAEYC & NCTM, 2002),implementing developmentally appropriate earlymathematics education becomes more significant.

Early childhood educators have long consideredquality early childhood education to be of criticalimportance. Developmentally appropriate practicehas been identified as a component of high-qualityearly childhood education since NAEYC published,Developmentally Appropriate Practice, in 1987 (Bre-dekamp) and revised the work in 1997 (Bredekamp& Copple). Developmentally Appropriate Practice(DAP) addressed the need to devise early childhoodeducation strategies that were in keeping with thedevelopmental needs of young children. Severalresearchers have supported DAP, which promotespositive effects on children's social-emotional andcognitive development (Buchanan, Burts, Bidner,White, & Charlesworth, 1998; Burts et al., 1993;Burts, Hart, Charlesworth, & Kirk, 1990; Carpenter,Fennema, Peterson, Chiang, & Loef, 1989;Jambunathan, Burts, & Pierce, 1999; McMullen,1999). Some empirical data have suggested consider-able educational implications of using DAP for earlymathematics education for young children (Frede& Barnett, 1992; Hirsh-Pasek, Hyson, & Rescorla,1990; Marcon, 1992). Buchanan et al. (1998) morespecifically indicated that using DAP benefited youngchildren's mathematics learning in first, second, andthird grade.

DAP is widely recommended in early childhoodeducation settings in order to provide children withquality programs. However, a low percentage of class-rooms have been observed to and identified as usingDAP (Dunn & Kontos, 1997). The low percentageof professionals implementing DAP has challengedteacher educators to assist future teachers in beingprepared to provide high-quality teaching practice.Research had revealed that both teacher attitude andteaching attitudes toward mathematics were primaryfactors that influence teaching practice (Kulm, 1980;

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Martinez & Martinez, 1996). However, very littleresearch has been conducted to investigate earlychildhood teachers' attitudes toward mathematicsthat could correlate with teachers' use of DAP inteaching early mathematics. Therefore, this studyattempted to examine correlations between teachers'attitudes (attitudes toward mathematics/attitudestoward teaching mathematics) and the practice ofdevelopmentally appropriate mathematics.

3. Teachers' attitudes toward mathematicsand teaching mathematics

Attitude has been addressed as linked to one'saffective domain, to his or her reaction, i.e., "attitudeis a relatively enduring system of affective, evaluativereactions based upon and reflecting the evaluative con-cepts or beliefs which have been learned about char-acteristics of a social object or class of social objects"(Shaw & Wright, 1967, p. 10). The affective domainhas been specifically addressed in Bloom's taxonomy.According to Bloom's taxonomy (Bloom, Mesia, &Krathwohl, 1964), affective domains have five majorcategories: receiving phenomena; responding to thephenomena; valuing; organizing; and internalizingvalues. Throughout one's experiences of the five cate-gories, Bloom et al. (1964) indicated that an individualwill have either positive or negative attitudes.

Attitudes evidently influence behavior. Ajzen andFishbein (1980) believe, "to predict one's behavior,we have to assess the person's attitude . . . " (p. 27).Behavior is consistent and predictable based onone's internalized value system and represents theindividuals' attitudes toward subjects (Bloom et al.,1964). Teachers' attitudes toward mathematics andteaching mathematics are strongly associated. Stipek(1998) reported that self-confidence (attitudes towardmathematics) in mathematics has been associatedwith enjoyment of teaching mathematics. Stipek,Giwin, Salmon, and MacGyvers (2001) assessed 21teachers throughout Los Angeles County (CA). Thesurvey of "Beliefs about Mathematics and Teaching"was used and videotapes of teachers' practices inmathematics teaching were reviewed and analyzed byresearchers. Research results indicated that teachers'high confidence toward mathematics was linked witha high-degree of enjoyment in teaching mathematics.This study also revealed that teachers who showedmore enjoyment when doing math expressed moreenjoyment in teaching mathematics than teacherswho demonstrated less enjoyment.

These teachers' attitudes (attitudes toward mathe-matics and teaching mathematics) strongly correlatedwith their teaching practice (Giordano, 1991). Karp(1991) examined whether teachers' attitudes toward

mathematics and teaching mathematics determinedthe different quality of instructional methods they usedin teaching mathematics. She found that teachers withpositive attitudes toward mathematics and teachingmathematics used various instructional methods topromote students' independence and often incorpo-rated instructional materials during the mathematicsclass. This was compared to teachers with negative at-titudes toward mathematics. Karp (1991)also reportedthat teachers with negative attitudes more frequentlyused teacher-dependent instructional methods, ask-ing one-way questions while often ignoring problem-solving processes. Study results indicated that teacherswith positive attitudes toward mathematics enhancedstudents' autonomous learning behaviors in mathe-matics, but teachers with negative attitudes producedstudents with a teacher-dependent learning style.

Fennema and Peterson (1985) agreed that teach-ers' positive attitudes toward mathematics and teach-ing mathematics influence students' autonomous mathlearning behaviors. Stipek et al. (2001) found teach-ers' attitudes toward mathematics and teaching mathe-matics impacted their teaching practice. In their study(Stipek et al., 2001), teachers with positive attitudestoward math (high degree of enjoyment toward math/teaching math) more often encouraged students' au-tonomous work in their mathematics problem-solvingprocess than teachers with less positive attitudes, whileteachers with less positive attitudes toward mathe-matics more frequently ignored wrong answers andasked another child, and made comments conveyinglow expectation (e.g., I did not expect you to getthat right). The potential problem, however, comesfrom negative teaching attitudes toward mathemat-ics. Teachers' negative attitudes and teaching atti-tudes toward mathematics were frequently linked withthe avoidance of mathematics instruction (Kelly &Tomhave, 1985; Quinn, 1997). Teachers who havemathematics anxiety and negative attitudes towardmathematics spend significantly less instructional timeon mathematics (Trice & Ogden, 1987). Students'deficiencies in mathematics are often revealed to befrom the lack of opportunities to perform mathemat-ics. When teachers have mathematics anxiety, theyattempt to accept only right answers from studentswithout considering the problem-solving process.

Teachers' failure in the responsive teaching ofmathematics has caused numerous students to failin mathematics (Giordano, 1991). This finding haschallenged teacher educators to consider poten-tial problems associated with preservice teachers'negative attitudes toward mathematics. Trice andOgden (1987) assessed 40 first year teachers' (secondthrough fifth grade) mathematics anxiety, and theseoutcomes were compared to their practice in teachingmathematics. Observation and analysis of teachers'

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lesson plans were used as sources of data. Investigateddata showed that the teachers most anxious aboutmathematics spent less time teaching mathematics.As Trice and Ogden (1987) reported, anxious teacherstended to avoid teaching mathematics compared toless anxious colleagues.

According to NAEYC and NCTM (2002), chil-dren's early mathematics experiences are a strongfoundation for their future mathematics learning.Therefore, providing children with challenging, acces-sible, and high-quality early mathematics educationbecomes an important concern for early childhoodeducators. Being an effective teacher requires positiveattitudes toward the subject, proficient subject matterknowledge, and pedagogical knowledge (Marks,1990). Unfortunately, prior studies regarding highquality mathematics teaching practices have mostlyinvolved middle elementary or secondary educationlevels. Very few studies have been conducted relatingto how early childhood teachers' attitudes towardmathematics impact their mathematics teachingpractices. Therefore, this study attempted to inves-tigate correlation between teachers' attitudes towardmathematics/teaching mathematics and the use of thepractice of developmentally appropriate mathematics.

4. Operational definition of terms

For the purpose of this study, the following opera-tional definitions were used.

. 1. Developmentally appropriate practice (DAP):• educational philosophy publicized by NAEYC

(Bredekamp, 1987; Bredekamp & Copple,1997) that emphasizes children's develop-ment across domains in relation to teachingpractice as well as individual and culturalappropriateness (Bredekamp & Copple, 1997).

2. Practice of developmentally appropriatemathematics: mathematics teaching practiceaddressing the following categories: (a) achild-centered mathematical environment,(b) developmentally appropriate mathematicsactivities, (c) developmentally appropriatemathematics manipulatives, (d) a positive-non evaluative mathematics environment,and (e) authentic mathematics assessment(Carlan, 2000, p. 12).

3. Attitudes toward mathematics: an emotionalgeneral disposition toward mathematics inwhich there are negative or positive feelingstoward mathematics involving ease, enj oyment,and confidence in mathematics (Aiken, 1972,1974).

4. Attitudes toward teaching mathematics: anemotional general disposition in which thereare negative or positive feelings toward teach-ing mathematics involving ease, enjoyment,and confidence in teaching mathematics(Aiken, 1972,1974).

5. Methodology

5.7. Participants

A sample of 200 kindergarten teachers was ran-domly selected from the state of Indiana. Thenames of all of the kindergarten teachers in thestate of Indiana were obtained from the websiteof the Indiana Department of Education directory(http://doe.state.in.us/htmls/kl2.html). A total of 1283names of kindergarten teachers were gathered fromthe directory. In order for the selection to be random,the researcher used a table of random numbers whichwas designed by Snedecor and Cochran (1967). Everykindergarten teacher was assigned a number. Partici-pants were selected using the table of random numbersuntil the researcher obtained 200 kindergarten teach-ers. The researcher sent a survey questionnaire packetwhich contained a hard copy of the questionnaire, aself-addressed envelope from the researcher, the re-search consent form, and the cover letter which in-cluded information to help participants complete thesurvey questionnaire in the manner they preferred.

Of the 200 kindergarten teachers who were con-tacted, 81 teachers returned the survey questionnaire tothe researcher via the postal service (n = 68), e-mailing{n = 7), or posting the response over the Internet (n = 6).The 81 kindergarten teachers who replied to the re-searcher via mail, e-mailing, or posting the responseover the web, were determined to be the sample of thisstudy.

6. Instrumentation

A survey questionnaire was developed by the re-searcher. The instrument was composed of the follow-ing four sections: (a) kindergarten teachers' practiceof developmentally appropriate mathematics, (b) atti-tudes toward mathematics, (c) attitudes toward teach-ing mathematics, and (d) informational background.

6.1. Practice of developmentally appropriatemathematics

Previously, early childhood educators and nationalassociations had developed several instruments toassess quality early childhood programs under the

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guidelines of developmentally appropriate practice(DAP) including: (a) the second edition of Earlychildhood education and the elementary schoolprincipal: Standards for Quality Programs for YoungChildren: Early Childhood Education (NAESP,1998); and (b) the revised edition of The Early Child-hood Environment Rating Scale (ECERS) (Harms,Clifford, & Cryer, 1998), and; (c) DevelopmentallyAppropriate Mathematics Inventory (Carlan, 2000).

For the purpose of this study, the researcher utilizedexisting inventories as source material and deviseda 25-item questionnaire with use of a five-pointLikert Scale to assess the practice of developmentallyappropriate mathematics. The items to assess DAP inmathematics were composed of the following five cat-egories: (a) a child-centered physical environment; (b)developmentally-appropriate mathematical activities;(c) a positive and non-evaluative environment; (d)developmentally appropriate materials and manipula-tives; and (e) the use of authentic student assessment.

6.2. Attitudes toward mathematics and teachingmathematics

Aiken's (1972, 1974) inventories to assessteachers' attitudes toward mathematics and teachingmathematics are most frequently used in the field of ed-ucation. Many researchers and educators have adoptedand modified these to assess teachers' attitudes to-ward either mathematics or teaching mathematics(Haladyna, Shaughnessy, & Shaughnessy, 1983;McGriff Hare, 1999; Nolen, Archambault, & Greene,1977; Rech, Hartzell, & Stephens, 1993; Schofield,1981). The researcher followed earlier models andalso modified an Aiken inventory (1974) to assesskindergarten teachers' attitudes toward mathematicsand the teaching of mathematics. The survey question-naire that was devised is composed of 14 items witha five-point Likert Scale, which addresses whetherteachers enjoy mathematics/teaching mathematics,are anxious about mathematics/teaching mathemat-ics, and/or are confident with mathematics/teachingmathematics. Seven of the items assess teachers'attitudes toward mathematics, and seven items assessteachers' attitudes toward teaching mathematics.

6.2.1. ValidityContent validity indicates the degree to which

the content measures what it is intended to measureand whether or not the instrument elicits accurateinformation (Cox, 1996). Content validation wasestablished during the design of the instrumentby cross-referencing several instruments (surveyquestionnaires). To build the content validity, relatedliterature was reviewed which purported to measure ei-ther the same or similar elements of teachers' personal

attributes. These involved the practice of developmen-tally appropriate mathematics, and attitudes towardmathematics and teaching mathematics, as well aspedagogical content knowledge of mathematics.

6.2.2. ReliabilityAccording to Cox (1996), the term "reliability" is

explained by the word consistency. The consistencyis the degree to which an instrument provides simi-lar results for the same individuals even though it isused at different times (Wiersma, 1995). According toWiersma (1995), when an observed score is consis-tent, the instrument has "high reliability." To measurethe reliability of the instrument (questionnaire), a pilotstudy was conducted with ten kindergarten teachers.These teachers' names were selected from the direc-tory of the Vigo County School Corporation, TerreHaute, Indiana. Each subject was directly contactedby the researcher either via phone or e-mail to obtainher or his participation in the pilot study before thequestionnaire was distributed. The questionnaire wasdelivered to each teacher who consented to participatein the pilot study. The completed questionnaires weredirectly picked up by the researcher during a scheduledappointment. Subjects consisted of all female whiteteachers with varied years of teaching experiencesranging from 4 to 11 years (M=6.7 years). The ageof subjects ranged from 27 to 43 years (M= 34 years).

To measure reliability of the instrument (question-naire), the researcher calculated "Cronbach's Alpha,"which is frequently used to test the reliability of ques-tionnaire items (Cronk, 1999). The reliability score ofthe instrument using Cronbach's coefficient alpha was.85, which is categorized in the range of "very goodreliability" (Cronk, 1999). Therefore, based on the pi-lot study conducted by the researcher, the instrumenthad an acceptable amount of reliability.

7. Procedures

7.1. Data collection procedures

Survey methodology was used to collect data forthe study. The researcher's approach to distributingthe survey questionnaires to kindergarten teachers wasthree-fold: mailing a hard copy of the questionnaire,sending the questionnaire via e-mail, and postingquestionnaire items on the Internet. Kindergartenteachers were asked to complete the questionnaire inthe way they preferred, that is filling out the hard copyof the questionnaire, filling out the questionnaire viae-mail, or filling out the questionnaire on the Internet.They were instructed to complete the questionnaireonly once using one of the procedures indicatedabove. The researcher sent the survey questionnaire

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packet to each of the randomly selected kindergartenteachers.

To identify participants who returned the hard copyof the questionnaire, the researcher numbered eachquestionnaire on the back, and utilized these numbersto identify who had returned the questionnaire to theresearcher. If participants returned the questionnairevia e-mail, their e-mail addresses were used to iden-tify their participation in this study. In addition, theInternet protocol (IP) addresses were traced to iden-tify participants who responded over the web. The IPaddresses were gathered at the same time participantssubmitted the questionnaire over the web.

7.2. Data analysis procedures

To determine correlation between the practice ofdevelopmentally appropriate mathematics and kinder-garten teachers' attitudes (toward mathematics andteaching mathematics), a simple linear regression wasconducted in this study. Lomax (1998) notes that,"multiple linear regression involves the use of two ormore predictor variables and one criterion variable"(p. 49). A multiple linear regression is generally usedto analyze the variance in the criterion variable whilecontrolling for two or more sets of multiple predictors(Aiken & West, 1991). For the purpose of this study,the scores of the practice of developmentally appropri-ate mathematics were assigned as a dependent variable(criterion variable) and the scores of teachers' attitudestoward mathematics and teaching mathematics as in-dependent variables (predictors). All predictor vari-ables were tested using a multiple regression from theStatistical Package for the Social Sciences (SPSS) toexamine whether each individual predictor accountedfor a significant portion of the variance in predictingthe criterion variable.

The significant correlation between predictors andcriterion variable was interpreted by r-score and de-termined by the significance level using alpha level,p<.01. In addition, R2 was analyzed in this study tomeasure the proportion of variability in the criterionvariable that could be determined by the relationshipwith the predictors. The results of R2 were interpretedusing the guidelines in Statistics for the BehavioralSciences (Gravetter & Wallnau, 2000). A value of R2

of .09-.25 was interpreted to mean that the correla-tions between criterion variable and predictors can beexplained by 9-25% of proportion of variability. Avalue of R2 of .25-.49 was interpreted to mean that thecorrelations between criterion variable and predictorscan be explained by 25-49% of proportion of vari-ability. A value of R1 of .49—.81 was interpreted tomean that the correlations between criterion variableand predictors can be explained by 49-81 % of propor-tion of variability. Finally, a value of R2 of .81-1.00

indicated very high correlation that can be interpretedto mean the correlations between criterion variable andpredictors can be explained by 81-100% of proportionof variability.

8. Results

8.7. Frequency distribution data of participants

A total of 81 kindergarten teachers participated inthis study by completing a survey questionnaire. De-scriptive data of participants are presented in the fol-lowing by three categories: participants' demographicinformation (age, race, and gender), professionalinformation (acquired degree, years teaching kinder-garten and number of mathematics relevant workshopsin which they have participated). Table 1 presents thefrequency distribution of participants' age.

As Table 1 demonstrates, the present study'sparticipants represented a diverse age range, whichadequately reflected the population. Among partic-ipants (/"=81), 24.7% ranged from 20 to 30 years ofage (/"= 20), 16% ranged from 31 to 40 (f= 13), 34.6%ranged from 41 to 50 (/"=28), and 24.7% were over51 (f=20).

According to Table 2, the participants werecomposed of 4.9% male (f=4) and 95.1% female(f=ll). The participants' demographic statisticsrevealed a wide range of age difference. However,these statistics also revealed homogeneity in gender,with only 4.9% male, and in race, as all teacherparticipants were Caucasian.

The following tables. Tables 3-5, demonstrate par-ticipants' professional information including acquired

Table 1Frequency distribution of participants' age

Age20-3031-4041-50Over 51

Total

Frequency (f)

20132820

81

Table 2Frequency distribution of participants' gender

GenderFemaleMale

Total

Frequency (f)

774

81

Percent (%)

24.716.034.624.7

100.0

Percent (%)

95.14.9

100.0

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J. Lee/Journal of Early Childhood Teacher Education 25 (2005) 173-184 179

Table 3Frequency distribution of participants' acquired degree

Degree

Acquired degreeBachelor's degreeMaster's degreeDoctoral degreePost doctoral degree

Total

Frequency (/) Percent (%)

3445

20

81

41.955.6

2.50

100.0

Table 5Frequency distribution of the number of workshops attended

Number of workshop Frequency (/) Percent (%)

Participation in mathematics relevant workshopsNoneOnce a year2-3 times a year4-5 times a year

2238154

More than 6 times a year 2

Total 51

27.246.918.54.92.5

100.0

degrees, years taught at kindergarten level, and thenumber of workshops attended. Table 3 shows partic-ipants' acquired degrees. According to Table 3, morethan half of the participants held a graduate degree ateither the master's or doctoral level - 55.6% of partic-ipants (/=45) had obtained the master's degree, and2.5% of participants (f=2) had earned the doctoraldegree.

Table 4 shows that years of teaching experience atthe kindergarten level varied from one to three yearsto more than 16 years. According to Table 4, thehighest frequency of years of participants' teachingexperiences at the kindergarten level was 34.6% ofparticipants, who responded they had taught morethan 16 years. This indicates that more than one-thirdof participants in this study were experienced teach-ers. At the same time, about one-fifth of participants(22.2%) were composed of beginning teachers whohad taught one to three years at the kindergartenlevel. An additional one-third of participants (33.3%)had taught 4—15 years at the kindergarten level. Interms of years teachers had taught at the kindergartenlevel, the participants somewhat represent the generalteaching population, in that they represent a range ofyears in teaching kindergarten level.

Regarding the amount of participation in mathe-matics relevant workshops (Table 5), about 27% ofparticipants (f= 22) had not attended any workshopsto enhance their mathematics teaching. Near halfof the participants (/=38) had attended a workshoponly once a year for their professional growth inmathematics teaching practice. In addition, 18.5%

Table 4Frequency distribution of years taught at kindergarten level

Year Frequency (/) Percent (%)

Years taught at kindergarten level1-3 years4—7 years8-15 yearsMore than 16 yearsNo response

Total

18161128

8

81

22.219.813.534.69.9

100.0

of participants (/= 15) responded that they attendedmathematics related workshops two or three timesa year, while only 7.4% of participants (f=6)responded that they participated in mathematicsrelevant workshops more than four times a year.

9. Data analysis

9.1. Descriptive data of each variable

This study analyzed whether kindergarten teach-ers' attitudes toward mathematics and attitudes towardteaching mathematics were effective predictors for thepractice of developmentally appropriate mathematics.Tables 6-8 show the descriptive data of mean scores

Table 6Descriptive statistics of developmentally appropriatemathematics

Subcategoriesdevelopmentallyappropriate mathematics

M S.D.

A child-centered environmentDevelopmentally appropriate

mathematics activitiesDevelopmentally appropriate

materials andmanipulatives

Use of authentic studentassessment

Developmentally appropriatemathematics (overallmean)

8181

81

81

81

4.063.64

3.98

3.22

3.72

.53

.53

.60

.34

.50

Table 7

Descriptive statistics of attitude toward mathematics

Subcategories of attitude toward mathematics n M S.D.

Ease of mathematics (anxiety related) 81 3.72 .82

Enjoyment of mathematics 81 3.68 .63Confidence in mathematics 81 3.49 .71Attitudes toward mathematics (overall mean) 81 3.63 .72

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180 /. Lee/Journal of Early Childhood Teacher Education 25 (2005) 173-184

Table 8Descriptive statistics of attitudes toward teachingmathematics

Subcategories of attitudestoward teachingmathematics

Ease of teaching mathematics(anxiety related)

Enjoyment of teachingmathematics

Confidence in teachingmathematics

Attitudes toward teachingmathematics (overallmean)

n

81

81

81

81

M

4.22

3.77

3.65

3.88

S.D.

.70

.64

.49

.61

and standard deviations of subcategories of each vari-able: practice of developmentally appropriate math-ematics, attitudes toward mathematics, attitudes to-ward teaching mathematics, and pedagogical contentknowledge of mathematics.

The mean scores of the practice of developmentallyappropriate mathematics were acquired from the five-point Likert rating scale. Therefore, the possible scoreranges of these items were from one to five.

According to Table 6, the overall mean score of thepractice of developmentally appropriate mathematicswas 3.72 (S.D. = .50). Considering the mean score ofeach subcategory of the practice of developmentallyappropriate mathematics, the highest mean scorewas acquired from the items of "a child-centeredenvironment." while, the data show that kindergartenteachers rated lowest on the "use of authentic studentassessment" which involved communications withchildren/parents, observations of children's play, andassessing children's artifacts.

The mean scores of kindergarten teachers'attitude toward mathematics were acquired fromthe questionnaire with a five-point Likert ratingscale. Therefore, the possible score ranges of theseitems were from one to five. Overall mean scores ofkindergarten teachers' attitudes toward mathematicswere acquired (Af=3.63, S.D. = .5O). Regardingthe mean score from each subcategory, teachers'confidence is shown as the lowest score (M=3.49,S.D. = .71) among subcategories of attitudes towardmathematics, while teachers showed highest scores on"ease of mathematics" (M=3.72, S.D. = .82). Thesedata indicate that kindergarten teachers possessedsome level of enjoyment and ease with mathematicsas compared with the levels of their confidence inmathematics.

The mean scores of kindergarten teachers' attitudetoward teaching mathematics were acquired from thequestionnaire with five-point Likert rating scale. The

. scores acquired from this five-point Likert rating scaleranged from one to five.

As illustrated in Table 8, the overall mean scoresof kindergarten teachers' attitudes toward teachingmathematics were acquired (M=3.88, S.D. = .61).Regarding the mean score from each subcategory,teachers' confidence in teaching mathematics isshown as the lowest score (Af=3.65, S.D. = .49)among subcategories used to assess teachers' at-titudes toward mathematics. Teachers showed thehighest scores on "ease of mathematics" (Af=4.22,S.D. = .7O). The mean score reflected in "ease ofteaching mathematics" was the highest, while themean score on "confidence in teaching mathematics"was the lowest. Though kindergarten teachers pos-sessed some degree of comfort teaching mathematics,these data revealed they still showed a lower level ofconfidence in teaching mathematics.

9.2. Correlation between the use of the practiceof developmentally appropriate mathematics andkindergarten teachers' attitudes

The correlation between the use of practiceof developmentally appropriate mathematics andkindergarten teachers' attitudes (toward mathematicsand teaching mathematics) was tested in this study byusing a simple linear regression method. The results ofR- were interpreted using the guidelines in Statisticsfor the Behavioral Sciences (Gravetter & Wallnau,2000). A value of R2 of .09-.25 is interpreted tomean the correlations between criterion variable andpredictor can be explained by 9-25% of proportion ofvariability. A value of R2 of .25-.49 is interpreted tomean the correlations between criterion variable andpredictor can be explained by 25-49% of proportionof variability. A value of R1 of .49-.81 is interpreted tomean the correlations between criterion variable andpredictor can be explained by 49-81% of proportion ofvariability. Finally, a value of/?2 of .81-1.00 indicatesa very high correlation mat can be interpreted to meanthe correlations between criterion variable and pre-dictor can be explained by 81-100% of proportion ofvariability.

A simple linear multiple regression (stepwise) wasconducted to investigate whether teachers' attitudestoward mathematics accounted for a significant pro-portion of variance as a positive predictor of the prac-tice of developmentally appropriate mathematics. Thestepwise method automatically excluded the predictorof "attitudes toward mathematics" which did not makea significant contribution in predicting the dependentvariable (the practice of developmentally appropriatemathematics). The value of R2 was adjusted from .36to .32 in predicting the practice of developmentallyappropriate mathematics. It was considered that 32%

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Table 9Summary of stepwise regression analysis for excluded vari-able predicting the practice of developmentally appropriatemathematics

Excluded variable S

Attitudes toward mathematics .10 .56 .57

Table 10Summary of stepwise regression analysis for retained vari-ables predicting the practice of developmentally appropriatemathematics

Variables 8 S.E.

Teachers' attitudes towardteaching mathematics

.38 .09 3.08 .003

Note: R2 = .38 (p<.01).

of variability in the developmentally appropriatemathematics can be predicted from the relationshipwith the attitudes toward mathematics. Regarding theguidelines in Statistics for the Behavioral Sciences(Gravetter & Wallnau, 2000), the values of R2

acquired were interpreted as a moderate variability inpredicting the practice of developmentally appropriatemathematics with attitudes toward mathematics.

A multiple stepwise regression was also conductedto investigate whether teachers' attitudes toward teach-ing mathematics accounted for a significant proportionof variance as a positive predictor of the practice of de-velopmentally appropriate mathematics (Table 9).

The stepwise multiple regression added the predic-tor (teachers' attitude toward teaching mathematics)which made the largest contribution to the explanationof the dependent variable. As Table 10 shows, teach-ers' attitudes toward teaching mathematics were foundto be significant in predicting the practice of devel-opmentally appropriate mathematics F (1, 79) = 9.48,p = .003. According to Table 10, 38% of variabilityin the practice of developmentally appropriate math-ematics was predicted from the relationship with theattitudes toward teaching mathematics. According tothe guidelines in Statistics for the Behavioral Sciences(Gravetter & Wallnau, 2000), the acquired value of R2

can be interpreted as a moderate variability, since thevalue of R2 fell between .25 and .49.

10. Conclusions and educational implications

The results of this study revealed that kinder-garten teachers' attitudes toward teaching math-ematics were found to be a significant factor inpredicting the practice of developmentally appropri-ate mathematics. However, kindergarten teachers'attitudes toward mathematics were not a significant

factor in predicting the practice of developmentallyappropriate mathematics.

Even though teachers' attitudes toward mathe-matics were not found to be a significant factor inpredicting the practice of developmentally appropriatemathematics, some educational implications were de-rived from these study results. Created subcategoriesto measure teachers' attitudes toward mathematicsincluded the three subcategories of: ease of mathe-matics, enjoyment of mathematics, and confidence inmathematics. According to the study results, teachersshowed comparatively lower scores on the confidence-related items than on ease or enjoyment of mathemat-ics related items. Therefore, it is necessary for schooldistrict administrators to consider ways of improvinginservice teachers' confidence level toward mathemat-ics. Confidence in a certain subject is closely relatedJo the knowledge of the subject (Fennema & Franke,1992). According to the study results, 74.1% of teach-ers reported they had attended mathematics relatedworkshops one time or less per year. This implies thatkindergarten teachers should have more professionaldevelopment opportunities, especially in the contentarea of mathematics, to enhance their confidencelevel.

In addition, it is also recommended that teacherpreparation institutions examine preservice teachers'attitudes toward mathematics in confirming whetherthey possess adequate mathematics content knowl-edge. When preservice teachers display some negativeattitudes toward mathematics (e.g., less confidenceor more anxiety), they should receive immediatehelp from a support group of professional mathe-matics teachers (e.g., university professors or schoolteachers) who understand mathematics anxiety.

From the study results, teachers' attitudes towardteaching mathematics were found to be significantlycorrelated with the practice of developmentally ap-propriate mathematics. To measure teachers' attitudestoward teaching mathematics, the same subcategoriesused to assess attitudes toward mathematics wereadopted: ease of teaching mathematics, enjoymentof teaching mathematics, and confidence in teach-ing mathematics. Since teachers' attitudes towardteaching mathematics were found to be significantlycorrelated with the practice of developmentallyappropriate mathematics, it was essential to furtherconsider each subcategory of attitudes toward teachingmathematics. When investigating scores from eachsubcategory, teachers showed higher scores on the easeof teaching mathematics. According to the questionsused in this study, teachers reported that diey had lowconfidence in teaching mathematics. The study resultsshowed that teachers demonstrated an easy feelingtoward teaching mathematics but still were less con-fident when teaching mathematics. Therefore, school

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182 J. Lee /Journal of Early Childhood Teacher Education 25 (2005) 173-184

district administrators should consider how to enhanceteachers' confidence level in teaching mathematics.When teachers possess more knowledge of how toteach each mathematics content area, they will havemore confidence in teaching mathematics. For thisreason, a variety of opportunities (mathematics work-shops, seminars, or hands-on activities) on teachingpedagogy should be provided for teachers to enhancetheir confidence level in teaching mathematics.

In addition, teacher preparation programs also haveto focus on improving preservice teachers' attitudestoward teaching mathematics—especially in improv-ing their confidence level in teaching mathematics. Toenhance preservice teachers' confidence level in math-ematics, mathematics education methodology coursescan be effectively utilized to provide preservice teach-ers opportunities to possess a meaningful knowledgeof mathematics by utilizing hands-on activities, coop-erative group activities, or technology (e.g., variousmathematics software or calculators).

11. Recommendations for future research

DAP has been widely recommended, especially inearly childhood education, as a critical component ofquality programs for young children. However, therehas been very little research conducted which relatesto developmentally appropriate mathematics. Carlan(2000) has found the elements of developmentallyappropriate mathematics and listed five categorieswhich should be used to determine DAP in mathe-matics: (a) a child-centered physical environment; (b)developmentally appropriate mathematical activities;(c) a positive and non-evaluative environment; (d) theavailability of developmentally appropriate materialsand manipulatives; and (e) authentic/holistic studentassessment. This study utilized survey methodologyto measure kindergarten teachers' teaching practice ofdevelopmentally appropriate mathematics based onthose five categories. However, it was difficult to mea-sure developmentally appropriate teaching pedagogydue to the limitations of using a survey methodology.To determine DAP, it is essential to consider teachingpedagogy, such as variations in presenting activities ormaterials. Even though teachers incorporate develop-mentally appropriate activities and materials in theirclassrooms, how they present those items is of greatersignificance than the mere presence of materials.Therefore, it is recommended that future research tomeasure DAP make use of qualitative methodology,such as observing kindergarten teachers' teachingpractice in a natural environment or interviewingthem regarding their teaching pedagogy.

This study found that teachers' attitudes towardteaching mathematics were a significant factor in

the prediction of the practice of developmentallyappropriate mathematics, but teachers' attitudestoward mathematics were not. This study was not ableto exactly answer why this happened. According toother numerous studies (e.g., Giordano, 1991; Karp,1991; Kelly & Tomhave, 1985; Kulm, 1980; Quinn,1997), both teachers' attitudes toward mathematicsand their attitudes toward teaching mathematicshave been found to be significant factors for DAPin mathematics. However, this study found onlyteachers' attitudes toward teaching mathematics wasan effective factor in predicting the practice of devel-opmentally appropriate mathematics. Therefore, thisconclusion should be further analyzed in a qualitativemanner to learn why teachers' attitudes toward mathe-matics turned out to be a less effective predictor of thepractice of developmentally appropriate mathematics.

Finally, a recommendation for future researchis to consider the necessity of controlling teachers'demographic backgrounds, as well as the classroomphysical environment and students' social economicstatus (SES). According to Buchanan et al. (1998),teachers' characteristics (beliefs and area of certifica-tion), as well as classroom characteristics (e.g., classsize, number of children with disability, or SES ofchildren's family) impacted implementing DAP. Theteachers' demographic information and classroomcharacteristics were not controlled in this study.However, these variables were presented in severalstudies as significant predictors of DAP (Buchanan etal., 1998; Mangione & Maniates, 1993; McMullen,1999). Therefore, to find the predictors of develop-mentally appropriate mathematics it is recommendedthat further research control teachers' demographicinformation, as well as classroom characteristics.

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