Sign up

Teacher Interpersonal Behavior and Elementary Students' Outcomes.
Article Type:
Statistical Data Included
Subject:
Education, Elementary (Research)
Teaching (Social aspects)
Teacher-student relationships (Research)
Authors:
Goh, Swee Chiew
Fraser, Barry J.
Pub Date:
03/22/2000
Publication:
Name: Journal of Research in Childhood Education Publisher: Association for Childhood Education International Audience: Academic Format: Magazine/Journal Subject: Education Copyright: COPYRIGHT 2000 Association for Childhood Education International ISSN: 0256-8543
Issue:
Date: Spring-Summer, 2000 Source Volume: 14 Source Issue: 2
Geographic:
Geographic Scope: Singapore Geographic Code: 9SING Singapore

Accession Number:
63567050
Full Text:
Abstract. This study examined teacher's interpersonal behavior and its associations with affective and cognitive outcomes among elementary mathematics students. A random sample of 1,512 boys and girls from government elementary schools in Singapore was involved. For the analysis of behavior-outcome associations, simple, multiple, and canonical correlation analyses and multilevel (hierarchical linear model) analyses were conducted for two levels of analysis; namely, the individual student and the class mean. The study led to the validation of a widely applicable and convenient questionnaire to assess teacher interpersonal behavior for future use by researchers and teachers at the elementary school level. Overall, the different methods of analysis yielded consistent associations between teacher interpersonal behavior and student outcomes.

Doyle's (1979) recommendation that the classroom be viewed from an ecological viewpoint emphasizes the interrelationships and communications among all members in the classroom community. Learning activities always are accompanied by interpersonal interaction and interpersonal sentiments. The reciprocal nature of teacher-student communication makes it a powerful influence on the learning environment and, subsequently, on student performance. In the last 20 years, this long-standing recognition has inspired a tradition of studying classroom learning environment through the perceptions of both teachers and students (Fraser, 1986, 1994, 1998a; Fraser & Walberg, 1991). In addition, in an attempt to understand better the impact of teacher-student communication on the learning process, Wubbels and his colleagues embarked on the study of interpersonal teacher behavior in secondary classrooms (Wubbels & Brekelmans, 1998; Wubbels & Levy, 1993). Since the behavior of both teacher and student influence each other, it fol lows that such interactions are crucial to student learning in the classroom.

Because the data for many educational research studies are derived from students in intact classes, they are inherently hierarchical, and consequently could benefit from the use of multilevel analysis (Bock, 1989; Bryk & Raudenbush, 1992; Goldstein, 1987). Despite the potential advantages of this technique in learning environment research, however, its use has been virtually nonexistent. The main advantage in using multilevel analysis is that it is cognizant of the multilevel, or hierarchical, nature of classroom settings. Because ignoring the nested structure of this type of data gives rise to problems of aggregation bias (within-group homogeneity) and imprecision (Raudenbush, 1988), multilevel analysis was included in the present research.

The present study investigated an aspect of the classroom learning environment (interpersonal teacher behavior) in elementary mathematics classes in Singapore. In addition to cross-validating a widely applicable instrument for use at the elementary level, the study investigated associations between two student outcomes (attitudes and achievement) and interpersonal teacher behavior. Overall, this research made numerous distinctive contributions to the field of learning environment research. First, although much research on learning environments has been completed at the secondary school level, this study provides one of the most comprehensive of the relatively small number of studies undertaken at the elementary school level. Second, this study is one of a small handful that marks the beginning of the field of classroom environment research in Singapore. Third, for the first time in any country, an elementary version of the Questionnaire on Teacher Interaction (QTI) was developed, validated, and used in resear ch applications. Fourth, the study provided one of the first uses of multilevel analysis in learning environment research (and included a comparison of results from using well-established multiple regression techniques).

Review of Research

Field of Learning Environment Research

Over the previous quarter of a century, considerable interest has been shown internationally in the conceptualization, measurement, and investigation of perceptions of psychosocial characteristics of the learning environment of classrooms at the elementary, secondary, and higher education levels (Fraser, 1986, 1994, 1998a, 1998b; Fraser & Walberg, 1991; McRobbie&Ellett, 1997). Classroom environmentinstruments have been used as sources of predictor and criterion variables in a variety of research studies. Use of student perceptions of actual classroom environments as independent variables in several different countries has established consistent relationships between the nature of the classroom environment and various student cognitive and affective outcomes (Fraser, 1986; Fraser & Fisher, 1982; Haertel, Walberg, & Haertel, 1981). Research involving a person-environment fit perspective has shown that students achieve better where there is greater congruence between the actual classroom environment and that whi ch is preferred by students (Fraser & Fisher, 1983). The combination of qualitative and quantitative methods has been a feature of several recent learning environment studies (e.g., Fraser & Tobin, 1991; Tobin & Fraser, 1998).

Studies involving use of the actual form of classroom environment scales as criterion variables have revealed that classroom psychosocial climate varies between different types of schools (Trickett, 1978) and between coeducational and single-sex schools (Trickett, Trickett, Castro, & Schaffner, 1982). Both researchers and teachers have found it useful to employ classroom climate dimensions as process criteria of effectiveness in curriculum evaluation, because they have differentiated revealingly between alternative curricula when student outcome measures have shown little sensitivity (Fraser, Williamson, & Tobin, 1987). For example, in an evaluation of an innovation in computer-assisted learning (CAL), it was found that students using CAL perceived their classrooms as having higher levels of gender equity, investigation, innovation, and resource adequacy than did a control group (Fraser & Teh, 1994; Teh & Fraser, 1994). Research in the United States (Moos, 1979), Australia (Fisher & Fraser, 1983), and The Ne therlands (Wubbels, Brekelmans, & Hooymayers, 1991) compared students' and teachers' perceptions and found that, first, both students and teachers preferred a more positive classroom environment than that perceived as being actually present and, second, teachers tended to perceive the classroom environment more positively than did their students in the same classrooms. In promising small-scale practical applications, teachers have used assessments of their students' perceptions of their actual and preferred classroom environment as a basis for identification and discussion of actual-preferred discrepancies, followed by a systematic attempt to improve classrooms (Fraser&Fisher, 1986; Thorp, Burden, & Fraser, 1994; Yarrow, Millwater, & Fraser, 1997).

Other lines of classroom environment research involve: developing an instrument for evaluating the degree to which a classroom is consistent with a constructivist epistemology (Taylor, Fraser, & Fisher, 1997); investigating the links among and the joint influence of classroom, school, family, and other environments on student outcomes (Moos, 1979, 1991); incorporating classroom environment as one factor in a multi-factor model of educational productivity (Fraser, Walberg, Welch, & Hattie, 1987); exploring ways in which classroom environment instruments can be used to their advantage by school psychologists (Burden & Fraser, 1993); incorporating learning environment ideas into teacher education (Fraser, 1993); investigating changes in classroom environment during the transition from elementary to high school (Ferguson & Fraser, 1998; Midgley, Eccles, & Feldlaufer, 1991); incorporating the assessment of classroom environment in teacher assessment schemes (Ellett, 1997); research into science laboratory classro om environments (Fraser, Giddings, & McRobbie, 1995; Fraser & McRobbie, 1995); research on the distinctiveness of the learning environment of Catholic schools (Dorman, Fraser, & McRobbie, 1997); and cross-cultural studies of learning environments in more than one country (Aldridge, Fraser, & Huang, 1999).

Because the quality of interpersonal interactions between the teacher and students is such an important aspect of the classroom learning environment, Wubbels and Levy (1993) initiated a major program of research in this area. This work on teacher interpersonal behavior, which formed the main thrust within the present study, is discussed in the next section.

Teacher Interpersonal Behavior

Inspired by the theory of Watzlawick, Beavin, & Jackson (1967), a systems approach to communication was adapted to describe teacher behavior within the classroom setting (Wubbels & Brekelmans, 1998; Wubbels, Cretan, & Holvast, 1988; Wubbels & Levy, 1993). According to Creton, Wubbels, & Hooymayers (1993), systems communication theory is underpinned by the interdependent relationship of circularity and change. Circularity refers to the interrelatedness of all aspects of the communication system; changes in one aspect affect changes in another (Creton et al., 1993). Therefore, in the classroom setting, the behavior of the teacher determines, and is determined by, students' behavior (Wubbels et al., 1991).

Leary (1957) developed a model that allows the graphic representation of interpersonal behaviors along two dimensions--influence and proximity--that measure specific interpersonal behaviors. Interpersonal communication can be plotted according to how much the participant is cooperative or dominant. Leary's model uses an influence dimension (Dominance, D -- Submission, S) to measure the degree of dominance or control over the communication process, and a proximity dimension (Cooperation, C -- Opposition, O) to measure the degree of affinity or cooperation felt by those involved in the communication process. Leary's model was adapted to form a model for interpersonal teacher behavior (Wubbels et al., 1991; Wubbels, Creton, Levy, & Hooymayers, 1993) that uses the same axes of proximity and influence as Leary's model, and that describes the types of teacher interpersonal behaviors (see Figure 1).

The model for interpersonal teacher behavior has eight sectors, each describing different facets of teacher behavior: Leadership (DC), Helping/Friendly (CD), Understanding (CS), Student Responsibility/Freedom (SC), Uncertain (SO), Dissatisfied (OS), Admonishing (OD), and Strict (DO) behavior. By using this model, each instance of teacher behavior can be placed within the eight sectors (Wubbels et al., 1991; Wubbels, 1993). Figure 1 provides examples of typical teacher behaviors for each sector, which is labeled according to its coordinate position (DO, DC, CD, etc.). For example, the sectors SC and CS are both characterized by Cooperation and Submission. A teacher plotted in the SC sector, where the presence of Submission predominates over the presence of Cooperation, would be more likely to provide students with responsibility and to assume a role that allows students more freedom. Such behavior would be evident during a lesson that was student-guided, such as the use of learning centers. The CS sector, how ever, would describe a teacher with more cooperation and less submission. This teacher would be seen as understanding and empathic with students.

The Questionnaire on Teacher Interaction (QTI) was developed to examine interpersonal teacher behaviors through students' perceptions (Wubbels & Brekelmans, 1998; Wubbels et al., 1991), using eight scales corresponding to the eight sectors of the model for interpersonal teacher behavior in Figure 1.

The original Dutch version of the QTI incorporated about 10 items in each scale, with a total of 77 items (Wubbels et al., 1993). An English-language version of the QTI was developed in the late 1980s (Wubbels & Levy, 1991), incorporating eight items for each scale (a total of 64 items), and administered in the USA. Both questionnaires were developed for educational research purposes in secondary schools and used a five-point response format. Subsequently, the QTI also has been used in studies in Israel (Kremer-Hayon & Wubbels, 1992) and Australia (Fisher, Fraser, & Rickards, 1997; Fisher, Fraser, & Wubbels, 1993; Fisher, Henderson, & Fraser, 1995; Wubbels, 1993). Wubbels developed a short 48-item version, in English, of the QTI, to enable secondary school teachers to obtain feedback on their own interpersonal relationships within the classroom (Wubbels, 1993).

Past research using the QTI is reviewed in Wubbels and Brekelmans (1998) and Wubbels and Levy (1993). A typology of eight types of teacher communication styles was identified by Brekelmans, Levy, and Rodriguez (1993): directive, authoritative, tolerant/authoritative, drudging, tolerant, uncertain/aggressive, uncertain/tolerant, and repressive. In numerous studies of relationships between teacher behavior and student outcomes (Wubbels & Brekelmans, 1998), medium to strong associations have been found, but relationships are stronger for affective than cognitive outcomes. Whereas leadership, helpful/friendly and understanding behaviors are positively related to student outcomes; uncertain, dissatisfied, and admonishing behaviors are negatively related to outcomes. Brekelmans and Cr[acute{e}]ton (1993) found that teachers' dominant behavior intensifies during the first 10 years of teaching and stabilizes thereafter; on the other hand, cooperative behavior remains consistent throughout the entire teaching career.

Past Research in Singapore

Although the study of learning environments has a history of 25 years in other countries, it made its first appearance in Singapore only recently with a study of student perceptions of computer-assisted classroom environments (Fraser & Teh, 1994; Teh & Fraser, 1994). This study led to the development and validation of an instrument for computer-assisted instructional settings, established that computer-assisted learning for below-average secondary students was a more efficacious instructional method than a traditional teaching method, and replicated past research findings showing that students achievement and attitudes were better in classes perceived to have positive classroom environments.

Wong and Fraser's (1996, 1997) study of chemistry laboratory classroom environments in secondary schools revealed differences in perceptions between teachers and students; namely, that preferred chemistry laboratory environments were more favorable than actual perceptions, and that students from different streams differed in their preferred (but not their actual) perceptions. Also, relationships were found between student affective outcomes and the perceived environment of chemistry laboratories, and gender differences in perceptions emerged.

Khoo and Fraser (1998) used a modified version of the "What Is Happening in This Class" (WIHIC) questionnaire in evaluating computer courses for adults. The study provided support for the validity and reliability of the questionnaire, identified some age and sex differences in students' reactions to the courses, and established associations between student satisfaction and their classroom environment perceptions. Chionh and Fraser (1998) cross-validated an actual and a preferred form of the WIHIC questionnaire among 2,310 geography and mathematics students, as well as establishing associations between WIHIC scales and students' examination results, attitudes, and self-esteem.

Quek, Wong, and Fraser (1998) cross-validated the Questionnaire on Teacher Interaction (QTI) among 497 10th-grade chemistry students, reported some sex and stream (gifted vs express) differences in perceptions of teacher-student interaction, and established associations between QTI scales and student enjoyment of chemistry lessons.

As practically all past learning environment studies in Singapore were undertaken in secondary classrooms, it was timely to initiate the present study at the elementary level. Therefore, it was appropriate to examine, through student perceptions, the impact of teacher-student relationships on student cognitive and affective outcomes in elementary mathematics classes. This study is the first classroom learning environment research done in elementary mathematics classes in Singapore. In view of the importance of mathematics in the Singapore elementary school curriculum, it was beneficial to focus the present study on whether the teacher-student-context triad promotes or hinders students' mathematics achievement in elementary schools in Singapore.

Sample and Instruments

Sample

A random sample of 39 mathematics classes from 13 government co-educational elementary schools provided a teacher sample size of 39 mathematics teachers, one for each of the 39 classes, together with a student sample of 1,512 (815 boys and 697 girls). The 13 schools out of 108 government elementary schools in Singapore represent about 12% of the available population of schools. These students were 10 to 11 years of age, of mixed ability, and in the EM2 stream (where they learn English as a first language, Chinese/Malay/Tamil as a second language, and Mathematics and Science). These 39 Grade 5 classes were "intact" classes, because the principals gave the researchers permission only to administer the questionnaires to whole classes during mathematics curriculum time. The learning environment instrument used was the Questionnaire on Teacher Interaction (Elementary), and the outcome measures were the Liking Mathematics Scale and the Mathematics Exercise.

Questionnaire on Teacher Interaction (Elementary)

A new elementary version was adapted from two versions of the Questionnaire on Teacher Interaction (QTI) for secondary schools: the long form (64 items) used in an Australian study; and the short form (48 items) designed for Australian teachers to obtain feedback from their classes (Wubbels, 1993). The present study involved further adaptation of the QTI to make it suitable for use at the elementary school level, and for its subsequent validation in Singapore. For example, the item "The teacher takes a personal interest in us" was changed to "The teacher cares about us." The QTI's original five-point response scale was changed to a three-point scale to make it more suitable for elementary students. The 48-item QTI (Elementary) assesses the eight dimensions of teacher behavior described in Figure 1. Table 1 provides a description and sample item for each scale in the elementary version of the QTI.

Appendix A contains a complete copy of the QTI (Elementary). Items are arranged in cyclic order so that the first, second, third, fourth, fifth, sixth, seventh, and eighth item in each group of eight items assesses, respectively, Leadership, Helping/Friendly, Understanding, Student Responsibility/Freedom, Uncertain, Dissatisfied, Admonishing, and Strict behavior. Items are scored 1, 2, and 3, respectively, for the responses "Seldom," "Sometimes," and "Most of the Time." Omitted or invalid responses are scored 2.

Student cognitive achievement was assessed with a 10-item mathematics achievement test, the Mathematics Exercise, which was based on a sample of school mathematics assessment papers and elementary mathematics textbooks and workbooks. This instrument was developed by the researchers in three stages, taking cognizance of feedback from experts in the field (school mathematics teachers and mathematics experts or content experts). Items in the Mathematics Exercise were developed after a careful examination of the Grade 5 mathematics syllabus for Singapore elementary schools and of samples of mathematics assessments (class tests or continuous assessments). Each item was designed with a problem/situation as the stem and with four alternative responses.

Affective and Cognitive Outcome Measures The affective outcome was assessed with the Liking Mathematics Scale (LMS), which was based on a 10-item instrument developed specifically by the researchers to measure student liking and interest for mathematics, with guidance provided by attitude scales developed by Keeves (1974) and Fraser (1981). Statements are expressed simplly, directly, and concisely, as in "I enjoy mathematics classes" and "Mathematics is fun." The LMS uses the same three-point respons e scale, consisting of "Seldom," "Sometimes," and "Most of the Time," as the QTI (Elementary) and MCI.

Pilot Testing of Instruments

A pilot study was carried out with two Grade 5 classes in one government elementary school to gather subjective information to guide smooth administration of instruments during the main study, to check the comprehensibility and clarity of the items in the three instruments, to gauge the suitability of the three-point Likert response scale consisting of "Seldom," "Sometimes," and "Most of the Time," to evaluate procedures for data collection, and to estimate the approximate amount of time required by students to complete each of the instruments. The researchers interviewed six students concerning the clarity of the instruments and the three-point rating scale.

To improve the comprehensibility and clarity of the instruments, especially the QTI, difficult words identified by students during interview were substituted with simpler words, if possible or appropriate. Also, a few other items were reworded to ensure that the reading level was more appropriate. The response format in the questionnaires was found to be appealing and clear to the students. The procedures used for data collection in the two classes proved logical and systematic, and students found the directions simple and straightforward. Overall, the total time taken by the students to respond was less than an hour.

Although the present study involved extensive use of quantitative methods, the qualitative methods used in the pilot study were an important part of the overall study. Moreover, now that the present initial study has used quantitative methods to validate widely applicable instruments for future use, it is highly desirable to combine qualitative and quantitative methods in future research with these instruments, as recommended by Fraser and Tobin (1991).

Data Collection

One of the researchers personally administered the four instruments in every class involved in the study. Students used 2B pencils to shade their responses on optically read answer sheets. Students began with the QTI (Elementary) and, after a short rest, responded to the LMS and ME. Each instrument was printed on paper of a different color,, to aid administration and add variety to. the process.

Validation of Instruments

Questionnaire on Teacher Interaction (QTI) Data for the Singapore sample were analyzed to furnish evidence for the QTI regarding scale internal consistency reliability, the pattern of scale intercorrelations, and the ability of each scale to differentiate between classrooms. The Cronbach alpha coefficient was computed for each QTI scale as a measure of internal consistency reliability at two levels of analysis; namely, the individual student score (N = 1,512) and the class mean score (N = 39). Table 2 suggests that the QTI (Elementary) has quite good reliability, with five out of eight scales (namely, Leadership, Helping/Friendly, Understanding, Dissatisfied, and Admonishing) having values above 0.90 for class means, and the same five scales having values between 0.63 and 0.78, with the individual student as the level of analysis. As expected, the reliability estimates were higher when the class mean was used as the unit of analysis. These values for the Singaporean sample are comparable to those reported by Wubbels (1993) and Wubbels and Levy (1991) for secondary students in the Netherlands, the U.S. and Australia. In all four countries, the highest reliability occurred for Helping/Friendly teacher behavior, and the lowest for Student Responsibility/Freedom behavior.

Further evidence regarding the validity of the elementary version of the QTI was obtained by examining the scale intercorrelation matrix for two units of analysis (the individual student and the class mean). According to the circumplex model in Figure 1, adjacent scales (for example, Helping/Friendly, CD, and Understanding, CS), should correlate most highly and positively with each other, and the magnitude of the correlation should diminish as the scales become increasingly different as they move further apart from each other until they are diametrically opposite to each other (Wubbels & Levy, 1993). Diametrically opposite scales, such as Helping Friendly (CD) and Dissatisfied (OS), should have the highest negative correlation (Wubbels, 1993). Generally, the QTI scale intercorrelations satisfied this assumption, except for with minor discrepancies.

Another desirable characteristic of a classroom environment scale is that students within a class see their classroom environment relatively similarly, and that average class perceptions vary from class to class. A series of analyses of variance, with class membership as the main effect, revealed significant differences (p[less than]0.0l) for every QTI scale between the perceptions of students in different classes. The [eta.sup.2] statistic, which represents the amount of variance in interpersonal teacher behavior scores accounted for by class membership, ranged from 0.13 to 0.38 for different QTI scales (Table 2).

Environment-Outcome Associations

In order to examine associations between classroom environment (interpersonal teacher behavior) and student outcomes (attitude and achievement), the data were subjected to a series of correlational analyses (including simple, multiple, and canonical) and multilevel (hierarchical linear model) analyses, using the student and the class as two levels of analysis.

Simple, Multiple, and Canonical Correlation Analyses Involving the QTI and Student Outcomes

The first type of correlational analysis reported in Table 3 involved the simple correlation between each outcome and each QTI scale. The major advantage of this analysis is that it furnishes information to educators interested in associations between a particular teacher interpersonal behavior and a particular outcome. The number of significant simple correlations (p[less than]0.01) in Table 3 is 13 with the individual as the unit of analysis and 13 with the class as the unit of analysis (16 times that expected by chance). Generally, the simple correlational analysis suggests that all of the behaviors, except Strict, assessed by the QTI are related to student attitudes and achievement.

Table 3 presents for the QTI the results of simple, multiple, and canonical correlation analyses separately for the two student outcomes (Liking and Achievement). Using both the student and class levels of analysis, the present findings generally replicate past research into associations between interpersonal teacher behavior and student learning (Fisher, Fraser, & Rickards, 1997; Fisher, Henderson, & Fraser, 1995; Wubbels & Brekelmans, 1998; Wubbels & Levy, 1993).

The second type of analysis was a multiple regression involving the set of eight QTI scales performed separately for the two student outcomes and for two levels of analysis (Table 3). Relative to the simple correlational analysis, the multiple regression analysis provides a more parsimonious picture of the joint influence of correlated teacher interpersonal behavior dimension outcomes and it reduces the overall Type I error rate. The multiple correlation was statistically significant (p[less than]0.o1) for both units of analysis for both outcomes, with the magnitude being 0.89 for the attitude outcome and 0.82 for the achievement outcome at the class level of analysis (Table 3).

In order to interpret which of the correlated teacher behavior dimensions were making the largest contribution to explaining variance in learning outcomes, the standardized regression coefficients ([beta]) in Table 3 were examined to provide information about which individual QTI scales are related significantly to an outcome when the other seven QTI scales are mutually controlled. Although the number of significant results for the multiple regression analysis was smaller (10 at the individual level and four at the class level) than for the simple correlational analysis, Strict behavior, again, was the only QTI scale that was not related significantly to either outcome for either unit of analysis.

Although the use of multiple regression analysis overcomes the problem of relationships among QTI scales, relationships between the two outcome measures still could give rise to an inflated Type I error rate for the study as a whole. Canonical analysis can provide a parsimonious picture of relationships between a set of correlated learning outcomes and a set of correlated teacher behavior variables. The bottom row of Table 3 shows that one significant canonical correlation (p[less than[0.0l) of 0.54 emerged at the student level and a significant canonical correlation of 0.92 emerged at the class level.

To interpret the results of the canonical analysis, we examined the magnitudes and signs of the structure coefficients (i.e., the simple correlations between a canonical variate and its constituent variables). Substantive interpretations were based on structure coefficients in preference to canonical weights, because the latter can be misleading because of redundancy and suppression effects (Cooley & Lohnes, 1976). The overall conclusion from the canonical analysis was that achievement, and especially attitudes, were linked with greater levels of teacher Leadership, Helping/Friendly, and Understanding behaviors.

Multilevel Analyses Involving the QTI and Student Outcomes

In addition to the simple, multiple, and canonical correlational analyses reported in Table 3, a multilevel analysis was computed because of the inherently hierarchical data for the 1,512 students to ensure that adequate consideration was given to the variability among students and among classes arising from the nesting of students within classrooms and schools (Wong, Young & Fraser, 1997). The Hierarchical Linear Model (HLM) provides an integrated strategy for handling problems such as aggregation bias in standard error estimates and erroneous probability values in hypothesis testing of school effects (Bock, 1989; Bryk & Raudenbush, 1992; Goldstein, 1987; Young & Fraser, 1993).

Using the HLM2L (Bryk, Raudenbush, Seltzer, & Congdon, 1989) computer package, the following equation was used for student attitude towards mathematics as the outcome measure:

[MathAtt.sub.ij] = [[beta].sub.0j] + [[beta].sub.1j] [Leadership.sub.ij] + [[beta].sub.2j] [Helping.sub.ij] + [[beta].sub.3j] [Understanding.sub.ij] + [[beta].sub.4j] [Responsibility.sub.ij] + [[beta].sub.5j] [Uncertain.sub.ij] + [[beta].sub.6j] [Dissatisfied.sub.ij] + [[beta].sub.7j] [Admonishing.sub.ij] + [[beta].sub.8j] [Strict.sub.ij] + [r.sub.ij]

[[beta].sub.0j] = [[gama].sub.00] + [[gama].sub.01] [Cohesion.sub.j] + [[gama].sub.02] [Competition.sub.j] + [[gama].sub.03] [Friction.sub.j] + [[gama].sub.04] [Task.sub.j] + [[gama].sub.05] [Uncertain.sub.j] + [[gama].sub.06] [Dissatisfied.sub.j] + [[gama].sub.07] [Admonishing.sub.j] + [[gama].sub.08] [Strict.sub.j] + [[mu].sub.0j]

[[beta].sub.1j] = [[gama].sub.10]

[[beta].sub.2j] = [[gama].sub.20]

[[beta].sub.3j] = [[gama].sub.30]

[[beta].sub.4j] = [[gama].sub.40]

[[beta].sub.5j] = [[gama].sub.50]

[[beta].sub.6j] = [[gama].sub.60]

[[beta].sub.7j] = [[gama].sub.70]

[[beta].sub.8j] = [[gama].sub.80]

The random intercept and fixed slopes are described as follows:

[[beta].sub.0j] is the mean student attitude to mathematics in class j after controlling for student difference in perceptions of classroom climate between classes

[[beta].sub.1j] is the fixed effect of student-perceived teacher Leadership behavior on attitude towards mathematics in class j

[[beta].sub.2j] is the fixed effect of student-perceived teacher Helping/Friendly behavior on attitude toward mathematics in class j

[[beta].sub.3j] is the fixed effect of student-perceived teacher Understanding behavior on attitude towards mathematics in class j

[[beta].sub.4j] is the fixed effect of student-perceived teacher Student-Responsibility/Freedom behavior on attitude towards mathematics in class j

[[beta].sub.5j] is the fixed effect of student-perceived teacher Uncertain behavior on attitude towards mathematics in class j

[[beta].sub.6j] is the fixed effect of student-perceived teacher Dissatisfied behavior on attitude towards mathematics in class j

[[beta].sub.7j] is the fixed effect of student-perceived teacher Admonishing behavior on attitude towards mathematics in class j

[[beta].sub.8j] is the fixed effect of student-perceived teacher Strict behavior on attitude towards mathematics in class j.

A similar equation was used with mathematics achievement as the outcome measure.

In the above equation, the eight predictors investigated at the student level of analysis were student perceptions of the eight QTI dimensions. At the classroom level of analysis, these eight predictors were aggregated and investigated for their influence on student outcomes. These predictors reflected the peer effect of interpersonal teacher behavior on individual mathematics attitude and achievement.

Table 3 presents a comparison of results from the multiple linear regression and hierarchical linear model regression analyses. The results from the HLM and multiple regression analyses were identical in terms of both patterns of significance and the direction of relationships for four predictors of student outcomes for both levels of analysis (student or class levels). These four predictors are Leadership, Student Responsibility/Freedom, Dissatisfied, and Strict teacher behaviors. Different patterns of statistical significance emerged for Helping/Friendly, Understanding, Uncertain, and Admonishing behaviors, depending on the level of analysis. Strict teacher behavior consistently showed a nonsignificant linkage to student outcomes for both HLM and multiple regression analyses at either level of analysis.

With regard to the overall picture detected from the multiple regression and HLM analyses concerning associations between teacher behavior and the two student outcomes, the multiple regression analysis (Table 3) indicated 14 significant values as opposed to nine for the HLM analysis. The 5 significant values (that of Helping/Friendly, Understanding, Uncertain and Admonishing teacher behavior scales) in the multiple regression analysis that were not replicated in the multilevel analysis pertained only to associations between teacher behavior and student attitude. It is interesting to note that, in terms of the interrelationships between teacher behaviors and student achievement, the same four significant results were obtained for the HLM and multiple regression analyses (Leadership behavior at the individual student level, Understanding behavior at the individual level, and Uncertain behavior at both levels of analysis).

For the student affective outcome, five significant values in the multiple regression analysis were not replicated in the HLM analysis. The main difference revealed in Table 3 pertained to Understanding and student liking for mathematics at both levels. There was no significant association between teacher Understanding and student liking for mathematics at either level of analysis using the HLM approach, although the multiple linear regression in dicated a significant association at both levels. The second difference occurred for the relationship between Helping/Friendly teacher behavior and the student affective outcome at the class level of analysis. In contrast to the multiple regression results, the HLM analysis showed no significant relationship at the class level between teacher Helping/Friendly behavior and student liking for mathematics. The third difference concerned the negative relationship between teacher Uncertain behavior and student liking for mathematics that was statistically significant in the multiple regression analysis (at the individual student level), but which was not significant in the multilevel analysis. Lastly, the significant negative relationship of teacher Admonishing behavior and student liking for mathematics in the multiple regression analysis (at the individual student level) was not replicated in the HLM analysis.

Generally, findings from the HLM analyses were consistent with the findings of traditional simple, multiple, and canonical correlation analyses. The multilevel analysis suggests that the types of teacher behavior that were associated with student learning are greater Leadership, Helping/Friendly, and Understanding teacher behaviors, and less Uncertain and Dissatisfied teacher behavior. Because these teacher behaviors foster positive student attitudes towards mathematics learning and/or higher achievement scores, it is desirable for elementary mathematics teachers in Singapore to cultivate consciously these positive behaviors and exhibit them more often in their interactions with students, and to refrain from demonstrating negative behaviors (Uncertain and Dissatisfied) in classroom interactions.

Generally, Admonishing and Strict teacher behavior did not seem to influence either student attitudes towards learning of mathematics or student achievement in the HLM analysis. Teachers, thus, need not feel anxious about undesirable side effects associated with being either too strict or not strict enough with students.

Conclusion and Discussion

As one of the first studies in Singapore in the area of classroom learning environment, this research made important contributions in the modification and cross-validation of the Questionnaire on Teacher Interaction (QTI) for assessing teacher-student interpersonal behavior. Data from the administration of these instruments to a random sample of 1,512 students in 39 Grade 5 mathematics classes confirmed that each scale exhibited satisfactory internal consistency reliability (with either the student or the class mean as the unit of analysis), and that each was able to differentiate among the students' perceptions indifferent classrooms.

In order to explore outcome-environment associations in elementary mathematics classrooms, data were subjected to a series of correlational analyses (simple, multiple and canonical correlation) and multilevel (hierarchical linear model) analyses, using two levels of analysis (the student and the class). The results were fairly similar (in both patterns of significance and the direction of relationships) for the different types of statistical analysis. In particular, better achievement and student attitudes were found in classes with more of an emphasis on a teacher's Leadership, Helping/Friendly, and Understanding behaviors, and less so with Uncertain behavior. These findings suggest a way to improve student achievement and attitudes; namely by giving greater emphasis to learning environment aspects correlated positively to outcomes and less emphasis to dimensions negatively correlated with outcomes.

Although the present study predominantly involved the use of quantitative methods, the qualitative methods used in the pilot study formed an important part of the overall study, because they confirmed the readability of questionnaire items, as well as the suitability of the questionnaire's response format and the procedures for questionnaire administration. Moreover, now that the present initial study has used quantitative methods to validate widely applicable instruments for future use, it is highly desirable to combine qualitative and quantitative methods in future research with these instruments, as recommended by Fraser and Tobin (1991). The use of qualitative methods in conjunction with quantitative methods is likely to: increase the confidence in findings that emerge from more than one contrasting method (i.e., methodological triangulation); extend and clarify our understanding of results emerging from the use of quantitative methods by adding meaningful qualitative information; and provide valuable ad ditional information that could expose any limitations of the particular questionnaire chosen, as well as suggest salient aspects that extend the research beyond the scope of the questionnaire. As Tobin and Fraser (1998) said, "We cannot envision why learning environment researchers would opt for either qualitative or quantitative data, and we advocate the use of both in an effort to obtain credible and authentic outcomes" (p. 639).

Before generalizing the present findings, it should be remembered that this research involved a large and representative sample of Grade 5 mathematics students of mixed ability in Singapore. The careful sampling procedures followed mean a high degree of generalizability to other elementary mathematics classes in Singapore. However, because of cultural differences, the results are not necessarily generalizable to students in other countries. Therefore, it would be desirable to replicate and extend the present study by using the new elementary version of the Questionnaire on Teacher Interaction (QTI) with other samples in other countries.

Within the limits of generalizability discussed above, this study has several important practical implications for teachers and classroom practice. First, because the new elementary version of the QTI is economical, readable by elementary school students, and valid and reliable, teachers can use the QTI with confidence for assessing and monitoring their students' perceptions of teacher interpersonal behavior in the classroom. Second, the emphases in teacher interpersonal behavior that are likely to promote student achievement are the same emphases that promote positive student attitudes; therefore, teachers need not choose between promoting student achievement or student attitude when deciding which teacher interpersonal behaviors to emphasize. Third, teachers are likely to enhance both student achievement and attitudes through emphasizing more leadership behavior (providing leadership to the class and holding students' attention), more helping/friendly behavior (being friendly and helpful toward students), more understanding behavior (showing understanding, care, and concern for students), and less uncertain behavior (exhibiting uncertainty).

References

Aldridge, J.M., Fraser, B.J., & Huang, T.-C.I. (1999). Investigating classroom environments in Taiwan and Australia with multiple research methods. Journal of Educational Research, 93, 48-62.

Bock, D. R. (Ed.). (1989). Multilevel analysis of educational data. San Diego, CA: Academic Press.

Brekelmans, M., & Cr[acute{e}]ton, H. (1993). Interpersonal teacher behavior through out the career. In Th. Wubbels & J. Levy (Eds.), Do you know what you look like?: Interpersonal relationships in education (pp. 81-102). London: Falmer Press.

Brekelmans, M., Levy, J., & Rodriguez, R. (1993). A typology of teacher communication style. In Th. Wubbels & J. Levy (Eds.), Do you know what you look like?: Interpersonal relationships in education (46-55). London: Falmer Press.

Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA: Sage.

Bryk, A. S., Raudenbush, S. W., Seltzer, M., & Congdon, R.T. (1989). An introduction to HLM: Computer program and users' guide. Chicago: University of Chicago.

Burden, R., & Fraser, B. J. (1993). Use of classroom environment assessments in school psychology: A British perspective. Psychology in the Schools, 30, 232-240.

Chionh, Y.H., H., & Fraser, B. J (1998, April). Validation and use of the "What Is Happening in This Class" (WIHIC) questionnaire in Singapore. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

Cooley, W. W., & Lohnes, P.R. (1976). Evaluation research in education. New York: Irvington.

Cr[acute{e}]ton, H.A., Wubbels, T., & Hooymayers, H.P. (1993). A systems perspective on classroom communication. In Th. Wubbels & J. Levy (Eds.), Do you know what you look like?: Interpersonal relationships in education (pp. 1-12). London: Falmer Press.

Dorman, J. P., Fraser, B. J., & McRobbie, C. (1997). Classroom environment in Australian catholic and government secondary schools. Curriculum and Teaching, 12(1), 3-14.

Doyle, W. (1979). Making managerial decisions in classrooms. In D. Duke (Ed.), Classroom management (pp. 42-74) (78th Yearbook of the National Society for the Study of Education, Part 2). Chicago: University of Chicago Press.

Ellett, C. D. (1997). Classroom-based assessments of teaching and learning. In J. Stronge (Ed.), Evaluating teaching: A guide to current thinking and best practice (pp. 107-128). Newbury Park, CA: Corwin.

Ferguson, P. D., & Fraser, B. J. (1998). Changes in learning environment during the transition from primary to secondary school. Learning Environments Research, 1, 369-383.

Fisher, D. L., & Fraser, B. J. (1983). A comparison of actual and preferred classroom environments as perceived by science teachers and students. Journal of Research in Science Teaching, 20, 55-61.

Fisher, D. L., Fraser, B. J., & Rickards, T. (1997, March). Gender and cultural differences in teacher-student interpersonal behavior. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

Fisher, D. L., Fraser, B.J., & Wubbels, T. (1993). Interpersonal teacher behavior and school environment. In Th. Wubbels & J. Levy (Eds.), Do you know what you look like?: Interpersonal relationships in education (pp. 103-112). London: Falmer Press.

Fisher, D. L., Henderson, D., & Fraser, B. J. (1995). Interpersonal behaviour in senior high school biology classes. Research in Science Education, 25(2), 125-133.

Fraser, B. J. (1981). Test of science-related attitudes (TOSRA). Melbourne, Australia: Australian Council for Educational Research.

Fraser, B. J. (1986). Classroom environment. London: Croom Helm.

Fraser, B. J. (1993). Incorporating classroom and school environment ideas into teacher education programs. In T. A. Simpson (Ed.), Teacher educators' annual handbook 1993 (pp. 135-152). Brisbane, Australia: Queensland University of Technology.

Fraser, B. J. (1994). Research on classroom and school climate. In D. Gabel (Ed.), Handbook of research on science teaching and learning(pp. 493-541). New York: Macmillan.

Fraser, B. J. (1998a). Science learning environments: Assessments, effects and determinants. In B.J. Fraser & K. G. Tobin (Eds.), International handbook of science education (pp. 527-564). Dordrecht, The Netherlands: Kluwer.

Fraser, B. J. (1998b). Classroom environment instruments: Development, validity and applications. Learning Environments Research, 1(1), 7-33.

Fraser, B. J., & Fisher, D. L. (1982). Predicting students' outcomes from their perceptions of classroom psychosocial environment. American Educational Research Journal, 19, 498-518.

Fraser, B. J., & Fisher, D. L. (1983). Use of actual and preferred classroom environment scales in person environment fit research. Journal of Educational Psychology, 75, 303-313.

Fraser, B. J., & Fisher, D. L. (1986). Using short forms of classroom climate instruments to assess and improve classroom psychosocial environment. Journal of Research in Science Teaching, 23, 287-413.

Fraser, B. J., Giddings, G. J., & McRobbie, C. J. (1995). Evolution and validation of a personal form of an instrument for assessing science laboratory classroom environments. Journal of Research in Science Teaching, 32, 399-422.

Fraser, B. J., & McRobbie, C. J. (1995). Science laboratory classroom environments at schools and universities: A cross-national study. Educational Research and Evaluation: An International Journal on Theory and Practice, 1, 289-3 17.

Fraser, B. J., & Teh, G. (1994). Effect size associated with micro-PROLOG-based computer assisted learning. Computers and Education: An International Journal, 23, 187-196.

Fraser, B. J., & Tobin, K. (1991). Combining qualitative and quantitative methods in classroom environment research. In B. J. Fraser & H. J. Walberg (Eds.), Educational environments: Evaluation, antecedents and consequences (pp. 271-292). Oxford, England: Pergamon.

Fraser, B. J., & Walberg, H. J. (Eds.). (1991). Educational environments: Evaluation, antecedents and consequences. Oxford, England: Pergamon Press.

Fraser, B. J., Walberg, H. J., Welch, W. W., & Hattie, J. A. (1987). Syntheses of educational productivity research [Special issue]. International Journal of Educational Research, 11(2).

Fraser, B. J., Williamson, J. C., & Tobin, K. (1987). Use of classroom and school climate scales in evaluating alternative high schools. Teaching and Teacher Education, 3, 219-231.

Goldstein, H. (1987). Multilevel models in educational and social research. London: Charles Griffin.

Haertel, G. D., Walberg, H. J., & Haertel, E. H. (1981). Socio-psychological environments and learning: A quantitative synthesis. British Educational Research Journal, 7, 27-36.

Keeves, J. P. (1974). Some attitude scales for educational research purposes. Melbourne, Australia: Australian Council for Educational Research.

Khoo, H. S., & Fraser, B. J. (1998, April). Using classroom environment dimensions in the evaluation of adult computer courses. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

Kremer-Hayon, L., & Wubbels, T. (1992). Interpersonal relationships of cooperation teachers and students teachers' satisfaction with supervision. Journal of Classroom Interaction, 27(1), 31-38.

Leary, T. (1957). An interpersonal diagnosis of personality. New York: Ronald Press.

McRobbie, C. J., & Ellett, C. D. (Guest Eds.). (1997). Advances in research on educational learning environments [Special issue]. International Journal of Educational Research, 27(4).

Midgley, C., Eccles, J. S., & Feldlaufer, H. (1991). Classroom environment and the transition to junior high school. In B. J. Fraser & H. J. Walberg (Eds.),Educational environments: Evaluation, antecedents and consequences (pp. 113-140). Oxford, England: Pergamon Press.

Moos, R. H. (1979). Evaluating educational environments: Procedures, measures, findings and policy implications. San Francisco, CA: Jossey-Bass.

Moos, R. H. (1991). Connections between school, work, and family settings. In B. J. Fraser & H. J. Walberg (Eds.), Educational environments: Evaluation, antecedents and consequences (pp. 29-54). Oxford, England: Pergamon Press.

Quek, C. L., Wong, A., & Fraser, B. J. (1998, April). Teacher-student interactions among gifted chemistry students in Singapore secondary schools. Paper presented at the annual meeting of the National Association for Research in Science Teaching, San Diego, CA.

Raudenbush, S. W. (1988). Educational applications of hierarchical linear models: A review. Journal of Educational Statistics. 13(2), 85-116.

Taylor, P. C., Fraser, B. J., & Fisher, D. L. (1997). Monitoring constructivist classroom learning environments. International Journal of Educational Research, 27, 293-302.

Teh, G., & Fraser, B. J. (1994). An evaluation of computer-assisted learning in terms of achievement, attitudes and classroom environment. Evaluation and Research in Education, 8, 147-161.

Thorp, E., Burden, R., & Fraser, B. J. (1994). Assessing and improving classroom environment. School Science Review, 75, 107-113.

Tobin, K, & Fraser, B. J. (1998). Qualitative and quantitative landscapes of classroom learning environments. In B. J. Fraser & K. G. Tobin (Eds.), International handbook of science education (pp. 623-640). Dordrecht, The Netherlands: Kluwer.

Trickett, E. J. (1978). Toward a social-ecological conception of adolescent socialization: Normative data on contrasting types of public school classrooms. Child Development, 49, 408-414.

Trickett, E. J, Trickett, P. K., Castro, J. J., & Schaffner, P. (1982). The independent school experience: Aspects of normative environments of single sex and coed schools. Journal of Educational Psychology, 74, 374-381.

Watzlawick, P., Beavin, J. H. & Jackson, D. (1967). The pragmatics of human communication. New York: Norton.

Wong, A., & Fraser, B. (1996). Environment-attitude associations in the chemistry laboratory classroom. Research in Science & Technological Education, 14, 91-102.

Wong, A. F. L., & Fraser, B. J. (1997). Assessment of chemistry laboratory classroom environments. Asia Pacific Journal of Education, 17(2), 41-62.

Wong, A. F. L., Young, D. J., & Fraser, B. J. (1997). A multilevel analysis of learning environments and student attitudes. Educational Psychology, 17, 449-468.

Wubbels, T. (1993). Teacher-student relationships in science and mathematics classes. In B. J. Fraser (Ed.), Research implications for science and mathematics teachers, Volume 1 (pp. 65-73) (Key Centre Monograph No. 5). Perth, Australia: Curtin University of Technology.

Wubbels, T., & Brekelmans, M. (1998). The teacher factor in the social climate of the classroom. In B. J. Fraser & K.G. Tobin (Eds.), International handbook of science education (pp. 565-580). Dordrecht, The Netherlands: Kluwer.

Wubbels, T., Brekelmans, M., & Hooymayers, H. P. (1991). Interpersonal teacher behavior in the classroom. In B. J. Fraser & H. J. Walberg (Eds.), Educational environments: Evaluation, antecedents and consequences (pp. 141-160). Oxford, England: Pergamon Press.

Wubbels, T., Cr[acute{e}]ton, H. A., & Holvast, A. (1988). Undesirable classroom situations: A systems communication perspective. Interchange, 19(2), 25-42.

Wubbels, T., Cr[acute{e}]ton, H. A., Levy, J., & Hooymayers, H.P. (1993). The model for interpersonal teacher behavior. In T. Wubbels & J. Levy (Eds.), Do you know what you look like?: Interpersonal relationships in education (pp. 13-28). London: Falmer Press.

Wubbels, T., & Levy, J. (1991). A comparison of interpersonal behavior of Dutch and American teachers. International Journal of Intercultural Relations, 15, 1-18.

Wubbels, T. & Levy, J. (Eds.) (1993). Do you know what you look like?: Interpersonal relationships in education. London: Falmer Press.

Yarrow, A., Millwater, J., & Fraser, B. (1997). Improving university and primary school classroom environments through preservice teachers' action research. International Journal of Practical Experience in Professional Development, 1(1), 68-93.

Young, D. J., & Fraser, B. J. (1993). Socioeconomic and gender effects on science achievement: An Australian perspective. School Effectiveness and School Improvement, 4, 265-289.

APPENDIX A

Questionnaire on Teacher Interaction (QTI) (Elementary)

Directions: This questionnaire is not a test. We want to know your opinion about how your teacher works with you. We want you to answer honestly. Read each sentence carefully. Show your opinion about your teacher by circling one of the following:

1 if you think that your teacher behaves this way SELDOMLY

2 if you think that your teacher behaves this way SOMETIMES

3 if you think that your teacher behaves this way MOST OF THE TIME

Please answer all questions. If you want to change an answer, just cross it out and circle another answer.

1. We all listen to this teacher.

2. This teacher is friendly.

3. This teacher trusts us.

4. This teacher allows us to work on things that we like.

5. This teacher doesn't seem sure.

6. This teacher is unhappy.

7. This teacher gets angry quickly.

8. This teacher makes us work hard.

9. We learn a lot from this teacher.

10. This teacher likes to laugh.

11. This teacher knows when we do not understand.

12. We can decide some things in this teacher's class.

13. This teacher is not sure of himself/herself.

14. This teacher is bad-tempered.

15. This teacher looks down on us.

16. We have to be quiet in this teacher's class.

17. This teacher gets our attention.

18. This teacher's class is pleasant.

19. This teacher is willing to explain things again if we don't understand.

20. This teacher gives us a lot of free time in class.

21. This teacher is shy.

22. This teacher thinks that we can't do things well.

23. This teacher makes fun of us.

24. This teacher's tests are hard.

25. This teacher knows everything that goes on in this classroom.

26. We like this teacher.

27. This teacher takes notice of what we say.

28. This teacher allows us to choose who we work with.

29. This teacher is not sure what to do when we fool around.

30. This teacher thinks we cheat.

31. This teacher shouts at us.

32. This teacher is strict when marking our work.

33. This teacher explains things clearly.

34. This teacher helps us with our work.

35. This teacher knows how we feel.

36. This teacher allows us to fool around in class.

37. This teacher allows us to tell him/her what to do.

38. This teacher thinks that we know nothing.

39. It is easy to make this teacher angry.

40. We are afraid of this teacher.

41. This teacher is sure about what he/she wants to take place in the classroom.

42. This teacher cares about us.

43. This teacher listens to us.

44. This teacher allows us to choose what we want to work on.

45. This teacher acts as if he/she does not know what to do.

46. This teacher says that he/she will punish us.

47. This teacher has a bad temper.

48. This teacher is strict.

Items are arranged in cyclic order so that the first, second, third, fourth, fifth, sixth, seventh, and eighth item in each group of eight items assesses, respectively, Leadership, Helping I Friendly, Understanding Student Responsibility/Freedom, Uncertain, Dissatisfied, Admonishing, and Strict behaviors. Items are scored 1, 2, and 3, respectively, for the responses Seldom, Sometimes, and Most of the Time. Omitted or invalid items are scored 2.
Gale Copyright:
Copyright 2000 Gale, Cengage Learning. All rights reserved.