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Associations between teacher-student interpersonal behaviour and student attitudes in mathematics classes

Darrell Fisher and Tony Rickards
Curtin University


Most mathematics teachers believe that good relationships with their students are important. But are the students' perceptions of teacher-student interpersonal behaviour the same as their teachers? Is there a difference in mathematics teachers' perceptions of their actual teacher-student interpersonal behaviour in the classroom and what they perceive to be ideal? What associations are there between student attitudes and teacher-student interpersonal behaviour in the mathematics classroom?

The purposes of this paper are to outline a convenient questionnaire designed to assess teacher-student interpersonal behaviour and to report its use in answering such questions as these. The paper describes various forms of the Questionnaire on Teacher Interaction (QTI) and reports its use in past research. Associations between QTI scales and students attitudinal outcomes in mathematics classrooms are made. Finally, the paper describes how mathematics teachers have used the questionnaire to assess perceptions of their own teacher-student interpersonal behaviour and used this as a basis for reflecting on their own teaching.

The questionnaire on teacher interaction

International research efforts involving the conceptualisation, assessment and investigation of perceptions of psychosocial aspects of the classroom environment have firmly established classroom environment as a thriving field of study (Fraser, 1994; Fraser & Walberg, 1991). Recent classroom environment research has focused on science laboratory classroom environments (McRobbie & Fraser, 1993), constructivist classroom environments (Taylor, Dawson & Fraser, 1995) and computer-assisted instruction classrooms (Teh & Fraser, 1994).

Recently, a team of researchers in The Netherlands extended this research by focusing specifically on the interpersonal relationships between teachers and their students as assessed by the QTI (Wubbels, Crèton & Hoomayers, 1992; Wubbels & Levy, 1993). The Dutch researchers (Wubbels, Crèton & Holvast, 1988) investigated teacher behaviour in a classroom from a systems perspective, adapting a theory on communications processes developed by Waltzlawick, Beavin and Jackson (1967). Within the systems perspective of communication, it is assumed that the behaviours of participants mutually influence each other. The behaviour of the teacher is influenced by the behaviour of the students and in turn influences the student behaviour. Thus, a circular communication process develops which not only consists of behaviour, but determines behaviour as well.

With the systems perspective in mind, Wubbels, Crèton and Hooymayers (1985) developed a model to map interpersonal teacher behaviour using an adaptation of the work of Leary (1957). In the adaptation of the Leary model, teacher behaviour is mapped with a Proximity dimension (Cooperation, C - Opposition, O) and an Influence dimension (Dominance, D, - Submission, S) to form eight sectors, each describing different behaviour aspects: Leadership, Helpful/Friendly, Understanding, Student Responsibility and Freedom, Uncertain, Dissatisfied, Admonishing and Strict behaviour. Figure 1 shows typical behaviours for each sector. The Questionnaire on Teacher Interaction (QTI) is based on this model.


Figure 1: The model for interpersonal teacher behaviour

The items of the QTI belong to eight scales, each consisting of six items and corresponding to one of the eight sections in the model. Examples of items are "This teacher is friendly"(Helping/Friendly) and "This teacher gets angry unexpectedly"(Admonishing). The scores for each item within the same sector are added to obtain a total scale score. The higher the scale score the more a teacher shows behaviours from that sector. Scale scores can be obtained for individual students, or can be combined to form the mean of all students in a class.

An Australian version of the QTI

The original version of the QTI developed in the early 1980s in The Netherlands had 77 items (Wubbels, Crèton, & Hooymayers, 1985). Later, an American version of the QTI was developed which had 64 items (Wubbels & Levy, 1991). The Australian version of the QTI described in this paper, is more economical and has 48 items which are answered using a five-point response scale. This version of the QTI is available for use by mathematics teachers to gather their own perceptions and the perceptions of their students about their mathematics classrooms. A complete copy of this Australian student version of the QTI, in a form that may be reproduced by mathematics teachers for use in their own classrooms, is available from the authors.

One advantage of the QTI is that it can be used to obtain the perceptions of interpersonal behaviour of either students or teachers. When the QTI is administered to both mathematics teachers and their students, information is provided about the perceptions of teachers and the perceptions of their students of the interpersonal behaviour of that teacher. The information obtained by means of the questionnaire includes perceptions of the behaviour of the teacher towards the students as a class, and reflects relatively stable patterns of behaviour over a considerable period. Similarly, teachers can be asked for their perceptions of their own behaviour or the behaviour that they consider to be ideal. The wording of the questionnaire is varied slightly when used to obtain teachers' self-perceptions and ideals. For example the question "This teacher talks enthusiastically about his/her subject", becomes "I talk enthusiastically about my subject" in the teacher self-perception version, and "This teacher would talk enthusiastically about his/her subject" in the teacher ideal version. These latter two versions are also available from the authors.

By using these three separate forms of the QTI it is possible to collect data on students' perceptions of teacher-student interpersonal behaviour, teachers' perceptions of their actual teacher-student interpersonal behaviour in the classroom and what they perceive to be ideal? These three sets of data can be represented graphically for ease of analysis by participants. For example, Figure 2 depicts the information that was provided to two mathematics teachers and visually indicates differences between the teachers' self perceptions, perceptions of an ideal teacher and how they are perceived by their students.

Past uses of the QTI

The QTI has been shown to be a valid and reliable instrument when used in The Netherlands (Wubbels & Levy, 1993). When the 64-item USA version of the QTI was used with 1,606 students and 66 teachers in the USA, the cross-cultural validity and usefulness of the QTI were confirmed. Using the Cronbach alpha coefficient, Wubbels and Levy (1991) reported acceptable internal consistency reliabilities for the QTI scales ranging from 0.76 to 0.84 for student responses and from 0.74 to 0. 84 for teacher responses.

Wubbels (1993) used the QTI with a sample of 792 students and 46 teachers in Western Australia and Tasmania. The results of this study were similar to previous Dutch and American research in that, generally, teachers did not reach their ideal and differed from the best teachers as perceived by students. It is noteworthy that the best teachers, according to students, are stronger leaders, more friendly and understanding, and less uncertain, dissatisfied and admonishing than teachers on average.

When teachers described their perceptions of their own behaviours, they tended to see it a little more favourably than did their students. On average, the teachers' perceptions were between the students' perceptions of actual behaviour and the teachers' ideal behaviour. An interpretation of this is that teachers think that they behave closer to their ideal than their students think that they do.

Another use of the QTI in The Netherlands involved investigation of relationships between perceptions on the QTI scales and student outcomes (Wubbels, Brekelmans & Hooymayers, 1991). Regarding students' cognitive outcomes, the more that teachers demonstrated strict, leadership and helpful/friendly behaviour, then the higher were cognitive outcomes scores. Conversely, student responsibility and freedom, uncertain and dissatisfied behaviours were related negatively to achievement.

Variations in the students' appreciation of the subject and the lessons have been characterised on the basis of the proximity dimension: the more cooperative the behaviour displayed, the higher the affective outcome scores (Wubbels, Brekelmans & Hooymayers, 1991). That is, student responsibility and freedom, understanding, helpful/friendly and leadership behaviours were related positively to student attitudes. Uncertain, dissatisfied, admonishing and strict behaviours were related negatively to student attitudes. Overall, previous studies have indicated that interpersonal teacher behaviour is an important aspect of the learning environment and that it is related strongly to student outcomes.

Levy, Crèton and Wubbels (1993) analysed data from studies in The Netherlands, the USA and Australia involving students being asked to use the QTI to rate their best and worst teachers. Students rated their best teachers as being strong leaders and as friendly and understanding. The characteristics of the worst teachers were that they were more admonishing and dissatisfied. In a further investigation into the characteristics of teachers, Wubbels and Levy (1991) compared Dutch and American teachers and found very few differences, although American teachers were perceived as stricter and Dutch teachers as giving their students more responsibility and freedom.

The QTI also has been used to develop typologies of teacher interpersonal behaviour in The Netherlands (Wubbels, Brekelmans, Crèton & Hooymayers, 1990). Using cluster analysis, eight types were distinguished. The behavioural patterns on the eight teacher types were characterised as directive, authoritative, tolerant/authoritative, tolerant, uncertain/tolerant, uncertain/aggressive, repressive, and drudging. Teacher types associated with the greatest student cognitive and affective gains were directive (characterised by a well structured task oriented learning environment) and tolerant/authoritative (characterised by a pleasant well structured environment in which the teacher has a good relationship with students). Uncertain/aggressive (characterised by an aggressive kind of disorder) and uncertain/tolerant teacher types were associated with the lowest student gains.

Australian applications of the QTI

In one of the first uses of the QTI in Australia (Fisher, Fraser & Wubbels, 1993), associations were investigated between teachers' perceptions of their work environment, using the School Level Environment Questionnaire (SLEQ), and students' and teachers' perceptions of their classroom interactions (Fisher & Fraser, 1990) . Results from this study indicated that relationships between SLEQ and QTI scores generally were weak, thus suggesting that teachers believed that they had considerable freedom to shape their own classrooms regardless of their school environment.

Recently, a team of researchers in Australia completed the first use of the 48 item QTI in senior biology classes with a sample of 489 students in 28 biology classes (Fisher, Henderson & Fraser, 1995). Although past studies have examined associations between student perceptions of the learning environment mostly in science classes and student outcomes, this Australian study was unique in that it examined student outcomes in three distinct areas, student attitude, achievement in a written examination, and performance on practical tests. This study confirmed the validity and reliability of the QTI when used in senior secondary biology classes. The alpha reliability figures for the different QTI scales ranged from 0.63 to 0.83 when the individual student was used as the unit of analysis and from 0.74 to 0.95 when the class mean was used (Fisher, Henderson & Fraser, 1995). Generally, the dimensions of the QTI were found to be associated significantly with student attitude scores. In particular, students' attitude scores were higher in classrooms in which students perceived greater leadership, helpful/friendly, and understanding in their teachers' interpersonal behaviours. Conversely, students' attitude scores were lower in classrooms in which students perceived greater uncertainty, dissatisfaction, admonishing, and strictness in their teachers' interpersonal behaviours. It was concluded that, if biology teachers want to promote favourable student attitudes in their class and laboratory work, they should ensure the presence of these interpersonal behaviours.

Methodology

This study is distinctive in that it is centred on students in mathematics classes, whereas previous research using the QTI has focused largely on students in science classes. The study involved students in grades 8, 9 and 10 mathematics classes in Australia and was composed of 405 students in 9 schools with their 21 teachers.

Associations between students' perceptions of their interpersonal relationships with their teachers and their attitudinal outcomes were examined in this study. The 48-item version of the QTI (Wubbels, 1993) was used to gauge students' perceptions of student-teacher interpersonal behaviour and student attitudes were assessed with a seven-item Attitude To This Class scale, which was based on the the Test of Science-Related Attitudes [TOSRA] (Fraser, 1981).

Using the scales of the QTI as independent variables, associations were computed with attitude to the class. Simple correlations were calculated between each QTI scale and each student attitude. Also a multiple regression analysis, involving the whole set of QTI scales, was conducted to provide a more conservative test of the association between each QTI scale and attitude when all other QTI scales were mutually controlled.

Results

Validity of the QTI

Table 1 provides some cross-validation information for the QTI when used specifically in the present sample of mathematics classes. Statistics are reported for two units of analysis, namely, the student's score and the class mean score. As expected, reliabilities for class means were higher than those where the individual student was used as the unit of analysis. Table 1 shows that the alpha reliability figures for different QTI scales ranged from 0.62 to 0.88 when the individual student was used as the unit of analysis, and from 0.60 to 0.96 when th e class mean was used as the unit of analysis. The values presented in Table 1 for the present sample provide further cross-validation information supporting the internal consistency of the QTI, with either the individual student or the class mean as the unit of analysis.

Another desirable characteristic of any instrument like the QTI is that it is capable of differentiating between the perceptions of students in different classrooms. That is, students within the same class should perceive it relatively similarly, while mean within-class perceptions should vary from class to class. This characteristic was explored in mathematics classrooms for each scale of the QTI using one-way ANOVA, with class membership as the main effect. It was found that each QTI scale differentiated significantly (p<.001) between classes and that the eta2 statistic, representing the proportion of variance explained by class membership, ranged from 0.14 to 0.43 for different classes.

Table 1: Internal consistency (Cronbach Alpha Coefficient) and
ability to differentiate between classrooms of the QTI
Scale Alpha ReliabilityANOVA results
eta2
StudentClass
DC Leadership 0.860.930.43*
CD Helping/friendly 0.880.940.29*
CS Understanding 0.880.960.36*
SC Student responsibility/ freedom 0.690.790.23*
SO Uncertain 0.780.870.29*
OS Dissatisfied 0.830.910.28*
OD Admonishing 0.840.890.36*
DO Strict 0.620.600.14*
* p < .001

Associations between interpersonal teacher behaviour and student outcomes

Table 2 reports the results for associations between students' perceptions of teacher-student interpersonal behaviour and students' attitudinal outcomes when the data were analysed using both simple and multiple correlations. Whereas the simple correlation (r) describes the bivariate association between attitudinal outcome and a QTI scale, the standardised regression weight (beta) characterises the association between attitudinal outcome and a particular QTI scale when all other QTI dimensions are controlled.

Table 2: Associations between QTI Scales and Students' Attitudinal Outcomes in
terms of Simple Correlations (r) and Standardised Regression Coefficients (beta)
QTI scale Strength of Environment - Outcome association
Attitude to class
rbeta
Leadership 0.53**0.24**
Helpful/friendly 0.64**0.19*
Understanding 0.61**0.13
Student responsibility/freedom 0.15**0.07
Uncertain -0.35**0.07
Dissatisfied -0.58**-0.15*
Admonishing -0.54**-0.06
Strict -0.40**-0.18**
Multiple correlation, R 0.71**
* p < .05 ** p < .01 n = 405

An examination of the simple correlation (r) figures in Table 2 indicates that there were eight significant relationships (p<.05), out of eight possible, between student-teacher interactions and the student attitudinal outcome; this is 20 times that expected by chance alone. An examination of the beta weights reveals four out of eight significant relationships (p<.05), which is ten times that expected by chance alone.

The simple correlation (r) figures indicate statistically significant associations between the students' attitude to class and all QTI scales. The beta weights show that some of these associations retain their significance in a more conservative test with all other QTI scales controlled. In classes where the students perceived greater leadership and helpful/friendly behaviours in their teachers, there was a more favorable attitude towards the class. The converse was true when the teacher was perceived as strict and dissatisfied.

Teachers use of the QTI

A number of mathematics teachers have used the QTI as a basis for self-reflection. The process begins with the teacher completing the two teacher versions of the QTI which ask the teacher to rate how they see themselves and how they see their ideal teacher. The teacher self questionnaire asks the teacher to respond to questions about their perceptions of the actual classroom environment as they perceive it. The teacher ideal questionnaire asks the teacher to respond to questions that refer to an ideal teacher in their classroom environment. By completing these two questionnaires, the teacher is able to provide details about interpersonal behaviour in their actual classroom environment as well as their ideal classroom environment. The students of that teachers' class are asked to complete the student version of the QTI.

Once the three versions of the QTI have been completed the totals for each scale for each version can be calculated, together with the mean for student perceptions. The results then can be plotted onto sector profiles similar to those shown in Figure 2. The authors are able to assist in this process. Thus, a profile of classroom interpersonal teacher-student behaviours for a particular teacher can be produced.

The scores for the teachers' perception of their ideal teacher, how they see themselves, and the mean scores for how their students see them are presented on the same page for ease of comparison. Although the results for teacher and student responses to the questionnaire could be shown in tabular form the graphical presentation is considered more useful and easier to interpret by teachers and results can readily be compared to the model for interpersonal teacher behaviour. For example, Figure 2 depicts the profiles recently provided by the authors to two mathematics teachers who participated in a recent data collection.

The sector profile diagrams of Teacher 1 suggest that this teacher perceives herself as being close to her ideal teacher in all sections of the model of interpersonal behaviour. The students perceive this teacher to have a greater level of understanding than she believes. Furthermore, the teacher perceives much more uncertainty in her own behaviour than do her students.

The second teacher's sector profiles suggest his ideal teacher would exhibit greater leadership behaviour than he perceives he demonstrates. The students have a different perception of the classroom interpersonal behaviour to that of their teacher. They perceive less Helping/Friendly and Understanding behaviours and more Admonishing behaviour.

Both teache rs could use the data provided by the sector profile diagrams to reflect on their classroom behaviours and use the results as a basis for modifying their behaviour when interacting with students. For example, Teacher 2 may decide to exhibit more leadership behaviour in the classroom whilst trying to be more cooperative with students and give them more assistance while they are working.

After having completed the questionnaire and having had time to consider the profiles, mathematics teachers reported that the results had stimulated them to reflect on their own teaching. For example, the results from the QTI led one teacher to comment on verbal communication in her classroom. Based upon her sector profile diagrams, she concluded that she had become more aware of the students' needs for clear communication. This subsequently became a focus for her in improving her classroom environment and her teaching.

Conclusions

This study confirmed the reliability and validity of the QTI when used in mathematics classes. Generally, the dimensions of the QTI were found to be significantly associated with student attitude scores. In particular, students' attitude scores were higher in classrooms in which students perceived greater leadership and helpful/friendly behaviours in their teachers' interpersonal behaviours. If mathematics teachers want to promote favorable student attitudes to their class, they should ensure the presence of these interpersonal behaviours. Conversely students' attitude scores were lower in classrooms in which students perceived greater dissatisfaction and strictness in their teachers' interpersonal behaviours.

The three versions of the QTI allow mathematics teachers to obtain their students' perceptions of their interpersonal behaviour, their own perceptions and the behaviour that they consider to be ideal. This valuable information then can be used as a basis for self-reflection by teachers on their teaching performance. Based on this information, teachers might decide to change the way they behave in an attempt to create a more desirable classroom environment.

Sector profiles could be used when considering staff development activities as they provide individual mathematics teachers with information about their actual and preferred classroom environments. This information can be used to identify areas for personal development in specific classroom environments. The sector diagrams also could be used as a basis for discussion of teaching behaviours. For example, mathematics teachers wanting to improve their leadership behaviours could organise professional development activities accordingly.

Mathematics teachers can make use of the QTI to monitor students' views of their classes, investigate the impact that different interpersonal behaviours have on student outcomes, and provide a basis for guiding systematic attempts to improve this aspect of their teaching. Furthermore, the QTI could be used in assessing changes that result from the introduction of new curricula or teaching methods, and in checking whether the mathematics teacher's interpersonal behaviour is seen differently by students of different genders, abilities or ethnic backgrounds.

References

Fisher, D. L., & Fraser, B. J. (1990). SLEQ: School level Environment Questionnaire. Set: Research Information for Teachers, Item 5. Melbourne: Australian Council for Educational Research.

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

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

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

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

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

Levy, J., Crèton, H., & Wubbels, T. (1993). Perceptions of interpersonal teacher behaviour. In T. Wubbels, & J. Levy, (Eds.), Do you know what you look like? Interpersonal relationships in education, (pp. 29-45). London: The Falmer Press.

McRobbie, C. J., & Fraser, B. J. (1993). Associations between student outcomes and psychosocial mathematics laboratory environments. Journal of Educational Research, 87, 78-85.

Taylor, P. C., Dawson, V., & Fraser, B. J. (1995, April). CLES: An instrument for monitoring the development of constructivist learning environments. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.

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.

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

Wubbels, T. (1993). Teacher-student relationships in mathematics and mathematics classes(What research says to the mathematics and mathematics teacher, No. 11). Perth: National Key Centre for School Mathematics and Mathematics, Curtin University of Technology.

Wubbels, T., Brekelmans, M., Crèton, H., & Hooymayers, H. (1990). Teacher behavior style and learning environment. In H. C. Waxman, & C. D. Ellett (Eds.), The study of learning environments, Vol.4 (pp. 1-12). Houston, TX: University of Houston.

Wubbels, T., Brekelmans, M., and Hooymayers, H. (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., Crèton, H. A., & Holvast, A. J. (1988). Undesirable classroom situations. Interchange, 19,(2), 25-40.

Wubbels, T., Crèton, H. A., & Hooymayers, H. P. (1985, March-April). Discipline problems of beginning teachers, interactional teacher behaviour mapped out. Paper presented at annual meeting American Education Research Association, Chicago, IL.

Wubbels, T., Crèton, H. A., & Hooymayers, H. P. (1992). Review of research on teacher communication styles with use of the Leary model. Journal of Classroom Interaction, 27, 1-12.

Wubbels, T. & Levy, J. (1991). A comparison of interpersonal behaviour 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, England: Falmer Press.

Authors: Darrell Fisher and Tony Rickards, Curtin University
erickards@cc.curtin.edu.au

Please cite as: Fisher, D. and Rickards, A. (1996). Associations betweenteacher-student interpersonal behaviour and student attitudes in mathematicsclasses. Proceedings Western Australian Institute for Educational Research Forum 1996. http://www.waier.org.au/forums/1996/fisher.html


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