THE EFFECTS OF CLASSROOM PROCESSES ON STUDENT ATTITUDES AND MATHEMATICS ACHIEVEMENT Sid Bourke & Max Smith Faculty of Education University of Newcastle ABSTRACT This paper focuses on the effects of classroom processes on senior secondary student quality of school life (Ainley, 1986), self ratings of ability (Bourke & Smith, 1995) and mathematics achievement. The processes of interest include instructional delivery systems, and a wide range of student and teacher behaviours, roles and instructional activities (Bourke & Smith, 1993). School, teacher and student questionnaires and lesson observations were used to gather appropriate information about 327 Year 11 students in 28 mathematics classes at 16 schools. A three-level, two-stage model including school, class and student variables was developed and tested. The model proposed that school and student background variables would affect classroom structures, teaching practices and class activities, which would in turn affect student attitudes to school and their own ability and student achievement. Previous achievement in the School Certificate at the end of Year 10 was also included in the model as an explanatory variable and teacher assessment of student mathematics achievement in Year 11 was an outcome or response variable. Relationships in the model are described and discussed. ______________________________ Paper presented at the Joint Conference of the Australian Association for Research in Education and the Singapore Educational Research Association, Singapore, November 1996. (Available on the AARE Homepage http://www.swin.edu.au/aare/confpap.htm) Authors' e-mail contact address: edsfb@cc.newcastle.edu.au THE EFFECTS OF CLASSROOM PROCESSES ON STUDENT ATTITUDES AND MATHEMATICS ACHIEVEMENT INTRODUCTION It is well known that teachers teach in many different ways. Variations in approaches to teaching result from many different sources, both between teachers and for the individual teacher from time to time (Anderson & Burns, 1989, pp.343-354. School factors may also be important for teaching. Among differences between teachers the approach varies with the ages of the students involved, teacher knowledge, experience and personality, individual teacher preferences and beliefs about the nature of education and pedagogy, and subject taught. Among sources of differences in approach from time-to-time for individual teachers are the ability level and other characteristics of classes, year level, time of year and time of day, and the varying goals for particular lessons or lesson segments, particular classroom contexts including pressures to get through a program of study. Recent work by Bourke and Smith (1993) focussed on differences between subjects taught and teaching practices in the upper secondary school. The subjects investigated were English, Mathematics and Social Science being taught to Year 11 students by 71 teachers in 26 schools in the Hunter Region of New South Wales, Australia. Of these 71 teachers, 24 taught English, 28 taught Mathematics and 19 taught a Social Science. The study collected data using questionnaires completed by students and teachers which focussed on perceptions of their workload, satisfaction and stress levels (Smith & Bourke, 1992), and the observation of lessons to determine their teaching contexts and practices over a range of five lessons for each teacher. The observations included minute-by-minute coding of activities, summaries of lesson segment purposes and practices, and lesson summary information of student and teacher behaviours. Bourke and Smith recognised that teachers used a variety of modes or patterns of delivery, but were interested in testing whether individual teachers generally had a dominant teaching mode which could be identified. The second aim was to determine whether different dominant teaching patterns could be identified for teachers of different subjects in Year 11 classes. Four basic categories of instructional orientation were identified, with most teachers using various combinations of the categories at some time during the observed lessons. When these four instructional orientations were crossed with the frequencies of seven modes of delivery identified, and then related to the frequency of introduction of new concepts and use of direct/indirect instruction methods in lessons, distinct modes of teaching on three of the four categories could be identified. Also, the approaches used by the Mathematics teachers differed from those of the English and Social Science teachers, which were very similar (Bourke & Smith, 1993, pp.7-8). In contrast to the other teachers, the Mathematics teachers were very high on use of the guided practice model, were high on class control, and were low on conceptual change. Use of the presentational model was variable for all teachers and there was no difference between subjects in this model. The distinct differences found for Mathematics teaching were most important when the subject taught was included as a dichotomous independent variable in a multivariate model incorporating student background, achievement measures and opinion, teacher and class characteristics and specific classroom practices and attitudes, and school characteristics as independent variables with general approach to teaching as the dependent variable. At intermediate stages in the model, subject taught was also important for observed classroom practices and teacher stress. It is the combination of the differences found for mathematics teaching with respect to approaches to teaching, classroom practices and teacher stress compared with the other subjects that has prompted the further investigation of mathematics lessons reported here. THE PRESENT STUDY The study of mathematics teaching and lessons in Year 11 classes reported here was based on the questionnaire responses and lesson observations of 327 students and their 28 mathematics teachers in 16 government schools across the Hunter Region of New South Wales, Australia. This was part of a larger study of 71 teachers discussed above (Bourke & Smith, 1993). The three variables of particular interest were student satisfaction with their achievement at school, student satisfaction with their relationships with teachers, and student achievement in mathematics. Student satisfaction with their achievement and teacher relationships are two of the scales of the secondary student quality of school life (QSL) questionnaire (Ainley, Reed and Miller, 1986) which is briefly described below. Each student's most recent Year 11 mathematics assessment was used as the measure of student achievement. The objective was to explain variation in student satisfaction with achievement and in actual achievement by variations in teaching practices and class activities. THE OUTCOME MEASURES The two attitudinal measures and one achievement measure used as outcomes in this investigation are now described. Student attitude to achievement and student actual achievement measures were developed to focus directly on Year 11 achievement by taking into consideration previous Year 10 achievement for individual students, as described below. The other attitudinal measure, student satisfaction with their relationships with teachers, was simply taken as the assessment made of this construct in mid-year, without any prior moderation as there was none directly available. Although the bulk of this report focuses on mathematics classes only, satisfaction with relationships with teachers is a more general measure for which students would have included their attitudes to other teachers as well as mathematics teachers in their responses. Student Attitudes to Achievement and Teachers There are seven dimensions of QSL which are divided into two groups: two general scales and five specific scales. The general scales are General Satisfaction and Negative Affect, and the specific scales concern relationships with teachers, a measure of future oriented opportunity, satisfaction with achievement, status within the school community and identity through knowledge of oneself. Student satisfaction with their achievement was previously found to be a significantly explanatory variable for variations in both General Satisfaction and Negative Affect for all 71 classes involved in this study (Bourke & Smith, 1995, p.7). The effect of student, teacher and class variables on the various QSL measures for these classes may be found in the same paper. The most important student variables for QSL were prior achievement, a sense of efficacy, satisfaction with recent assessments, stress levels, and gender. The important teacher variables were the amount of time spent teaching Year 11 classes, the amount of facilitation of learning, their administrative workload and their satisfaction with school administration. The only class variable found to be important for QSL was a collective commitment to learning (Bourke & Smith, 1995, p.12). Only the QSL scales assessing student satisfaction with their achievement and satisfaction with their relationships with teachers have been used as bases of measures of student attitude used in this paper, as described below. School Certificate achievement in English and Mathematics and level of mathematics studied were used to predict student satisfaction with achievement in Year 11. The predicted score was subtracted from the actual measure of student satisfaction with achievement to provide a residual attitude score for each student. The residual attitude scores had a mean of zero, a standard deviation of 0.44 and ranged from -1.64 to +1.22. Further details of this process are provided below when the development of a mathematics achievement measure is described. The QSL teacher scale was simply taken as the measure of satisfaction with their relationships with teachers because there was no prior measure of this variable for these students. The original four-point scale had a mean of 2.89, a standard deviation of 0.54 and the actual range was from 1.00 to 4.00. Mathematics Achievement It was considered necessary to recognise that, given the sequential nature of secondary mathematics syllabuses and perhaps the nature of the subject itself, the level of each student's mathematics achievement in Year 11 would be strongly dependent on individual mathematics achievement prior to Year 11. Consequently an estimate of mathematics learning which had taken place in Year 11, or additional mathematics learning, was developed for use as the dependent variable when relationships of achievement with classroom processes were considered. The estimate was developed by obtaining a residual mathematics score for Year 11 achievement, as is now described. First, Year 11 achievement was regressed on two variables: the mathematics score in the School Certificate at the end of Year 10 and the level of mathematics studied in Year 10. This produced for each student an expected Year 11 score based on their performance in Year 10 mathematics. The expected score was then subtracted from the actual Year 11 mathematics score obtained to give the remainder, which could be either positive or negative for each student depending on whether the student had done better or worse than expected compared with the performance of the other 326 students in the study. The residual scores thus obtained formed a distribution which had a mean of zero, a standard deviation of 15.4 and a range from approximately -50 to +38. This variable was used as the Year 11 achievement measure in this study. INITIAL DETERMINATION OF VARIANCE COMPONENTS BETWEEN SCHOOLS, CLASSES AND STUDENTS The analyses undertaken initially were to determine the relative proportions of variance which could be attributed to differences between schools, between classes and between individual students. This was done through the use of simple variance components models (Rasbash & Woodhouse, 1995) undertaken separately for the attitudinal and achievement variables. The outcome variable was entered in a regression equation as the response (or dependent) variable with the constant term only and without the addition of substantive explanatory (or independent) variables. For student attitude to their achievement, it was found that between-school and between-class variances were negligible (that is, too small to be estimated) and all the variance was attributable to between-student differences. For satisfaction with teacher relationships, between-school differences were again negligible, between-class differences accounted for 17.6 per cent of the total variance, and the remaining 82.4 per cent of the variance was accounted for by between-student differences. For mathematics achievement, any variance attributable to between-school variance was negligible, between-class differences accounted for 13.6 per cent of the variance and between-student differences accounted for the remaining 86.4 per cent of the total variance. The lack of between-school variance was discussed by Bourke and Smith (1995, p.12) in relation to the likely sameness of Hunter Region government schools and the relative precision of the multilevel analyses used. Explanation of the differences in teaching and class activities presumably related to the between-class variances and, to a lesser extent, the between-student variances found. Investigation of these relationships is the object of the final analyses reported in this paper. EXPLANATORY VARIABLES FOR ATTITUDE & ACHIEVEMENT As discussed above, it would seem that school variables were not related to student attitude and achievement during Year 11. Variables which were considered likely to provide some explanation of student attitude and achievement could then be grouped into two categories, those related to students and those related to teaching activities and class practices. The multilevel regression analysis program MLn (Rasbash & Woodhouse, 1995) was used to consider relationships of a range of explanatory student and teacher/class characteristics and activities with the response variables student attitude and achievement using an iterative generalised least squares regression analysis procedure. Significance has been reported at the 0.05 confidence level for a two-tailed test. A range of student characteristics, attitudes and ability were included as explanatory variables in the analyses as level 1 (student) variables. Level 2 variables, related to teachers and classes, included lesson delivery systems, a range of lesson segment characteristics such as purpose, teacher/class activities and behaviours, and lesson summary information about teacher relationships with and influences on students, organisational ability, and collective student behaviours. Level 3 (school) variables were not significant in any aspect of this study. The student, teacher and class variables at both levels which were significantly related to attitude towards achievement and actual achievement in Year 11 are shown in Table 1. Both unstandardised and standardised regression coefficients are shown, the latter to enable comparisons of the relative importance of explanatory variables for each of the response variables. Similar information for satisfaction with relationships with teachers is shown in Table 2. TABLE 1. Unstandardised and Standardised Regression Coefficients Linking Student and Teacher/Class Variables with Student Attitude and Mathematics Achievement in Year 11 _______________________________________________________________________ EXPLANATORY RESPONSE VARIABLE: RESPONSE VARIABLE: VARIABLES ACHIEVEMENT ATTITUDE ACHIEVEMENT b SEb Beta b SEb Beta ______________________________________________________________________ Constant -0.254 0.197 . 18.67 5.075 . STUDENT VARIABLES Stress -0.799 0.024 -0.179 -1.894 0.791 -0.123 Efficacy 0.141 0.043 0.171 . Yrs at this schl -0.037 0.019 -0.106 . TEACH/CLASS VARIABLES Tchr supervision . 5.796 1.239 0.308 Segment is practice . -0.164 0.047 -0.207 Tchr directives . -1.367 0.432 -0.186 Delivery Quest&answer . -5.276 1.676 -0.169 Tchr non-engaged . 1.545 0.654 0.139 Class content hard . -3.291 1.587 -0.107 Tchr monitor/assesses . -2.064 1.064 -0.104 No.segments per lesson 0.084 0.031 0.141 . ________________________________________________________________________ Explanation of Student Attitude to Achievement In the case of attitude to achievement as the response variable, only three student and one class variable were found to be significantly related to it. The student variables were the level of stress, efficacy (a sense of their ability to control their learning through effort) and the number of years they had attended their present school. Higher levels of stress reported were related to lower satisfaction with achievement, higher efficacy was related to higher levels of satisfaction, and students who had been at the same school throughout their secondary schooling had lower levels of satisfaction. The significant class variable was the mean number of segments in each lesson which, for different teachers, ranged from 1.4 to 5.6 with a mean of 2.7 segments per lesson. Students in classes with more segments per lesson had greater satisfaction with their levels of achievement in mathematics, perhaps because these would be lessons where a number of different purposes and teaching modes were attempted. Collectively these four variables accounted for 9.9 per cent of the variance in satisfaction with achievement. Explanation of Student Satisfaction with their Teacher Relationships When satisfaction with relationships with teachers was taken as the response variable, there were three student explanatory variables and five teacher/class explanatory variables which had significant relationships with it (see Table 2). The most prominent student variable was the teacher rating of ability of individual students - the higher the rating the greater was the satisfaction with teacher relationships. The other student variables indicated that the higher the School Certificate score in English and the higher their sense of efficacy, the greater was their satisfaction with teacher relationships. TABLE 2. Unstandardised and Standardised Regression Coefficients Linking Student and Teacher/Class Variables with Year 11 Student Satisfaction with their Relationships with their Teachers ___________________________________________________ EXPLANATORY RESPONSE VARIABLE: VARIABLES ATTITUDE TO TEACHERS b SEb Beta ___________________________________________________ Constant 3.501 0.531 . STUDENT VARIABLES Indiv tchr-rated Abil 0.105 0.026 0.231 SC English 0.117 0.034 0.193 Efficacy 0.157 0.048 0.158 TEACH/CLASS VARIABLES Tchr period load -0.058 0.013 -0.319 Tchr qualification -0.225 0.069 -0.247 Tchr Workload (Admin) 0.179 0.059 0.193 Tchr Satisif (Admin) -0.171 0.057 -0.188 Tchr intrinsic motiv 0.095 0.034 0.164 ___________________________________________________ For the teacher/class level, having a teacher with a higher period load was negatively related to student satisfaction with teacher relationships. Teaching load ranged from 21 to 30 periods per week, with a mean of 25.9 periods and a standard deviation of 3.0. Perhaps teachers with the higher teaching loads simply had less time to spend with students. Teacher satisfaction with senior administration of the school was also negatively related to student satisfaction although higher teacher satisfaction with their administrative workload was positively related to student satisfaction. The students of teachers who were intrinsically motivated towards teaching had higher satisfaction, as did the students of teachers who had a teaching diploma but not a degree. Collectively these eight variables accounted for 13.4 per cent of the previously unexplained variance in student satisfaction, with only 2.7 per cent of the remaining unexplained variance attributable to between-teacher/class differences. Approximately 75 per cent of the between-teacher/class variance in student satisfaction, previously unaccounted for in the variance components model, was accounted for by the five teacher variables shown in Table 2. Explanation of Student Achievement For student achievement in mathematics as the response variable, one student and seven teacher/class variables were found to be significantly related to student achievement in mathematics. The standardised regression coefficients for the teacher/class explanatory variables are shown in descending order of magnitude in Table 1 to facilitate comparison of the relative strength of each variable's relationship with achievement. Student stress was negatively related to achievement, as might be expected. It is likely that the relationship would be reciprocal with stress affecting achievement and achievement affecting stress levels for some students. At the teacher/class level, the proportions of time teachers spent on two of the 13 delivery systems identified were significantly related to achievement, both negatively. The first variable was the prevalence of a teacher-led question and answer session in which the student responses were an integral part of the lesson, and the second was the extent of directing in which the teacher provides instructions for what is to be done. It seems that the more these activities were necessary, the lower was student achievement. Teacher engagement with students throughout the lesson was an important variable with higher proportions of time spent non-engaged being related to higher achievement. It should be noted that, on average, teachers were non-engaged with students for 6 per cent of the time, 22 per cent were non-engaged for more than 10 per cent of the time and, at the maximum, one teacher was non-engaged for 29.3 per cent of the available lesson time. A number of lesson segment purposes, difficulty and behaviours were related to achievement. The proportion of segments where the purpose was practice was negatively related to achievement. Practice involved drill and repetition of exercises or skills. The proportion of segments where the material was hard or challenging for students was also negatively related to achievement. The importance of two teacher behaviours was significantly related to achievement. In these cases it was not the proportion of time teachers engaged in the behaviours, but the behaviour's importance for the purposes of the lesson segment. One behaviour which involved the task of supervising student work including the setting of standards was positively related to achievement. The other behaviour where the teacher role was one of watchfulness in monitoring and assessing student progress on the given task by close observation, perhaps by moving about the room, was negatively related to achievement. One could predict that such a relationship would be reciprocal. When these eight variables were included in the regression equation as explanatory variables with achievement as the response variable, there was a reduction of 16.5 per cent of the unexplained variance in mathematics achievement, and all of the remaining unexplained variance was at the between-student level. This suggests that the analysis was relatively more successful at explaining student variance in achievement related to between-class differences than between-student differences. CONCLUSION The analyses undertaken for this paper indicate that processes concerned with teaching practices and classroom activities in Year 11 mathematics lessons are related to student attitudes and achievement. Approximately 10 per cent of the variance in individual student attitude to achievement and 16.5 per cent of the variance in actual student achievement due to Year 11 experiences could be attributed to teacher/classroom variables. A total of about 13 per cent of the variance in student satisfaction with relationships with the class teacher was explained by student and teacher/classroom variables, the latter accounting for 75 per cent of the previously unexplained teacher/classroom differences. It is important that we understand better why some teachers seem to be more effective than others in promoting favourable student attitudes and higher student achievement. To this end it would seem to be necessary to investigate the efficacy of teaching practices and the classroom activities these foster relative to specific instructional purposes, content difficulty levels, use of resources, and class groupings for particular lessson segments. It was noted that each mathematics lesson observed was made up of one or more lesson segments, with a mean of 2.7 segments and the number of segments ranging from 1.4 to 5.6 over a series of observed lessons for each teacher. In these analyses of practices and activities, both the number of segments and the purpose of a segment were found to be important for student attitudes and achievement respectively. A segment was defined as a part of a lesson which is functionally discrete from other parts of the lesson, in particular having a distinct purpose. Typically segments vary in length from a minute or two to the majority of the time available in a lesson. It is possible that lesson segments, defined in this way, would be more informative units of analysis through which to examine relationships between teaching and student outcomes than either lessons or teachers. The purposes of lesson segments could be thought of as defined by functional clusters of teaching practices and activities as discussed by Burns and Anderson (1987; see also Anderson and Burns, 1989, p.350). The combination of practices and activities themselves would be likely to have different effects on students when present in segments with different purposes. An examination of segments and their relationships with attitudes and achievement, rather than the whole lessons considered in this paper, would be desirable and will be pursued in subsequent studies. ________________________________ REFERENCES Ainley, J., Reed, R. & Miller, H. (1986). School Organization and the Quality of Schooling: A Study of Victorian Government Secondary Schools. ACER Research Monograph No. 29. Hawthorn, Victoria: ACER. Anderson, L.W. & Burns, R.B. (1989). Research in Classrooms: The Study of Teachers, Teaching and Instruction. Oxford, England: Pergamon Press. Bourke, S. & Smith, M. (1993). Some relationships between teacher characteristics, subject taught and teaching practices in secondary schooling. Paper presented at the Annual Conference of the AARE, Fremantle, Western Australia. Electronically published and available at the website http://www.swin.edu.au/aare/confpap.htm. Bourke, S. & Smith, M. (1995). Student, teacher and school effects on student quality of school life: Some multilevel analyses. Paper presented in a symposium, School climate and teacher stress, at the 6th European Conference for Research on Learning and Instruction, Nijmegen, the Netherlands. Burns, R.B. & Anderson, L.W. (1987). The activity structure of lesson segments. Curriculum Studies, 17(1), 31-53. Rasbash, J. & Woodhouse, G. (1995). MLn Command Reference. Multilevel Models Project, Institute of Education, University of London. Smith, M. & Bourke, S. (1992). Teacher stress: Examining a model based on context, workload and satisfaction. Teaching and Teacher Education, 8(1), 31-46.