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APPLICATION OF RASCH MODEL AND TRADITIONAL STATISTICS TO DEVELOP A

MEASURE OF PRIMARY SCHOOL CLASSROOM LEARNING CULTURE

Robert F. Cavanagh Curtin University of Technology

Joseph Romanoski Curtin University of Technology

Geoffrey J. Giddings

Curtin University of Technology

Melinda Harris Curtin University of Technology

Graham B. Dellar

Curtin University of Technology

Paper presented at the 2003 Annual Conference of the Australian Association for Research in Education:

Auckland, New Zealand

This research was conducted as part of an ARC Linkage project between Curtin University of Technology and the Canning Education District

Address correspondence to Dr Rob Cavanagh, Department of Education, Curtin University of Technology, GPO Box U1987, Western Australia 6845. [email: [email protected]]

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ABSTRACT

The study developed and validated a scale of elementary school classroom culture through sequential application of Rasch model and traditional statistics. The conceptual framework for the study was a theoretical model of elementary school classroom culture comprised of two educational outcome factors (six sub-factors), two class group factors (seven sub-factors), a teacher factor (four sub-factors) and a parental involvement factor. Likert scale items were written for each factor and sub-factors to produce a 108-item scale. The scale was administered to a convenience sample of 622 students in 27 elementary school classrooms. The psychometric properties of the data were analysed using the computer programs SPSS and Rasch Unidimensional Measurement Models (RUMM). Both programs were then used for scale development and validation. The refined scale contained 59 items organised into five factors and 15 sub-factors. Each sub-factor was internally reliable and factors elicited data on a discreet construct. The items within each sub-factor were arranged in Guttman patterns from ‘easy’ to ‘hard’. Scale development ensured the data from the refined scale fitted the theoretical model. The study shows that the measurement capacity of a scale can be enhanced by application of both Rasch model and traditional statistics in scale development.

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BACKGROUND Methodological orientation

The instrument development process reported in this paper was conducted as part of an ARC Linkage project between Curtin University of Technology and the Canning Education District concerning school leadership and influences on classroom learning environments. The purpose of this phase of the project was to develop an instrument containing approximately 60 items that elicited data on multiple dimensions of the classroom environment on the understanding further refinement of the measure would be conducted when data were collected from a district-wide sample. Another consideration was that three other instruments were being developed and data from all the instruments will be eventually analysed using both Rasch and structural equation modeling. Although the use of both probabilistic and deterministic analytic techniques has been successfully conducted in other studies (see Banerji, Smith & Dedrick, 1997; Chatterji, 2002), sequentially or conjointly using both techniques is problematic. Consequently, one of the objectives of this study was to gain first hand experience with some of the inherent problems so that the strengths of both techniques could be effectively utilised.

Context and theoretical orientation

The influence of economic rationalism on government and private school systems has seen schools become more accountable for the outcomes of the instructional program and for identifying ways to increase their effectiveness in attaining these outcomes. Investigating relationships between internal aspects of the school and student outcomes is the major goal of school effectiveness research. The success of this research is highly dependent upon the availability of reliable and valid measures of educational outcomes and of the learning environment. These measures need to be conceptually consistent with a wide range of approaches to the curriculum and pedagogy including contemporary theory and practise.

The context for this study was pressure from the government and state educational system for school

improvement through curriculum reform. The Western Australian Curriculum Framework (Curriculum Council, 1997) is based upon the notion of outcomes based education. It is characterised by identification of sequential long-term educational goals in comparison to previous curricula which prescribed the objectives of specific courses of study, units of work or years of schooling. Five Core Values underpin the Curriculum Framework: pursuit of knowledge and achievement of potential; self-acceptance and self-respect; respect and concern for the rights of others; social and civic responsibility; and environmental responsibility. The Curriculum Framework also specifies seven Key Principles to guide schools in planning and curriculum development: an encompassing view of the curriculum; an explicit knowledge of the core values; flexibility; inclusivity; integration, breadth and balance; a developmental approach; and collaboration and partnerships.

The pedagogy underpinning the Curriculum Framework is based upon the social constructivist

view of learning. Social constructivism emphasises the importance of the social environment on the acquisition and development of knowledge (Good & Brophy, 2000; Blumenfield, Marx, Patrick, Krajcik, & Soloway, 1997; McCarthy, 1994). The interaction between peers and with the teacher are anticipated to influence student learning. Adoption of a social constructivist view of learning assumes everyone present within the classroom has the capacity to influence the social environment and enable learning. From this perspective, effective learning is influenced not just by the teacher, but also by individual students, groups of

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students and the class as a whole. The construction of cognitive and attitudinal mental schema within the minds of individual students occurs through discussion of learning and sharing experiences. Confidence and motivation are also a consequence of a supportive classroom social environment. This proposition is consistent with cooperative learning instructional methods (Johnson, Johnson & Stanne, 2000), and also assertions about the effectiveness of caring learning environments (Pena & Amrein, 1999; Battistitch, Solomon, Watson & Schaps, 1997).

However, development and implementation of a curriculum grounded in accepted pedagogy does not guarantee that effective learning will occur in classrooms (Cavanagh & Dellar, 2001). Both enacting the curriculum and engaging students in effective learning are dependent upon the prevailing beliefs, values, attitudes and behaviours of students and of the teacher. The culture within the individual classroom is a major determinant of student and teacher behaviours concerning attainment of educational outcomes (Waugh & Cavanagh, 2002a). This view is supported by the findings of many years of research into school improvement in which improving the educational outcomes of students is believed to be a process of re-culturing to change belief and value systems throughout the school (Harris, 2001; Sergiovanni, 2000 &1992; Dalin, Rolff & Kleekamp, 1993; Fullan, 1993; Glickman, 1992). Focus on classroom level effectiveness is also conceptually consistent with the notion of sustainable school change being driven by the engagement and commitment of teachers to improving the school and the lives of children, a moral imperative (Fullan, 2001 &1993). Advocates of school renewal oriented improvement emphasise the need for a bottom-up change process in which teachers challenge prevailing beliefs and practises within the school (Sirotnik, 1999; Soder, 1999). The renewal of schools requires re-culturing the individual classroom through development of alternative beliefs and attitudes towards classroom instruction and learning (Cavanagh, Waugh & Dellar, 2003).

The effect of family and home on student achievement and school improvement is well established

(Waugh & Cavanagh, 2002a & 2002b; Lingard, 2001; McCall, Smith, Stoll, Thomas, Sammons, Smees, MacBeath, Boyd & MacGilchrist, 2001; Coleman, 1998). The home environment influences student attitudes towards learning and also the culture in schools and individual classrooms (Cavanagh, Waugh & Dellar, 2003). Thus student perceptions of the prevailing culture in their classroom will be shaped by how they view themselves, the class-group, the teacher and their parent(s). In addition, student perceptions of the attainment of attitudinal and cognitive outcomes will also influence the culture although the attainment of these outcomes could also be viewed as the result or product of an effective classroom culture (Cavanagh, Dellar, Ellett and Rugutt, 2000). Learning environment research

Waugh and Cavanagh (2002b) questioned five aspects of learning environment research. First, there is a paucity of interval-level scales of classroom environment. Classroom environment items are rarely ordered from ‘easy’ to ‘hard’ by calibration against the distribution of student rankings of the environment. Second, scales of classroom environment are not usually constructed with the items being selected to fit a measurement model and form a uni-dimensional scale in which the items can be said to be affected by one dominant trait. Third, classroom environment and classroom outcomes are rarely measured on the same scale. Measuring classroom environment and classroom outcomes separately, and then correlating them is not the most satisfactory method of testing the relationship between them for at least two reasons. Measuring the two aspects separately using Classical Test Theory leaves other aspects or ‘noise’ in the measures, distorting the relationship. A Rasch model analysis tests that the classroom environment items and the classroom outcome items link together on the same scale through both being affected by the same dominant trait, something that correlation methods do not check. Four, many assessments of classroom

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environment utilise Likert or Likert-type response categories that can provide measurement problems. Provision of a neutral category that attracts different responses like don’t know, unsure, don’t want to answer, and neutral between (strongly) agree and (strongly) disagree reduces the contiguity of the categories and continuity of the response scale. The Rasch model checks that Likert type categories are answered consistently and logically; that is, that they provide an ordered set of responses from ‘easy’ to ‘hard’ (items with disordered response sets are discarded). Classical Test Theory does not make this test. Five, classroom environment and classroom outcomes have not been measured using a conceptual design of items in each factor based on a Guttman type pattern from ‘easy’ to ‘hard’. This design sets the items like a ruler and the design can be tested using a Rasch model. Classical Test Theory tries to have all items of ‘similar difficulty’ and does not have a conceptual measurement design in the preparation of the items.

These questionable aspects of learning environment research were recently addressed in the design

and validation of a scale to measure secondary school student’s views of the secondary school classroom learning environment (Cavanagh, Waugh & Dellar, 2003; Waugh & Cavanagh, 2002a). Classroom environment and classroom outcome items were created and arranged in Guttman patterns from ‘easy’ to ‘hard’ for the sub-aspects within each factor of an eight-factor classroom environment and two-factor classroom outcomes model. The ‘difficulties’ of the items and the student measures were then calibrated on the same scale. The computer program Rasch Unidimensional Measurement Models (RUMM) (Andrich, Sheridan, Lyne & Luo, 2000) was used to calibrate the items and then to examine the psychometric properties of the data. (see Andrich, 1988a, 1988b, 1985, 1982; Rasch, 1960/1980; Waugh, 2000).

The rationale for investigating secondary school classroom learning environments using the previously

described conceptual frame and data analysis techniques provided the impetus for conducting similar research in elementary schools. However, it was envisaged that the items and scale developed in the secondary school study would not be appropriate for measuring elementary school classroom culture. Elementary school students have lower levels of reading than secondary school students and the terminology used to describe teaching, learning and assessment processes is also different in these two types of schools. The secondary school model was hypothesised to be applicable in the writing of new items and development of a new scale to measure elementary school classroom learning environment factors and classroom outcome factors. The RUMM computer program (Andrich, Sheridan, Lyne & Luo, 2000), was again to be applied in item calibration and testing the hypothesised model. In cognisance of the predominant use of traditional parametric statistics in researching learning environments, traditional statistical tests were also applied to investigate the psychometric properties of the data and assist with scale development.

RESEARCH OBJECTIVES

The study sought to apply Rasch Model and traditional statistics to construct an interval-level uni-dimensional scale to measure elementary school classroom culture. Scale development was based upon a hypothesised model of elementary school classroom culture comprised of two educational outcome factors, two class-group factors, one teacher factor and one parent factor. Specifically, the study aimed to apply a scale development process that would:

1. Produce a scale to measure student self-reported educational outcome and attributes of classroom

culture; 2. Produce a scale with item difficulties and classroom culture measures calibrated on the same scale; 3. Produce a scale that elicited data to fit the theoretical model; and

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4. Examine the utility of applying both Rasch Model and traditional statistics in scale development and validation.

THOERETICAL MODEL Classroom culture was initially conceptualised as being comprised of four dimensions; the attitudes

and behaviours of the individual student, of the class group and of the teacher, and also parental involvement. The individual student dimension was then divided into self attitudes towards education and learning and also self learning outcomes and behaviours. Classroom culture is influenced by the individual student’s view of education and learning and also perceptions of his/her academic progress. The class group dimension was divided into attitudes and behaviours towards learning and attitudes and also behaviours towards class group support. Classroom culture is influenced by student interaction with peers concerning learning and building a supportive social environment. These six dimensions are the factors in the theoretical model (Figure 1). The factors were further divided into sub-factors. These sub-factors provide a more detailed representation of the phenomenon under investigation. The six factors and 18 sub-factors are presented in Figure 1.

The six factors are mutually influential and collectively comprise classroom culture. The interaction

between the factors is represented by the double arrows. The model provided a conceptual structure for developing a scale to measure elementary school classroom culture and it was expected that the data obtained from administering the scale would enable the model to be empirically validated.

Factor 1: Self attitudes towards education and learning Sub-factor 1: Importance of schooling Sub-factor 2: Desire to be successful Sub-factor 3: Desire to learn

Factor 2: Self learning outcomes and behaviours Sub-factor 1: Achievement Sub-factor 2: Experiencing success Sub-factor 3: Engaging in School-work

Factor 3: Class-group learning attitudes and behaviours Sub-factor 1: Class emphasis on learning Sub-factor 2: Class learning with peers Sub-factor 3: Class group expectations Sub-factor 4: Class discussion about learning

Factor 4: Class-group support attitudes and behaviours Sub-factor 1: Helping each other Sub-factor 2: Getting along together Sub-factor 3: Caring about each other

Factor 5: Teacher attitudes and behaviours Sub-factor 1: Negotiation with students Sub-factor 2: Child centred approach Sub-factor 3: Caring for students Sub-factor 4: Expectations of students

Factor 6: Parental involvement

Figure 1. Theoretical model

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RESEARCH METHODS

Development of a scale of elementary school classroom culture required the writing and testing of items in the knowledge that during scale development, some items may be rejected due to lack of empirically tested reliability and validity. In anticipation of this likelihood, the number of items written and tested was larger than that considered acceptable for the eventual scale (minimum of four items per sub-factor). The overall number of items in the developed scale was also considered in relation to ease of administration of the developed scale in future investigations. Approximately 60 items was considered appropriate for administration to elementary school students.

For each of the 18 sub-factors in the theoretical model, six items were written to elicit student

perceptions of the 18 constructs being investigated (see Appendix 1). Items were answered on a four point Likert scale from strongly agree, agree, disagree and strongly disagree, scored from 4 to 1.The items were created by researchers highly familiar with test construction, elementary school classroom environments and the reading ability of elementary school students. The items for each sub-factor were written to elicit data on a similar construct and also to provide data with sufficient variance to match the range of variation anticipated in classrooms. Within the respective sets of items, some items targeted what were believed to be commonly occurring aspects of the culture and others targeted aspects thought to be less common. The items were trialed and refined in a small pilot study.

The 108 items were administered to a convenience sample of 622 Grade Five, Six and Seven

students who were present in 27 classrooms in four local elementary schools on the day of administration. The schools were located in areas of markedly different socio-economic status, however all four schools were reputedly implementing innovative instructional programs. Restriction of the sample to the higher grades was necessary due to anticipation that middle and junior grade students would have difficulty completing the survey. Participation of schools, teachers and students was voluntary and participants were assured of confidentiality of results. Data were coded according to school and class group for data analysis purposes and also to make the results available upon request to schools and teachers.

The psychometric properties of the data were explored with the computer programs SPSS (SPSS,

2001) and the Rasch Unidimensional Measurement Models (RUMM) (Andrich, Sheridan, Lyne & Luo, 2000). A variety of Rasch Model and parametric tests were conducted.

RESULTS AND DISCUSSION

Data were entered into a computer spreadsheet and checked for missing responses. Of the 67,176 expected responses, 45 were missing (0.07%). Data analysis required complete data for all students so missing data were entered as ‘2’. The data were transferred into the computer program Rasch Unidimensional Measurement Models (RUMM) (Andrich, Sheridan, Lyne & Luo, 2000). RUMM (2000) requires data be non-delimited for each respondent which necessitated intermediate conversion with a word processing program to remove item separation syntax. RUMM calibrates the items by conjointly ranking items in order of ‘difficulty’ and ranking students by their overall level of agreement with the items. This is analogous to item calibration with performance tests. The questions have varying levels of difficulty, the students have varying levels of performance and only the most capable students should be correctly answering the most difficult questions. Since attitude scale items are not scored as ‘correct’ or ‘incorrect’, the distribution of student responses across the Likert scale categories is critical. Ideally, the order of responses for an item should mirror the rank order of students. Students who have indicated they have a

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highly affirmative view of their classroom culture should also have consistently selected the ‘strongly agree’ category. While this may seem obvious, it does not necessarily occur for all items. RUMM (2000) tests this by calculating un-centralised item thresholds. For a four point Likert scale, there are three thresholds. In Rasch measurement, threshold values are calculated so that there are odds of 1:1 for students answering in adjacent response categories. Discrimination is satisfactory when the thresholds are ordered in correspondence with the ordering of the response categories. Calculation of item thresholds for the data on 108 items identified 36 items that did not meet this requirement and the data from these items were discarded.

The psychometric properties of data for the 72 items were examined by calculating RUMM (2000)

Summary Test of Fit statistics. These are presented in Table 1. The item-student interaction indicates the degree to which students answer items of different

‘difficulty’ in a logical and consistent manner. When the data fit the model, the fit statistic has a mean near zero and a standard deviation near 1. A negative fit statistic indicates that the data fit the model very closely. A positive fit statistic indicates that some ‘noise’ is present. In this case the means of 0.19 and –0.35 indicate the students were logical and consistent in their responses to items of different ‘difficulty’. The standard deviations of 3.51 and 2.59 indicate the variance in item and student data were somewhat lower than would be observed in an ideal data to model fit.

The item-trait interaction indicates the consistency of the item ‘difficulties’ across the range of

different student classroom culture measures on the scale; that is how well students agree on the ‘difficulties’ of the items along the scale. When the data fit the model, the item-trait interaction (a Chi-square) has a probability more than 0.05. In this case, p < 0.000 indicating the scale was measuring one dominant trait comprised of several dimensions. The proportion of observed variance considered true should be close to 1. In this case the proportion of observed variance considered true was 0.97. The power of the tests-of-fit indicates how closely the data fit the model. In this case the fit between the data and the model was ‘excellent’.

Table 1 Summary of Rasch psychometric statistics for the 72 item Elementary School Classroom Culture Scale (n = 622) Item-Student Interaction Items Students Location Fit Statistic Location Fit Statistic Mean 0.00 0.19 1.23 -0.35 SD 0.46 3.51 1.06 2.59 Item-Trait Interaction Total Item Chi Sq 2429.41 Total Degree Freedom 666 Total ChiSq Probability 0.0000 Proportion of observed variance considered true for the scale is 0.97 (97%) Cronbach Alpha is 0.97 Power of Tests-of-Fit Power is EXCELLENT (Based upon Separation Index of 0.97)

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The distribution of the 72 items across the hypothesised sub-factors in the theoretical model was

examined to check that each sub-factor contained a sufficient number of items to ensure sub-factor internal reliability (Oppenheim, 1992). Five sub-factors containing less than four items were identified and consequently two new sub-factors were conceptualised - importance of school and learning and achievement. At the completion of this stage of development, the instrument contained 72 items conceptually organised into five factors and 15 sub-factors.

Individual item-fit statistics for the 72 items were then calculated. These included item locations

measured in logits (logarithmic units based on the logarithmic odds of answering positively), standard errors, residuals and fit to the model (Chi-square probability). Items that fitted the model well were identified. These items had low residual values (< ? 2.0) and high Chi Square probability values (p > 0.05). Also, the locations of the items within each sub-factor were examined. The item locations show the relative ‘difficulty’ of items and in an ideal sub-factor, there should be a range of item locations. The capacity of a sub-factor to discriminate between different classroom environments requires that different items measure respectively both common and uncommon attributes of the environment. A further 12 items were deleted leaving 60 items organised into 15 four-item sub-factors.

RUMM (2000) Summary Test of Fit statistics were calculated for the 60-item scale. These are

presented in Table 2. The results of these analyses are very similar to those for the 72 item scale and the 60 item scale was also shown to have an ‘excellent’ fit between the data and the model although the standard deviations of 3.59 and 2.40 indicate the variance in item and student data were still lower than would be observed in an ideal data to model fit.

Table 2 Summary of Rasch psychometric statistics for the 60 item Elementary School Classroom Culture Scale (n = 622) Item-Student Interaction Items Students Location Fit Statistic Location Fit Statistic Mean 0.00 0.24 1.25 -0.31 SD 0.46 3.59 1.08 2.40 Item-Trait Interaction Total Item Chi Sq 2039.37 Total Degree Freedom 540 Total ChiSq Probability 0.0000 Proportion of observed variance considered true for the scale is 0.96 (96%) Cronbach Alpha is 0.96 Power of Tests-of-Fit Power is EXCELLENT (Based upon Separation Index of 0.96)

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RUMM was also used to produce an item map displaying location of item thresholds and also location of students (see Appendix 2). The left plot shows the distribution of the relative locations of students in logits (‘X’ = three students) and the right plot shows the distribution of item thresholds (un-centralised). In the item plot, the first two digits are the item number and the third digit after the decimal point is the threshold. The respective thresholds for the 60 items are distributed from ‘easy’ to ‘hard’ The distribution of the ‘difficulty’ of the items closely matches the student distribution although some of the items could be too ‘easy’.

The structure of the data for the scale was then explored by application of principal components

factor analysis with oblique rotations. Of the 60 items, 59 items loaded on five components within a nine-component structure matrix. The structure matrix reflected the basic structure of the original theoretical model and the groupings of factors and sub-factors were logical. The exception to this pattern was the data for the four items comprising class group expectations that loaded on a separate component. The items in this sub-factor elicited data on a dimension of classroom culture that were independent of the data for the other four factors. The factor analysis structure matrix provides evidence for the 15 sub-factors being organised within five factors:

1. Self attitudes and behaviours (four sub-factors - importance of school and learning, desire to

learn, achievement & engaging in schoolwork); 2. Class group expectations; 3. Class group attitudes and behaviours (six sub-factors - class emphasis on learning, class

learning with peers, class discussion about learning, helping each other, getting along together & caring about each other);

4. Teacher attitudes and behaviours (three sub-factors - negotiation with students, child-centred approach & caring for students); and

5. Parental involvement. Table 3 presents the factor analysis structure matrix. Bold type has been used to show loadings

above 0.33 and when an item loaded above this on more than one component, only the highest loading is indicated. The factor loadings have been ordered according to the above five-factor structure.

Table 3 Factor analysis structure matrix and model factors/sub-factors (n = 622) Component

1 2 3 4 5 6 7 8 9 Factor & sub-factor

0.38 0.64 0.26 0.23 -0.42 -0.35 0.13 -0.01 -0.02 Factor 1 0.37 0.44 0.16 0.23 -0.57 -0.28 0.03 -0.06 -0.03 Sub-factor 1 0.35 0.48 0.28 0.21 -0.55 -0.38 0.05 0.34 -0.11 0.31 0.40 0.16 0.23 -0.50 -0.37 0.04 0.06 0.16 0.22 0.15 0.13 0.20 -0.72 -0.22 0.18 0.05 0.01 Factor 1 0.31 0.34 0.15 0.26 -0.70 -0.34 0.19 0.09 -0.05 Sub-factor 2 0.33 0.36 0.25 0.16 -0.76 -0.31 0.13 0.08 -0.24 0.35 0.39 0.21 0.12 -0.70 -0.31 0.11 0.06 -0.27 0.14 0.67 0.14 0.15 -0.20 -0.22 0.17 0.08 -0.15 Factor 1 0.31 0.77 0.11 0.12 -0.31 -0.24 0.17 0.05 -0.20 Sub-factor 3 0.28 0.80 0.12 0.12 -0.30 -0.23 0.10 0.09 -0.16 0.29 0.82 0.15 0.18 -0.37 -0.28 0.08 0.11 -0.07

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Table 3 continued 0.25 0.45 0.28 0.19 -0.42 -0.31 0.09 0.58 -0.11 Factor 1 0.34 0.65 0.23 0.22 -0.47 -0.37 0.07 0.33 -0.10 Sub-factor 4 0.45 0.55 0.23 0.18 -0.59 -0.36 0.14 0.31 -0.19 0.34 0.63 0.27 0.26 -0.49 -0.39 0.04 0.47 -0.15 0.41 0.37 0.15 0.54 -0.40 -0.40 0.20 0.15 -0.28 Factor 2 0.12 0.09 -0.07 0.79 -0.20 -0.03 0.14 0.05 -0.14 0.18 0.13 0.09 0.81 -0.09 -0.17 0.09 0.02 -0.03 0.25 0.22 0.15 0.41 -0.26 -0.24 0.18 0.02 -0.62 0.46 0.40 0.30 0.16 -0.54 -0.49 0.20 0.03 -0.43 Factor 3 0.38 0.30 0.32 0.12 -0.33 -0.80 0.21 -0.01 -0.12 Sub-factor 1 0.48 0.32 0.27 0.12 -0.29 -0.69 0.24 0.21 -0.16 0.51 0.18 0.23 0.18 -0.33 -0.67 0.35 0.19 -0.32 0.56 0.28 0.25 0.18 -0.41 -0.60 0.27 -0.03 -0.23 Factor 3 0.53 0.36 0.22 0.28 -0.59 -0.53 0.24 0.16 -0.22 Sub-factor 2 0.61 0.35 0.15 0.22 -0.40 -0.51 0.28 0.06 -0.31 0.64 0.40 0.16 0.17 -0.37 -0.54 0.32 0.02 -0.26 0.54 0.32 0.46 0.20 -0.38 -0.65 0.18 -0.15 -0.26 Factor 3 0.52 0.31 0.36 0.21 -0.36 -0.78 0.25 -0.14 -0.21 Sub-factor 3 0.49 0.30 0.43 0.25 -0.30 -0.74 0.22 -0.15 -0.22 0.54 0.27 0.43 0.23 -0.39 -0.71 0.23 -0.12 -0.12 0.76 0.34 0.20 0.10 -0.28 -0.57 0.23 0.00 -0.29 Factor 3 0.81 0.35 0.26 0.16 -0.29 -0.53 0.24 -0.02 -0.27 Sub-factor 4 0.65 0.34 0.35 0.17 -0.34 -0.57 0.15 -0.13 -0.22 0.72 0.40 0.36 0.15 -0.34 -0.48 0.21 -0.10 -0.32 0.71 0.33 0.36 0.13 -0.37 -0.48 0.14 -0.04 -0.31 Factor 3 0.75 0.30 0.29 0.24 -0.30 -0.38 0.15 0.03 -0.17 Sub-factor 5 0.66 0.24 0.53 0.07 -0.36 -0.45 0.25 -0.02 -0.27 0.73 0.30 0.29 0.23 -0.33 -0.40 0.33 -0.04 -0.14 0.78 0.22 0.38 0.19 -0.36 -0.45 0.14 -0.02 -0.12 Factor 3 0.80 0.29 0.40 0.14 -0.36 -0.48 0.19 0.01 -0.21 Sub-factor 6 0.79 0.30 0.39 0.31 -0.44 -0.46 0.19 -0.03 -0.20 0.74 0.23 0.35 0.32 -0.33 -0.38 0.24 -0.08 -0.11 0.44 0.27 0.48 0.07 -0.26 -0.47 0.21 -0.26 -0.48 Factor 4 0.36 0.31 0.44 0.17 -0.32 -0.34 0.18 -0.31 -0.53 Sub-factor 1 0.40 0.26 0.53 0.13 -0.32 -0.47 0.13 -0.36 -0.39 0.27 0.22 0.35 0.05 -0.26 -0.42 0.22 -0.34 -0.32 0.37 0.21 0.56 0.03 -0.26 -0.41 0.13 -0.35 -0.05 Factor 4 0.45 0.28 0.62 0.21 -0.36 -0.45 0.25 -0.33 -0.19 Sub-factor 2 0.51 0.32 0.76 0.10 -0.40 -0.45 0.28 -0.14 -0.30 0.47 0.24 0.50 0.12 -0.21 -0.31 0.21 -0.03 -0.51 0.41 0.24 0.72 0.12 -0.18 -0.40 0.23 -0.06 -0.32 Factor 4 0.30 0.21 0.71 0.04 -0.16 -0.38 0.41 -0.05 -0.16 Sub-factor 3 0.27 0.07 0.63 0.06 -0.19 -0.26 0.30 0.07 -0.05 0.52 0.24 0.73 0.08 -0.27 -0.44 0.31 -0.07 -0.37 0.37 0.24 0.45 0.14 -0.26 -0.40 0.72 -0.21 -0.08 Factor 5 0.44 0.37 0.39 0.15 -0.34 -0.36 0.69 -0.14 -0.18 0.22 0.16 0.27 0.11 -0.24 -0.31 0.70 -0.07 -0.01 0.12 0.09 0.10 0.18 -0.06 -0.08 0.57 0.15 -0.24

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SPSS was then used to test the internal reliability of the sub-factor data. Cronbach Alpha values

were calculated for the four items comprising each sub-factor. The results are presented in Table 3. The internal reliability of the respective sub-factor data varied from 0.64 to 0.87. All of the sub-factors were internally reliable.

Table 4 Sub-factor internal reliability (60 items, n = 622) Factor Sub-factor Cronbach ? Factor 1 Importance of school and learning 0.68 Desire to learn 0.78 Achievement 0.81 Engaging in School-work 0.82 Factor 2 Class group expectations 0.64 Factor 3 Class emphasis on learning 0.77 Class learning with peers 0.80 Class discussion about learning 0.85 Helping each other 0.86 Getting along together 0.80 Caring about each other 0.87 Factor 4 Negotiation with students 0.70 Child centred approach 0.74 Caring for students 0.78 Factor 5 Parental involvement 0.69

SPSS was also applied to test the capacity of the scale to discriminate between the sub-factors in

different classrooms (see Table 4).

Table 4 ANOVA by class group (n = 622; 27 class groups) Factor Sub-factor F Sig. Eta2

Factor 1 Importance of school and learning 3.01 0.0000 0.12 Desire to learn 2.75 0.0000 0.11 Achievement 1.38 0.0995 0.06 Engaging in School-work 1.75 0.0128 0.07 Factor 2 Class group expectations 5.73 0.0000 0.20 Factor 3 Class emphasis on learning 8.82 0.0000 0.28 Class learning with peers 5.70 0.0000 0.20 Class discussion about learning 8.69 0.0000 0.28 Helping each other 4.87 0.0000 0.18 Getting along together 7.37 0.0000 0.24 Caring about each other 5.14 0.0000 0.18 Factor 4 Negotiation with students 8.15 0.0000 0.26 Child centred approach 11.80 0.0000 0.34 Caring for students 11.00 0.0000 0.32 Factor 5 Parental involvement 4.49 0.0000 0.16

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One-way analysis of variance within the 15 sub-factors was conducted with the class group as the

independent variable. The effect of membership of a class group on the variance in the data from the respective 15 dependent variables was assessed by calculating eta2. The ANOVA probability and eta2

values show that with the exception of achievement (p > 0.05; eta2 = 0.06) and engaging in schoolwork (p < 0.05; eta2 = 0.07) the variance in data for the majority of the sub-factors could be accounted for by membership of the 27 different class groups. The scale was highly sensitive to differences in 13 aspects of elementary school classroom culture across data from the class groups surveyed.

The refined scale of 59 items is presented in Appendix 3. The items are organised into the five-factor

and 15 sub-factor structure. The items within each sub-factor are ordered from ‘easy’ (common attribute) to ‘difficult’ (uncommon attribute) as indicated by the respective logits alongside each item. The item locations for the items comprising each factors/sub-factor show how the students perceived these factors/sub-factors to be attributes of their classrooms. For example the logits for the parental involvement items are positive (+0.22 to +0.97) as the result of many students ‘disagreeing’ when responding to these items. Alternatively, the predominantly negative logits for the self attitudes and behaviours items was due to many students responding affirmatively to these items.

CONCLUSION

The preceding description of the development and validation of a measure of elementary school classroom culture drew attention to a variety of conceptual and methodological issues. First, is the need to conceptualise clearly the nature of the phenomenon under investigation, to place boundaries around what is to be researched and then to flesh out the constructs hypothesised to comprise the phenomenon. The notion of classroom culture provides a view of classrooms consistent with contemporary assertions about effective learning, effective teaching and school improvement. In this study, it provided a logical frame inclusive of educational outcome attainment, peer interaction within the classroom, the teacher and instruction, and the involvement of parents. Second, when all of the variables to be investigated are included within a single theoretical model and this model is used to develop one scale to measure all these variables, the measurement errors are reduced. In this study, the data analyses clearly evidenced accuracy of measurement. Third is the issue of selecting appropriate statistical tests and assessing how these could be applied in instrument development and validation of the theoretical model under-pinning the research. This study applied a pluralist approach by applying both Rasch and traditional statistics in scale development and theoretical model validation. The utility of conjoint use of both methods of data analysis was evidenced. The study has shown the value of using Rasch statistics to check item thresholds prior to traditional principal components factor analysis to ensure Likert scale items have been answered consistently and logically. The fourth consideration is the difficulty in conjointly applying these methods of data analysis in instrument development to meet the inherent requirements of both methods. The issue here is that the stringencies of both methods may restrict development of instruments intended to meet the requirements of both methods. Alternatively, the solution to this matter might be to apply the strengths of both methods in anticipation of meeting these requirements but to recognise that conjoint fidelity may be difficult to achieve. For example an ideal final factor structure may not be possible.

The study has shown the utility of sequentially applying Rasch Model and traditional statistical tests

for classroom culture attitude scale development. Application of the Rasch Model ensured the ordinal and interval measurement properties of the scale. Application of principal components factor analysis further

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confirmed the construct validity of the scale and its constituent factors. Thus both methods ensured the data fitted the hypothesised theoretical model and the scale was a valid measure of elementary school classroom culture. REFERENCES Andrich, D. (1982) Using latent trait measurement to analyse attitudinal data: a synthesis of viewpoints, in: D. Spearitt

(Ed.), The Improvement of Measurement in Education and Psychology, (pp. 89-126). Melbourne: Australian Council for Educational Research.

Andrich, D. (1985) A latent trait model for items with response dependencies: Implications for test construction and analysis, in: S.E. Embretson (Ed.), Test Design: Developments in Psychology and Psychometrics (pp. 245-275). Orlando, FL: Academic Press.

Andrich, D. (1988a). A General Form of Rasch’s Extended Logistic Model for Partial Credit Scoring, Applied Measurement in Education, 1 (4), pp. 363-378.

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Andrich, D., Sheridan, B., Lyne, A. & Luo, G. (2000). RUMM: A windows-based item analysis program employing Rasch unidimensional measurement models. Perth: Murdoch University.

Banerji, M., Smith, R.M. & Dedrick, R.F. (1997). Dimensionality of an early childhood scale using Rasch analysis and confirmatory factor analysis. Journal of Outcome Measurement, 1(1), 56-85.

Battistitch, V., Solomon D., Watson, M. & Schaps, E. (1997). Caring school communities. Educational Psychologist, 32(3), 137-151.

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Cavanagh, R. F., Dellar, G. B., Ellett, C. D. & Rugutt, J.K. (2000). Development of an instrument for investigating classroom culture. Paper presented at the 2000 Annual Meeting of the American Educational Research Association.

Cavanagh, R.F. & Dellar, G.B. (2001). School improvement: organisational development or community building?. Paper presented at the 2001 Annual Conference of the Australian Association for Research in Education, Fremantle, December 3 -6, 2001.

Cavanagh, R.F., Waugh, R.F. & Dellar, G.B. (2003). The culture, outcomes and improvement of secondary school classrooms. Paper presented at the 2003 Annual Meeting of the American Educational Research Association: Chicago.

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Coleman, P. (1998). Parent, student and teacher collaboration: the power of three. Corwin Press Inc: California. Curriculum Council. (1997).Curriculum Framework . Perth: Curriculum Council of Western Australia. Dalin, P., Rolff, H. and Kleekamp, B. (1993). Changing the school culture. London: Cassell. Fullan, M. (2001). Leading in a culture of change. San Francisco: Jossey Bass. Fullan, M.G. (1993). Change forces probing the depths of educational reform. London: The Falmer Press. Glickman, C.D. (1992). The essence of school renewal: the prose has begun. Educational Leadership, 50 (1). Good, T. L., & Brophy, J. E. (2000). Looking in classrooms (8th ed.). New York, NY: Addison Wesley. Harris, A. (2001). Contemporary perspectives on school effectiveness and school improvement. Harris, A. & Bennett, N.

(eds). School effectiveness and improvement: alternative perspectives. London: Continuum. Johnson, D.W., Johnson, R.T. & Stanne, M.B. ( 2000). Cooperative learning methods: a meta-analysis. Minneapolis:

Cooperative Learning Center. [On-line] Available http://www.clcrc.com/pages/cl-methods.html Lingard, B. (2001). Some lessons for educational researchers: repositioning research in education and education in

research. The Australian Educational Researcher, 28(3), 1-46. McCall, J., Smith, I., Stoll, L., Thomas, S., Sammons, P., Smees, R., MacBeath, J., Boyd, B. & MacGilchrist, B. (2001).Views

of pupils, parents and teachers: vital indicators of effectiveness and for improvement. MacBeath, J. & Mortimore, P. (eds). Improving school effectiveness. Buckingham: Open University press.

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Pena, R.A. & Amrein, A.L. (1999). Classroom management and caring: a primer for administrators and teachers. International Electronic Journal for Leadership in Learning, 3(24).

Rasch, G. (1960/1980). Probabilistic models for intelligence and Attainment tests (expanded edition). Chicago, IL: The University of Chicago Press (original work published in 1960).

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schools. San Francisco: Jossey-Bass Publishers. Sirotnik, .K.A. (1999). Making sense of educational transformation. Phi Delta Kappan, 80(8), 606-610. Soder, R. (1999). When words find their meaning: transformation versus reform. Phi Delta Kappan, 80(8), 568-570. SPSS. (2001). SPSS version 11. Chicago: SPSS Inc. Waugh, R.F. & Cavanagh, R.F. (2002a). Linking classroom environment with educational outcomes using a Rasch

measurement model. Paper presented at the Australian Association for Research in Education Conference, Brisbane.

Waugh, R.F. & Cavanagh, R.F. (2002b). Measuring parent receptivity towards the classroom environment using a Rasch measurement model. Journal of Learning Environments Research, 5(3), 329-352.

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APPENDIX 1: PRIMARY SCHOOL CLASSROOM CULTURE QUESTIONNAIRE Office use only A1 School A2 Teacher A3 My year A4 Class year(s) A5 My gender INSTRUCTIONS If you strongly agree the words describe you or your class ? 3 2 1

If you agree the words describe you or your class 4 ? 2 1

If you disagree the words describe you or your class 4 3 ? 1

If you strongly disagree the words describe you or your class 4 3 2 ? 1. Attitudes towards education and learning Importance of schooling Strongly

Agree Agree Disagree Strongly

Disagree 1 My education is important to me. 4 3 2 1 2 School is important to me. 4 3 2 1 3 I need to do well at school. 4 3 2 1 4 I feel confident about my education. 4 3 2 1 5 I enjoy school 4 3 2 1 6 I don’t like missing school 4 3 2 1 Goal orientation Strongly


Disagree 7 I want to be successful. 4 3 2 1 8 I work towards achieving my goals. 4 3 2 1 9 I feel in charge of my own learning. 4 3 2 1 10 I like to do my work carefully. 4 3 2 1 11 I set goals for myself 4 3 2 1 12 I know what job I would like when I leave school 4 3 2 1 Desire to learn Strongly


Disagree 13 I enjoy finding out how things work. 4 3 2 1 14 Finding new ways to do things is important to me. 4 3 2 1 15 I feel good when I learn new things. 4 3 2 1 16 I ask for help when I get stuck. 4 3 2 1

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17 I enjoy learning. 4 3 2 1 18 I want to learn more 4 3 2 1 2. Learning outcomes and behaviours Achievement Strongly


Disagree 19 I understand the work I have to do. 4 3 2 1 20 I get good marks in my work or in portfolios 4 3 2 1 21 If we have a test or a project I get high marks 4 3 2 1 22 My parent(s) know I do well at school. 4 3 2 1 23 My school reports shows I am a good student. 4 3 2 1 24 I get prizes and rewards for being a good student. 4 3 2 1 Experiencing success Strongly


Disagree 25 I go well at school. 4 3 2 1 26 I am a successful student. 4 3 2 1 27 School-work is easy for me. 4 3 2 1 28 School-work is interesting 4 3 2 1 29 I feel good about the work I do in class 4 3 2 1 30 I learn quickly 4 3 2 1 Engaging in School-work Strongly


Disagree 31 I always do the best work I can do. 4 3 2 1 32 I complete my homework and projects. 4 3 2 1 33 I don’t waste time when I have work to get done. 4 3 2 1 34 I enjoy trying my best 4 3 2 1 35 I work hard at my school-work 4 3 2 1 36 I like to get my work done. 4 3 2 1 3. Peer learning attitudes and behaviours Class emphasis on learning Strongly


Disagree 37 Learning is really important in this class. 4 3 2 1 38 I find new ways to learn in this class. 4 3 2 1 39 We talk about how our learning is going. 4 3 2 1 40 We don’t waste time in this class. 4 3 2 1 41 We all work hard in this class 4 3 2 1 42 School-work is important in this class 4 3 2 1 Class learning with peers Strongly


Disagree 43 The students in this class learn from each other. 4 3 2 1 44 I am interested in what other students say about learning 4 3 2 1 45 We don’t stop each other from working. 4 3 2 1 46 We work well in groups. 4 3 2 1 47 We work together to get our work done 4 3 2 1 48 We help each other to get the work done 4 3 2 1

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Class emphasis on performing well Strongly


Disagree 49 We expect to get good marks in this class. 4 3 2 1 50 We expect the teacher to mark our work quickly. 4 3 2 1 51 We expect to get rewards for doing well. 4 3 2 1 52 There is competition to do the best work. 4 3 2 1 53 We talk about ways to do our work better. 4 3 2 1 54 Getting good marks for tests or projects is important in this

class. 4 3 2 1

Class discussion about learning Strongly


Disagree 55 We talk about important things in this class. 4 3 2 1 56 We talk about how we are going in our work. 4 3 2 1 57 We have discussions about what should happen in this

class. 4 3 2 1

58 We have discussions about things we should be learning. 4 3 2 1 59 We talk about gains we are making in our work. 4 3 2 1 60 We share how we are going with each other. 4 3 2 1 4. Peer support attitudes and behaviour

Helping each other Strongly


Disagree 61 Students look after each other. 4 3 2 1 62 We help each other. 4 3 2 1 63 Our class lets us say what we think. 4 3 2 1 64 We talk about our problems with each other. 4 3 2 1 65 Students who have problems are helped by others. 4 3 2 1 66 Helping each other is important in this class. 4 3 2 1 Getting along together Strongly


Disagree 67 Students look forward to being together. 4 3 2 1 68 Students try to get on well with each other. 4 3 2 1 69 Our classroom is a happy place. 4 3 2 1 70 Other students listen when I give my opinion. 4 3 2 1 71 We enjoy working in groups. 4 3 2 1 72 I have many friends in this class. 4 3 2 1 Caring about each other Strongly


Disagree 73 Students accept each other. 4 3 2 1 74 We care for each other. 4 3 2 1 75 Students are not mean towards each other. 4 3 2 1 76 We look out for each other around the school 4 3 2 1 77 We protect each other. 4 3 2 1 78 We don’t hurt each other. 4 3 2 1

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5. Teacher attitudes and behaviours Negotiation with students Strongly


Disagree 79 The teacher lets us have a say in how or work will be marked 4 3 2 1 80 The teacher gives us work and tests when we are ready. 4 3 2 1 81 We set the due dates for completing work with the teacher. 4 3 2 1 82 The teacher gives us a choice in what we will work on 4 3 2 1 83 We mark our own work quite a lot. 4 3 2 1 84 The teacher lets us set the classroom rules. 4 3 2 1 Child centred approach Strongly


Disagree 85 The teacher is not bossy with us. 4 3 2 1 86 The teacher asks us for helpful hints. 4 3 2 1 87 Our opinions and ideas are important for the teacher. 4 3 2 1 88 The teacher lets us try things ourselves 4 3 2 1 89 The teachers makes us all feel important. 4 3 2 1 90 The teacher takes notice of what we say. 4 3 2 1 Caring for students Strongly


Disagree 91 Our teacher helps students who are picked on by others. 4 3 2 1 92 Our teacher is tough on bullies. 4 3 2 1 93 Our teacher helps students who get in trouble. 4 3 2 1 94 Our teacher helps students with family problems. 4 3 2 1 95 Our teacher seems more like a mum or dad than a teacher. 4 3 2 1 96 Our teacher helps us with our problems 4 3 2 1 Expectations of students Strongly


Disagree 97 The teacher wants us to be focused on our work. 4 3 2 1 98 The teacher is proud of what we do 4 3 2 1 99 The teacher sets high standards for our work. 4 3 2 1 100 The teacher expects us to do well.. 4 3 2 1 101 The teacher encourages us to do our best work. 4 3 2 1 102 The teacher can be tough on students who do not do their

best. 4 3 2 1

6. Parent attitudes and behaviours Strongly Agree

Agree Disagree Strongly Disagree

103 My mum or dad takes an interest in my progress. 4 3 2 1 104 My mum or dad thinks my teacher is doing a good job. 4 3 2 1 105 When I do good work, the school lets my mum and dad

know. 4 3 2 1

106 The school lets my parent/s know how I am going. 4 3 2 1 107 My parent/s often speak or write to my teacher 4 3 2 1 108 My mum or dad helps me with my homework. 4 3 2 1

THANK YOU VERY MUCH FOR TAKING THE TIME TO COMPLETE THIS SURVEY

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APPENDIX 2: ITEM MAP OF LOCATION OF ITEM THRESHOLDS AND LOCATION OF STUDENTS --------------------------------------------------------------------------- LOCATION STUDENTS ITEMS [uncentralised thresholds] --------------------------------------------------------------------------- High Classroom Culture ‘Difficult’/uncommon Items 6.0 | | X | | 5.0 | | | | X | 4.0 X | X | XX | X | X | 3.0 XXX | XX | XXXXX | XXXXXXXXX | XXXXXXXX | 2.0 XXXXXXXXX | 20.3 XXXXXXXXXXXXX | 47.3 50.3 40.3 09.3 59.3 48.3 14.3 XXXXXXXXXXX | 23.3 26.3 44.3 55.3 42.3 43.3 19.3 32.3 31.3 XXXXXXXXXXXXXXX | 12.3 46.3 03.3 04.3 41.3 45.3 22.3 18.3 30.3 XXXXXXXXXXXXXXXXXX | 24.3 55.2 34.3 17.3 01.3 39.3 49.3 53.3 57.3 06.3 54.3 33.3

1.0 XXXXXXXXXXXXXXXXX | 51.3 27.3 05.3 60.3 16.3 55.1 35.3 21.3 02.3 38.3 13.3 25.3 36.3 15.3 58.3

XXXXXXXXXXXXXXXXX | 11.3 28.3 59.2 XXXXXXXXXXXXXXXXXXXX | 52.3 07.3 54.2 29.3 37.3 08.3 10.3 56.3 XXXXXXXXXXXXXXX | 54.1 57.2 60.2 49.1 49.2 XXXXXXXXXXXXX | 47.2 48.2 60.1 27.2 0.0 XXXXXXXXXX | 19.2 20.2 32.2 26.1 58.2 59.1 57.1 26.2 XXXXX | 14.2 39.2 53.2 30.2 45.1 50.2 18.2 45.2 46.2 XXXX | 46.1 43.2 51.1 53.1 04.2 22.2 31.2 56.2 50.1 35.2 44.2 51.2 XXX | 27.1 42.2 56.1 40.1 28.2 48.1 40.2 47.1 52.2 XX | 18.1 02.2 23.2 15.2 13.2 12.2 41.2 39.1 08.2 33.2 09.1 28.1

36.2 09.2 58.1 37.2 -1.0 X | 35.1 33.1 44.1 20.1 52.1 06.2 11.2 19.1 17.2 38.2 | 03.2 43.1 31.1 10.2 32.1 21.2 41.1 11.1 34.2 15.1 36.1 30.1 08.1 24.2 29.2 16.2 | 16.1 01.2 05.2 21.1 05.1 29.1 38.1 37.1 24.1 42.1 07.2 34.1

25.2 10.1 | 22.1 14.1 07.1 | 01.1 04.1 -2.0 | 23.1 25.1 03.1 13.1 12.1 17.1 | 06.1 | 02.1 X | | -3.0 | Low Classroom Culture ‘Easy’/common Items

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APPENDIX 3: REVISED UNI-DIMENSIONAL SCALE OF ELEMENTARY SCHOOL CLASSROOM CULTURE. Factor 1: Self attitudes and behaviours Sub-factor 1: Importance of school and learning Logits 1 I feel confident about my education. -0.64 2 I feel in charge of my own learning. -0.60 3 I like to do my work carefully. -0.57 4 I set goals for myself -0.15 Sub-factor 2: Desire to learn 5 Finding new ways to do things is important to me. -0.55 6 I enjoy finding out how things work. -0.54 7 I want to learn more -0.34 Sub-factor 3: Achievement 8 My parent(s) know I do well at school. -0.53 9 I am a successful student. -0.39 10 My school reports show I am a good student. -0.35 11 If we have a test or a project I get high marks +0.20 Sub-factor 4: Engaging in School-work 12 I always do the best work I can do. -0.47 13 I work hard at my school-work -0.43 14 I enjoy trying my best -0.21 15 I don’t waste time when I have work to get done. +0.12 Factor 2: Clas s group expectations

Logits

16 We expect to get good marks in this class. -0.67 17 Getting good marks for tests or projects is important in this

class. -0.06

18 We expect to get rewards for doing well. +0.28 19 We expect the teacher to mark our work quickly. +0.62

Factor 3: Class group attitudes and behaviours Sub-factor 1: Class emphasis on learning Logits 20 I find new ways to learn in this class. -0.48 21 We talk about how our learning is going. +0.23 22 We don’t waste time in this class. +0.30 23 We all work hard in this class +0.44 Sub-factor 2: Class learning with peers 24 The students in this class learn from each other. -0.44 25 We work together to get our work done -0.38 26 We help each other to get the work done -0.37 27 I am interested in what other students say about learning -0.10 Sub-factor 3: Class discussion about learning 28 We talk about important things in this class. -0.56 29 We talk about gains we are making in our work. +0.11 30 We talk about how we are going in our work. +0.13 31 We share how we are going with each other. +0.22

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Appendix 3 continued Sub-factor 4: Helping each other 32 Helping each other is important in this class. -0.41 33 We help each other. -0.37 34 Students who have problems are helped by others. -0.18 35 Students look after each other. -0.07 Sub-factor 5: Getting along together 36 Students try to get on well with each other. -0.31 37 Our class lets us say what we think. -0.30 38 Our classroom is a happy place. +0.13 39 Other students listen when I give my opinion. +0.30 Sub-factor 3: Caring about each other 40 Students accept each other. -0.11 41 We care for each other. -0.06 42 We look out for each other around the school +0.05 43 We protect each other. +0.15

Factor 4: Teacher attitudes and behaviours Sub-factor 1: Negotiation with students Logits 44 The teacher gives us work and tests when we are ready. +0.33 45 The teacher lets us have a say in how or work will be marked +0.44 46 We mark our own work quite a lot. +0.58 47 The teacher lets us set the classroom rules. +0.73 Sub-factor 2: Child centred approach 48 The teacher makes us all feel important. +0.14 49 The teacher asks us for helpful hints. +0.49 50 The teacher gives us a choice in what we will work on. +0.55 51 Our teacher seems more like a mum or dad than a teacher. +1.32 Sub-factor 3: Caring for students 52 Our teacher is tough on bullies. -0.23 53 Our teacher helps us with our problems. -0.03 54 Our teacher helps students who get in trouble. +0.27 55 Our teacher helps students with family problems. +0.81 Factor 5: Parental involvement

Logits

56 The school lets my parent/s know how I am going. +0.22 57 My mum or dad helps me with my homework. +0.61 58 When I do good work, the school lets my mum and dad

know. +0.62

59 My parent(s) often speak or write to my teacher +0.97

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