Teachers’ qualifications, characteristics, and practices are important prerequisites for student learning (Goe, 2007; Hattie, 2009). Teacher practices have been found to affect and promote students’ motivation, attitudes, behaviour, and achievement (Hattie, 2009; Wang & Degol, 2016; Nilsen & Gustafsson, 2016). During each lesson, teachers must be able to master a multitude of processes and complex social interactions and the teacher’s actions, attitudes and behaviour are important classroom factors that correlate with student achievement (Brophy & Good, 1984; Hattie, 2009). The main objective of the current study is to investigate the relationships between different processes of teacher practices, school climate and students’ mathematics achievement using data from Trends in International Mathematics and Science Study (TIMSS) 2019. 

Teacher practices can appropriately be described as instructional quality (InQua) which often includes the dimensions of classroom management, clarity of instruction, supportive climate, and cognitive activation (Nilsen & Gustafsson, 2016). The current study will include the first two dimensions. The first dimension, classroom management, refers to the activities undertaken by the teacher within the classroom to instruct and engage students in learning, establish rules and social norms (Nilsen & Gustafsson, 2016). The second dimension, clarity of instruction, is teachers’ use of pedagogical techniques in providing their students with clear instructions, support and challenges when needed and linking new concepts to students’ previous knowledge (Mullis & Martin, 2017; Nilsen & Gustafsson, 2016). No scales for investigation of a  supportive climate and cognitive activation are included in the student questionnaire in TIMSS 2019. InQua has been found to relate to student achievement in several studies (Fauth et al. 2014; Nilsen, Scherer, R & Blömeke, 2018) whereas other research has found that student achievement was not well predicted by InQua (e.g., Blömeke, Olsen & Suhl, 2016). This study aims to contribute to the field of InQua.

Out of several possible mediators, school climate could be related to achievement. School climate is a multidimensional concept and is currently lacking consensus on its definition. In this study, it is conceptualized as the social-psychological environment (Fan & Williams, 2018). The literature has shown some evidence that there is an association between InQua and school climate (Scherer, Nilsen & Jansen, 2016), and it is thus possible that school climate to some degree is mediated by InQua on achievement. In this study, school and classroom climate characteristics are indicated by students' self-reported sense of belonging and bullying. Another possible mediator, or moderator, could be the social composition of the school (Nilsen & Gustafsson, 2016). Nilsen and Gustafsson (2016) found an interaction effect with student social background, indicating that a positive school climate could compensate for the negative effects of students’ low socioeconomic background (SES) on achievement. This will be included in the analysis.

Against this background, the present study aims to investigate the relations between achievement in mathematics and InQua, using TIMSS 2019 data. This study will also investigate a mediation model where InQua has a direct effect on math achievement and mediate an indirect effect from school climate on math achievement. Three research questions will guide this study:

1. What are the relations between instructional quality and student achievement in mathematics? 

2. To what extent may background characteristics moderate the relation between instructional quality and student achievement in mathematics?
3. To what extent can school and classroom climate factors be mediated via instructional quality on achievement in mathematics?

TIMSS is a recurring international large-scale assessment of students’ achievement in mathematics and science. National samples of students are accomplished through a cluster design in which complete classrooms are drawn (Mullis & Martin, 2017). This allows for aggregating individual student responses on a classroom level and investigations of classroom effects. The total sample for Swedish TIMSS 2019 comprised 3,965 students in 224 classrooms (Grade 4). The measures selected for the current study are student self-reported assessments from the student questionnaire on the two dimensions related to InQua, in all, 12 indicators. As proxies for school- and classroom climate, the scales in TIMSS 2019 of students’ perceptions of bullying and sense of belonging (Rutowski & Rutowski, 2016) are used, in all 16 indicators. Background variables such as dummy-gender, SES, language, teacher- and school characteristics are included in the analysis to investigate possible moderating relations. For achievement, all five plausible values are included in the analysis. The statistical analysis consisted of confirmatory factor analysis (CFA) for testing each of the latent constructs included in the measurement model. These constructs were tested at both within and between levels. The measures of model fit, χ2 goodness-of-fit test, Root Mean Square Error Approximation (RMSEA), the Standardized Root Mean Square Residual (SRMR), and the CFI goodness-of-fit measure were used (Brown, 2006). Intraclass correlations (ICC) were estimated and due to the analysis of the ICC being close or above 10% for most items, full two-level models were estimated (Brown, 2006). Mplus version 8.6 was used for estimating and testing the models together with the missing data option (Muthén & Muthén, 1998-2017). SPSS version 27 was used to clean and prepare the data. To address the first two research questions, CFA and SEM models were estimated. In the first step, each of the three constructs of InQua was tested separately in a confirmatory factor model. The conceptual model was then tested in a full structural model including all three factors, InQua, school climate and math achievement. This resulted in a conceptual mediation model, where InQua is related directly to math achievement and mediates school climate and school climate to math achievement, thus school climate may be mediated in an indirect effect.

This is an ongoing study. So far, the first analysis with separate CFA for each construct was estimated with good fit. Second, a CFA was estimated with the two factors measuring InQua. The model had good fit, and standardized covariances between the factors ranging from .17 to .49, and standardized factor loadings ranging from .55 to .88. The first plausible value in mathematics was also included in the model which showed good fit (RMSEA = 0.042). Third, a two-level SEM model was estimated with the same relations for the within- and between-levels which showed good fit (RMSEA = .036; SRMRw = .026, SRMRb = .082). The standardized factor loadings ranged from .56 to .86 at the within-level and .84 to .99 at the between-level and the standardized covariances for the within-level ranged from -.13 to .46, and the between-level -.29 to .62. Including the first plausible value in mathematics showed good fit (RMSEA = .035; SRMRw = .024, SRMRb = .080). Next, in the forthcoming analysis, background variables will be added to the model, one at a time and, also modelling the relative effects of students’ prerequisites on mathematics achievement. Finally, models with mediation effects will be estimated with direct effects between the two dimensions of InQua and achievement and indirect relations from school climate. Grade 8 data may be included in the forthcoming analysis which enables investigations of possible differences and similarities between younger and older students. Taken together, these preliminary results suggest there is construct validity in the dimensions of InQua in TIMSS. Expected findings will show an association between InQua and school climate on student achievement in mathematics.

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