An extensive body of literature in the economic sciences has focused upon peer effects in education, showing that peer effects exist (Yeung & Nguyen-Hoang, 2016; Ewijk & Sleegers, 2010). In this literature, attention has been brought to the fact that the mechanisms creating the peer effects are still to a large extent hidden in obscurity (Lazear, 2001; Rutter & Maughan, 2002). In this research, distinctions are made between employing exogenous or endogenous independent variables for explaining peer effects (Epple & Romano, 2011). Research using endogenous variables (i.e. measures of students’ aptitude, prior knowledge or behaviour) shed some light on the issue of mechanisms creating peer effects, for instance reporting on the importance of counteracting disruptive classroom behaviour as a means to decrease influence of negative peer effects on student outcomes (Lavy, Paserman, & Schlosser, 2011; Bäckström, 2020).

The issue of peer effects is also addressed in educational sciences, but not as explicitly as in the economic sciences. In educational research it has been labelled as “contextual” or “compositional” effects (Dreeben & Barr, 1988). This literature investigates the peer effects in a wider scope, including issues such as why smaller classes would be better than large classes (Bourke, 1986; Blatchford et al, 2007) or how instruction is affected by class composition (Dumay & Dupriez, 2007; Hansson, 2011).

In educational sciences, there has been a theoretical debate concerning whether teachers’ instruction is dependent or independent of class composition. Benjamin Blooms’ model of Mastery Learning argues that teachers’ instruction is (or should be) independent of class composition, whilst Urban Dahllöfs’ emerging frame factor theory suggest that it is dependent of class composition (Barr & Dreeben, 1977). If the latter is true, I argue that this must be interpreted as a peer effect on instruction, probably also causing peer effects on student results.

The overall aim of the study presented in this paper is to test this argument, that the frame factor theory [ramfaktorteorin] (as later put forward by Ulf P. Lundgren, 1972) can be applied to the issue of peer effects.

At heart of the theory is the concept of “time needed” for students to learn a certain curricula unit, as it was suggested by John Carroll (1963). The relations between class-aggregated time needed and the actual time available, steers and hinders the actions possible for the teacher according to the theory. The theory predicts that the timing and pacing of the teachers’ instruction is governed by a “criterion steering group” (CSG), namely the pupils in the 10^th-25^th percentile of the aptitude distribution in class. Previous studies of Dahllöf (1967; 1971), Lundgren (1972) and Beckerman and Good (1981) report evidence of this hypothesis. The class composition hereby set the possibilities and limitations for instruction, creating peer effects on individual outcomes.

To test if the theory can be applied to the issue of peer effects, I employ multilevel structural equation modelling (M-SEM) on Swedish TIMSS 2015-data (Trends in International Mathematics and Science Study). Using confirmatory factor analysis (CFA) in the SEM-framework in MPLUS, I first specify latent variables according to the theory, such as “limitations of instruction” from TIMSS survey items. The results indicate a good model fit to data of the measurement model.

The preliminary results from this ongoing study verify a relation between the mean level of the CSG and the latent variable of limitations on instruction, a variable which have a great impact on individual students’ test results. The analysis hereby confirms the predictions derived from the theory and reveals that one important mechanism creating peer effects in student outcomes is the effect class composition has upon the teachers’ instruction.

The frame factor theory makes explicit claims about how teachers’ instruction will be affected by class composition during teacher led whole-class instruction. If such effects exist, I argue that this should be interpreted as a mechanism of peer effects in instruction. According to the theory, this effect will be mediated through the mean aptitude of the students in the range of the 10th-25th percentile of the aptitude distribution in class. The teacher will use this group of students (non-expressly) to make decisions concerning the timing and pacing of the instruction (Arlin, 1979). The aptitudes and prior knowledge of this group will also affect the level of the content being taught. In high-achieving classes, elementary units in the curricula will be covered much faster than in low-achieving classes, allowing the teacher to spend more time on advanced units (Dahllöf, 1971; Lundgren, 1972). Departing from the frame factor theory, and from results such as Dumay and Dupriez (2007) and Hansson (2011), I use multilevel structural equation modelling (M-SEM) to specify latent variables from the Swedish TIMSS 2015-data (students N = 4090, teachers N = 200). The method is chosen since the constructs derived from the theory, such as “the class compositions limitations on instruction”, often are not directly observable and are difficult to measure (Loehlin, 2004; Kline, 2015). The method suits educational research well, since it allows analysis of complex constructs and their relations in nested multi-level data (Parkerson et al, 1984; Wenglinsky, 2002; Hansson, 2011). I specify three latent variables. One measuring the limitations on instruction, one measuring occurrence of more advanced instruction and finally one measuring the teachers’ responsibility for students’ learning (derived from Hansson, 2011). The latent variables fit to data is tested using confirmatory factor analysis (CFA) in the SEM-framework of MPLUS. The results indicate a good model fit to data of the measurement model. In contrast to the original studies of Dahllöf and Lundgren, I lack information of students’ prior aptitudes (before receiving instruction and taking the TIMSS-test), information they used to specify the mean level of the CSG of each class. The problem is solved by using the test results for each student to specify a CSG mean level for each class. This solution is acceptable since the main analysis is concerned with the compositional effect on students’ outcomes, not the class.

My research is still in progress, but preliminary results from initial M-SEM-models verify a strong relation between the mean level of the CSG and the latent variable of limitations on instruction, a variable which in turn have a great impact on individual students’ test results. Further analysis is required, mainly concerning how the CSG affect the occurrence of more advanced instruction and the teachers’ responsibility for students’ learning, the two other latent variables specified in the measurement model. So far, the analysis indicates a confirmation of the predictions derived from the frame factor theory and reveals that one of the important mechanisms creating peer effects in student outcomes is the effect the class composition has upon the teachers’ instruction in class.

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