The three dimensional model of instructional quality (cognitive activation, classroom management, and supportive climate) is assumed to be essential for effective teaching irrespective of the subject taught (Klieme and Rakoczy, 2003). However, in order to compare teaching quality across subjects, measurement invariance must be established. In the German national extension of TIMSS 2015, fourth grade students gave their ratings on each of the three dimensions of instructional quality for their mathematics and science lessons. The same items were used for both subjects, once referring to mathematics and once to science classes. A similar approach was used in the Norwegian TIMSS Advanced sample asking for teaching quality in mathematics and physics lessons. In this paper, the ratings from Germany and Norway are used to check for measurement invariance across the two subjects. For that purpose hierarchical structural equation models (Goldstein & McDonald, 1988; Muthén, 1989; Rabe-Hesketh, Skrondal & Pickles, 2004; Mehta & Neale, 2005) are used. The clustered data structure will be taken into account by using a maximum-likelihood estimator with robust sandwich standard errors to protect against being too liberal (Muthén & Muthén, 2012). Missing data were handled by using the full-information-maximum-likelihood (FIML) procedure implemented in Mplus. Previous research on measurement invariance of teaching quality between subjects is scarce (e.g., Kember & Leung, 2011; Scherer & Gustafsson, 2015). However, first analysis using the German field test data indicate that the three dimensional structure can be found across subjects. Further hypotheses have to be formed based on the theoretical conceptualization of each dimension of instructional quality. It appears likely that measurement of supportive climate and classroom management does not vary substantially between subjects as both dimensions are conceptually independent from the content being taught (see also Praetorius et al. 2015; Scherer & Gustafsson, 2015). However, different aspects of cognitive activation might be stressed in teaching different content (Klieme, 2009). Therefore, measurement invariance might not be found for cognitive activation.

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