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The discrepancy between school and academic mathematics as well as the resulting problems for secondary mathematics teachers' content knowledge (CK) have been well known since Felix Klein pointed out the problem of so-called double discontinuity. However, even today, the field of mathematics education has no clear answer to the question as to what kind of profession-specific CK secondary mathematics teachers need and should be taught during the course of their teacher education. Hence, a model of professional CK for teaching secondary mathematics is required which takes into account the discrepancy between the academic mathematics that teachers learn at university and the school mathematics they teach in school. In order to characterize such a profession-specific CK, this theoretical paper traces and integrates different approaches to bridge this gap. Consequently, a construct called school-related content knowledge (SRCK) is introduced, which describes a profession-specific CK for teaching secondary mathematics concerning interrelations between academic and school mathematics. The conceptualization of this construct encompasses three facets that are illustrated by means of a corresponding operationalization. The distinction of SRCK from the construct of specialized content knowledge is discussed, as are emerging research questions.

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BackgroundConcerning students’ difficulties with fractions, many explanatory approaches are based on the distinction between conceptual knowledge and procedural knowledge. For further research in this field, it is thus crucial to make these constructs accessible to valid measurement.AimsIn this study, we aim at developing a test instrument that affords valid measurement of students’ conceptual and procedural fraction knowledge, including in particular empirical validation of this distinction.SampleThe data used in this study were from 8th‐ and 9th‐grade students (N = 235) in Germany.MethodsFacilitated by expert discussions, items from previous studies were developed further and assigned to either a conceptual scale or procedural scale. Confirmatory factor analysis was used to investigate the underlying structure of the data including model comparisons (1‐dimensional; conceptual–procedural, verbal–non‐verbal). Further analyses in terms of validation focused on reliability and on correlations of the knowledge types with general cognitive abilities.ResultsIt was found that the theoretically assumed 2‐dimensional model fitted the data best. Correlations of the two knowledge types with general cognitive abilities differed significantly. Furthermore, the latent constructs could be reliably estimated from its indicators.ConclusionsOur findings indicate that the empirical separation of conceptual and procedural fraction knowledge is possible: A theoretically grounded test instrument was developed that allows measuring the knowledge types with a sufficient degree of validity. These findings address a research gap that was pointed out repeatedly and gives rise to further research into reasons and remedies for students’ difficulties in dealing with fractions.