Out-of-field (OOF) teaching –when teachers are assigned to subjects outside their formal area of training – has become widespread internationally (Price et al., 2019). While often used to address shortages of subject-qualified teachers, OOF teaching raises concerns about instructional quality (Hobbs & Porsch, 2021; Porsch & Whannell, 2019).

Assuming that subject-specific teacher training leads to the development of specific pedagogical and content knowledge (Baumert et al., 2010), differences arise between OOF and in-field teachers. OOF teachers miss certain important learning opportunities; the resulting lack of knowledge of OOF teachers may impact their quality of teaching and instructional practice (Goos & Guerin, 2022) as knowledge (particularly in mathematics) is the foundation of effective teaching and good pedagogy (Goos et al., 2020). Further, in terms of specific knowledge domains in mathematics, research reveals a lower level of algebra knowledge of OOF teachers compared to the algebra knowledge of in-field teachers (Osei & Agyei, 2023).

In line with this assumption, OOF teachers frequently encounter challenges when bridging complex concepts, connecting content to students’ prior knowledge, and addressing diverse learning needs (Du Plessis, 2015). They also tend to focus their instruction on students with average performance, as the knowledge required to assist weaker or higher-performing students is not always adequately developed in such teachers (Du Plessis, 2015). Notably, OOF teachers often rate their own teaching quality as low (Porsch & Wilden, 2022) and heavily rely on textbooks for instruction (Du Plessis, 2013; Napier et al., 2020). In the field of mathematics, OOF teachers possess more direct transmission beliefs and teacher-centered teaching methodologies (Lane & Ní Ríordáin, 2020).

However, evidence regarding the effects of OOF teaching on student achievement remains unclear, partly due to methodological and conceptual heterogeneity across studies (Porsch & Whannell, 2019). Moreover, little is known about whether teaching experience can compensate for limited formal subject preparation, and whether OOF teaching affects not only cognitive outcomes but also motivational outcomes such as students’ interest in mathematics.

In Austria, OOF teaching is common practice in lower secondary education, especially in non-academic school tracks (Sengschmid et al., 2025). Yet empirical evidence on its effects on instructional quality, student performance, and motivation is scarce. Addressing this gap, the present study investigates the role of OOF teaching in lower secondary mathematics education in Austria, drawing on data from the 2023 cycle of the Trends in International Mathematics and Science Study (TIMSS) 2023.

The study examines both direct and indirect effects of OOF teaching on students’ mathematics achievement and interest in mathematics. Instructional quality is conceptualized as a potential mediating mechanism, while teaching experience is considered as a moderator that may reduce or enhance the impact of OOF teaching. Instructional quality is operationalized through three core dimensions: clarity of instruction, cognitive activation, and classroom management.

Given the pronounced structural differences between academic (AHS) and non-academic (MS) lower secondary schools in Austria, and the uneven distribution of OOF teaching across these tracks, analyses are conducted separately by school-type. The central research questions are:

1. What influence does out-of-field teaching in mathematics have on instructional quality and student outcomes in Austria?
2. To what extent are these relationships mediated by instructional quality and moderated by teaching experience?

Methodologically, the study employs multilevel structural equation modeling to account for the nested data structure and to simultaneously model direct and indirect effects. Instructional quality is modeled as classroom-level latent constructs based on student reports. Bayesian Markov Chain Monte Carlo estimation is applied to address missing data and estimation uncertainty. By jointly considering cognitive and motivational outcomes within a differentiated by school-type, this study contributes to a nuanced understanding of the implications of OOF teaching.

Data and Sample: The analyses are based on data from the Austrian sample of the 2023 Trends in International Mathematics and Science Study (TIMSS). TIMSS assesses eighth-grade students’ mathematics achievement using standardized tests and collects contextual information at the student, teacher, and school levels. The Austrian TIMSS sample is representative of lower secondary education and allows for differentiated analyses by school type. Because OOF teaching is not evenly distributed across school types in Austria—and because student achievement differs substantially between them—all analyses were conducted separately for academic and non-academic lower secondary schools. In non-academic schools, mathematics instruction is often shared by more than one teacher. To ensure a clear attribution of instructional quality to a specific teacher, the sample was restricted to classes taught by one single mathematics teacher. In addition, teachers instructing groups with fewer than five students were excluded to avoid unstable estimates. After applying these restrictions, the final analytical sample comprised 1,389 students in 109 classes in non-academic schools and 2,251 students in 98 classes in academic schools, resulting in a total of 4,629 students from 157 schools. Measures Student achievement in mathematics was measured using TIMSS plausible values. Students’ interest in mathematics was assessed using the TIMSS scale “Students Like Learning Mathematics.” Teaching quality was assessed via student questionnaires and modeled as latent classroom-level constructs, including clarity of instruction, cognitive activation, and classroom management. Teachers’ OOF status was operationalized based on their reported formal education in mathematics. Teaching experience (BTBG01) was included as a main effect as well as in interaction with OOF teaching to assess whether experience moderates potential OOF effects. Additional control variables were included at the student, teacher, and school levels, including indicators of socioeconomic background. Analytical Strategy Given the multilevel structure of the data and substantial missingness – particularly in the teacher education variable – fully Bayesian Markov Chain Monte Carlo (MCMC) estimation was applied using Blimp 4 (Enders et al., 2020). This approach is well suited for multilevel, mixed-type data and allows for principled handling of missingness. Multilevel SEMs were estimated to examine direct effects of OOF teaching on student outcomes, effects on instructional quality, and indirect effects mediated by instructional quality. Models predicting mathematics achievement were estimated separately for each plausible value and combined following procedures analogous to multiple imputation. Bayesian credible intervals and probabilities of direction were used to assess the strength and uncertainty of estimated effects.

This study examined the role of out-of-field teaching in lower secondary mathematics education in Austria, focusing on both cognitive (achievement) and motivational (interest) outcomes, considering instructional quality and teaching experience as key mechanisms. Across models and school types, the evidence for pronounced OOF effects is limited and characterized by uncertainty, indicating that OOF teaching on its own is not a strong determinant of students’ outcomes. For mathematics achievement, no substantial direct effects of OOF teaching were found. Instructional quality showed only weak and statistically uncertain associations with achievement. In AHS, OOF teaching was weakly negatively associated with achievement, but this relationship tend to be moderated by teaching experience and is largely offset by small, imprecise indirect effects via instructional quality. In MS, achievement was more strongly related to students’ socioeconomic background and class composition than to OOF teaching or instructional quality, highlighting the dominant role of contextual factors in this school track. Patterns differed for students’ interest in mathematics. In AHS, OOF teaching showed a tentative total positive association with math interest, although this effect weakened with increasing teaching experience and remained uncertain. In MS, instructional quality emerged as a more relevant predictor—instructional clarity and classroom management positive, cognitive activation negative—of math interest, while OOF teaching showed no meaningful total association. Overall, the findings caution against simplistic narratives that equate OOF teaching with systematically lower student outcomes. While OOF teaching in Austria does not appear to substantially disadvantage student achievement, it may relate to motivational outcomes in school-type-specific ways. Policy efforts should therefore move beyond a narrow focus on reducing OOF teaching and instead emphasize targeted professional support for teachers and, crucially, the reduction of persistent socioeconomic inequalities between students and schools.

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