Background
Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another.
Aims
Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics.
Sample(s)
We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects.
Methods
Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied.
Results
In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains.
Conclusions
Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain.
To teach effectively, teachers need subject-specific knowledge, such as content knowledge and pedagogical content knowledge, but also an ability to apply that knowledge to master demanding classroom situations. However, there is no consensus in research whether this ability should be modeled as a subject-specific ability or as a generic ability. This question is important for effective teacher training and especially for out-of-field teaching. In this exploratory study, we investigate the subject-specificity of the ability to apply subject-specific knowledge with German secondary pre-service teachers who are equally trained to teach mathematics and economics. We administered paper-pencil tests for subject-specific knowledge in both subjects to 37 pre-service teachers. In addition, video vignettes of instructional situations were used to elicit their ability to apply that knowledge. N = 6 cases showed apt subject-specific knowledge in both subjects to be analyzed regarding knowledge application. Based on a qualitative analysis of 93 responses to the video vignettes, teachers’ ability to apply that knowledge was examined. Our findings indicate systematic qualitative differences in the pre-service teachers’ responses in mathematics and economics. The results favor a subject-specific conceptualization of teachers’ ability to apply subject-specific knowledge in instructional settings. This implies for teacher training that learning opportunities for promoting teachers’ ability to apply their subject-specific knowledge in instructional settings should be designed specifically for the subject that will be taught. Our study also suggests that out-of-field teachers require training in both knowledge and an ability to apply this knowledge in teaching another subject, as their ability to apply knowledge may not transfer from their field of expertise.
University mathematics studies are known for high dropout especially in the freshmen year. This dropout is often traced back to the excessive demands freshmen have to face. Research aimed at identifying students’ characteristics that enable them to overcome the demands, for example through cognitive abilities, motivational constructs or self-beliefs. In this paper, we take a different perspective and suggest to include a construct that has not been considered in university mathematics education so far: mathematical resilience. Mathematical resilience is a well-established construct in school education to describe students’ attitude in handling everyday educational challenges like setbacks or frustration. We aim to transfer the construct to university mathematics education. Based on a literature review, we argue that the weekly mathematics assignments (i.e., compulsory exercises) pose a major emotional challenge for freshmen as they require advanced mathematical skills like proving, which students only scarcely learn at school. Failing at those mathematics exercises can lead to lasting frustration and, eventually, dropout. Mathematical resilience may thus be a relevant construct to consider when investigating dropout. We present a novel instrument measuring mathematical resilience against mathematics exercises. Findings of an empirical study with 424 mathematics freshmen confirm that mathematics assignments are in fact viewed as the most frustrating everyday challenge. Moreover, the data provide evidence on the validity and reliability of the novel instrument. The results show that mathematical resilience and the corresponding instrument contribute to research on academic success and failure of mathematics freshmen considering the specific conditions of university mathematics studies.
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