Background: Recent developments in STEM and computer science education put a strong emphasis on twenty-first-century skills, such as solving authentic problems. These skills typically transcend single disciplines. Thus, problem-solving must be seen as a multidisciplinary challenge, and the corresponding practices and processes need to be described using an integrated framework. Purpose: We present a fine-grained, integrated, and interdisciplinary framework of problem-solving for education in STEM and computer science by cumulatively including ways of problem-solving from all of these domains. Thus, the framework serves as a tool box with a variety of options that are described by steps and processes for students to choose from. The framework can be used to develop competences in problem-solving. Sources of evidence: The framework was developed on the basis of a literature review. We included all prominent ways of domain-specific problem-solving in STEM and computer science, consisting mainly of empirically orientated approaches, such as inquiry in science, and solely theory-orientated approaches, such as proofs in mathematics. Main argument: Since there is an increasing demand for integrated STEM and computer science education when working on natural phenomena and authentic problems, a problem-solving framework exclusively covering the natural sciences or other single domains falls short. Conclusions: Our framework can support both practice and research by providing a common background that relates the ways, steps, processes, and activities of problem-solving in the different domains to one single common reference. In doing so, it can support teachers in explaining the multiple ways in which science problems can be solved and in constructing problems that reflect these numerous ways. STEM and computer science educational research can use the framework to develop competences of problem-solving at a finegrained level, to construct corresponding assessment tools, and to investigate under what conditions learning progressions can be achieved.
The present study investigated the development of n = 129 early childhood teachers' mathematics content knowledge, mathematics pedagogical content knowledge, mathematics anxiety, and enjoyment of mathematics over 4 years from teacher training to practice. Latent autoregressive models with crosslagged effects were applied. Scalar measurement invariance of the model also allowed analyses of intraindividual change of knowledge and emotions. Results indicate a decline of mathematics anxiety, an increase of enjoyment and mathematics content knowledge and mathematics pedagogical content knowledge, and medium (emotions) to strong (knowledge) autoregressive but limited cross-lagged effects. No cross-lagged effects between emotions and knowledge over time were found. All but one of the correlations at training disappeared during transition to practice. Theoretically assumed differences between early childhood teachers' knowledge and emotions in teacher training and practice are discussed in light of the results. The transition seems to be more challenging on an emotional level than on a cognitive level. Implications for early childhood teachers' training are given-for example, that pleasant emotional experiences have to be made visible during training.
Educational Impact and Implications StatementThe study gives insight in the development of early childhood teachers' knowledge and emotions in mathematics from training to practice. The study is based both on theories on achievement emotions and on theories on teacher emotions. Based on the findings, implications for early childhood teacher training can be discussed-for example, making emotional facets of mathematics visible or connecting content knowledge with pedagogical content knowledge.
Children develop their mathematical competencies already during their early years. Therefore, effective learning environments provided by early childhood teachers are required. Early childhood teachers' professional competence in mathematics is assumed to consist of different facets such as mathematical content knowledge and affective-motivational dispositions. Mathematics anxiety appears to be a common phenomenon amongst early childhood teachers and it is assumed that children educated by high math anxious teachers develop less mathematical competencies. To test this assumption, n=48 early childhood teachers were tested regarding their mathematics anxiety and mathematical content knowledge and n=362 corresponding children were tested twice within eight months regarding their mathematical competencies. Results indicate that children gain mathematical competencies over the eight-month period and that early childhood teachers' knowledge and anxiety in mathematics are negatively related. However, no effects of teachers' knowledge or anxiety on children's mathematical development were found. The discussion considers methodological implications and emphasizes limitations with respect to differences between the preschool context and primary or secondary school contexts.
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