In math teacher education, dropout research relies mostly on frameworks which carry out extensive variable collections leading to a lack of practical applicability. We investigate the completion of a ...first semester course as a dropout indicator and thereby provide not only good predictions, but also generate interpretable and practicable results together with easy-to-understand recommendations. As proof-of-concept, a sparse feature space together with machine learning methods is used for prediction of dropout, wherein the most predictive features have to be identified. Interpretability can be reached by introducing risk groups for the students. Implications for interventions are discussed.
In an expertise study with 94 mathematics teachers varying in their relative teacher expertise (i.e., student teachers, trainee teachers, in-service teachers), we examined effects of teachers' ...professional knowledge and motivational beliefs on their ability to integrate technology within a lesson plan scenario. Therefore, we assessed teachers' professional knowledge (i.e., content knowledge, pedagogical content knowledge, technological knowledge), and their motivational beliefs (i.e., self-efficacy, utility-value). Furthermore, teachers were asked to develop a lesson plan for introducing the Pythagorean theorem to secondary students. Lesson plans by advanced teachers (i.e., trainee teachers, in-service teachers) comprised higher levels of instructional quality and technology exploitation than the ones of novice teachers (i.e., pre-service teachers). The effect of expertise was mediated by teachers' perceived utility-value of educational technology, but not by their professional knowledge. These findings suggest that teachers’ motivational beliefs play a crucial role for effectively applying technology in mathematics instruction.
•We examined effects of relative teacher expertise on the quality of technology-integration.•We used lesson plans to measure the quality of technology integration.•Relative teacher expertise accounted for quality of lesson plans.•Teachers utility-value mediated the relative teacher expertise effect.
We classify pairs (M,G) where M is a 3‐dimensional simply connected smooth manifold and G a Lie group acting on M transitively, effectively with compact isotropy group.
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