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Trotz vielfältiger Bemühungen, Problemlösen als prozessbezogene Kompetenz nachhaltig in den Mathematikunterricht zu integrieren, sind problemlösende Elemente im deutschen Mathematikunterricht nach wie vor unterrepräsentiert. Eine Möglichkeit, dem entgegenzuwirken, stellen Fortbildungsangebote für Mathematiklehrkräfte dar. Wie ein solches Fortbildungsangebot zum Problemlösen in Zeiten der Digitalisierung gestaltet werden kann, wird im folgenden Beitrag dargestellt. Ein besonderer Fokus liegt dabei auf der Gestaltung eines digitalen Angebots, das von den Teilnehmenden flexibel und adaptiv genutzt werden kann. Basierend auf Rückmeldungen von 166 Lehrkräften aus drei Durchführungen der Online-Fortbildung konnten das Angebot optimiert und Implikationen für zukünftige Konzeptionen vergleichbarer Fortbildungsangebote (Online-Fortbildung mit synchronen und asynchronen Elementen) herausgearbeitet werden.

The academic search for principles of high-quality subject-matter teaching has been informed by different perspectives, in particular normative, epistemological, empirical, and pragmatic perspectives. While these perspectives have sometimes been treated as competing, we emphasize the need of their integration to identify sets of principles that can inform professional development programs for quality development. This paper starts from characterizing the four perspectives, and then shows how they are iteratively intertwined in providing a research base for specifying high-quality principles for teaching, in our case exemplified for the school subject mathematics. For this goal, we present the set of five principles that we have deemed as core principles for a new nationwide, ten-year professional development program in Germany: Conceptual Focus, Cognitive Demand, Student Focus and Adaptivity, Longitudinal Coherence, and Enhanced Communication. We will discuss these five principles against their backgrounds stemming from combing normative, epistemological, empirical, and pragmatic perspectives. This set of principles serves as an exemplary case to substantiate our general argumentation that contemporary educational research and professional development activities should not choose between perspectives but strive for combining them.

The selection of tasks based on the evaluation of task features can be considered a core practice of teaching and a relevant component of teaching quality. This is typically part of teachers' preparation for their classroom teaching, which prompts the following question: What are the characteristics of the tasks that teachers use when selecting tasks for differentiated teaching? To answer this question, we analyzed systematic differences in the focus of 78 in-service high school and lower secondary school teachers during the evaluation of task features. The teachers had to select eight tasks about the practice of fractions with respect to their differentiation potential--operationalizing their adaptive teaching competence from a mathematics educational perspective. To analyze the differences, we performed a cluster analysis of the task features that the teachers drew upon. Three groups of teachers could be identified with variations in their focus on directly or indirectly relevant, domain-specific or domain-general task features. Taking into account such variations may explain differences in teaching quality and student outcomes and may be relevant when designing teacher professional development programs.