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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.