<p style="text-align: justify;">Research on instructional quality has been of great interest for several decades, leading to an immense and diverse body of literature. However, due to different definitions and operationalisations, the picture of what characteristics are important for instructional quality is not entirely clear. Therefore, in this paper, a scoping review was performed to provide an overview of existing evidence of both generic and subject-didactic characteristics with regard to student performance. More precisely, this paper aims to (a) identify both generic and subject-didactic characteristics affecting student performance in mathematics in secondary school, (b) cluster these characteristics into categories to show areas for quality teaching, and (c) analyse and assess the effects of these characteristics on student performance to rate the scientific evidence in the context of the articles considered. The results reveal that teaching characteristics, and not just the instruments for recording the quality of teaching as described in previous research, can be placed on a continuum ranging from generic to subject-didactic. Moreover, on account of the inconsistent definition of subject-didactic characteristics, the category of ‘subject-didactic specifics’ needs further development to establish it as a separate category in empirical research. Finally, this study represents a further step toward understanding the effects of teaching characteristics on student performance by providing an overview of teaching characteristics and their effects and evidence.</p>

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Zusammenfassung Als fachdidaktisches Prinzip ist ‚Orientierung an fundamentalen Ideen' keine neue, gleichwohl eine Forderung, die in ihren curricularen und unterrichtlichen Implikationen z.T. unklar erscheint. Ausgehend von einer Kontrastierung mit Konzeptionen lokaler Ideen wird eine Neuinterpretation einer Orientierung an fundamentalen Ideen vorgeschlagen. In dieser Neuinterpretation wird dem Finden einer geeigneten Balance in doppelter Hinsicht eine zentrale Rolle für die fachdidaktische Forschung und den Mathematikunterricht der gymnasialen Oberstufe zugewiesen; einerseits zwischen dem ‚Vollzug' und der Reflexion mathematischer Handlungen und Tätigkeiten, andererseits zwischen der Gewährung von Kohärenzerfahrun-gen und dem Zulassen offener Differenzerlebnisse.Schlüsselwörter Fundamentale Ideen · Bildungstheorie · Kohärenzstiftung · Mathematikunterricht in der Oberstufe Mathematics Subject Classification (2000) 97-D20 · 97-D30 · 97-B40 · 97-C99 · 97-H60 Abstract Using fundamental ideas as guidelines in mathematics education is a rather old didactical principle. However, up to now its implications for curriculum planning and classroom activity haven't been specified very precisely. By contrasting fundamental ideas with local ideas a revised interpretation of 'guidance by fundamental ideas' will be outlined as an alternative. This alternative emphasizes the importance A. Vohns ( ) 228 A. Vohns of finding a balance within mathematics education research and classroom practice in the upper secondary school; both between 'executing' mathematics and reflecting mathematics and between experiencing coherence and undergoing non-sequitorial moments and alienation.

In its day-today regime the mathematics classroom is mainly focused on students' mastery of specific knowledge and skills currently at hand. But do they see the bigger picture? Do they get an appropriate idea of what mathematics is essentially about? Fundamental ideas have been a regularly proposed way to outline the bigger picture. That is, to provide both mathematics educators and students with several central themes that interconnect the different areas of mathematics and its applications. Such ideas should be able to guide the selection, organization and presentation of curriculum content and subsequently make mathematics more understandable for students. This article aims to offer the English-speaking reader an overview of important stages in the specific development of the understanding of fundamental ideas within the German-speaking community of mathematics education. It embeds this line of research within the subject matter didactics tradition that this volume is dedicated to and it draws comparisons to and discusses relations between "Grundvorstellungen" and fundamental ideas.