By example of an excerpt of a lesson analysed by J. voigt we want to point to the importance of didactic aspects related to topics ("stoffdidaktisehe" Aspekte) in analysing, planning and performing mathematics education.

Basierend auf verschiedenen Modellen für die Beschreibung von professionellem Mathematiklehrerwissen (Shulman (1987), Ball, Thames und Phelps (2008), Ball und Bass (2009), Baumert und Kunter (2011)) sowie den Konzepten von Schnittstellenaktivitäten und Schnittstellenaufgaben (bspw. Bauer (2013)) wird mit dem sogenannten Schnittstellen-Tetraeder ein eigenes Modell vorgestellt, dass fachbezogenes Professionswissen mit speziellem Fokus auf die Schnittstellenproblematik beschreibt. Eine wesentliche Komponente dieses ...

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order ...

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. ...