Der Autor versucht mit dieser kurzen Einführung eine Übersicht über den Stand der Forschung zu einem Thema zu geben, das in der Forschung bisher noch nicht ausreichend berücksichtigt wurde: der außerschulischen, privatwirtschaftlich organisierten Zusatzbildung, der sogenannten Shadow Education. Der Fokus der Arbeit richtet sich dabei auf die Länder Japan, welches bereits seit den 1970er Jahren ein System außerschulischer Bildungsinstitutionen besitzt, dessen Einfluss auf den Bildungserwerb junger Menschen so stark ist wie in kaum einem anderen Land, und Deutschland, dessen Schattenbildungs- oder Nachhilfesystem noch keinen derartig starken Einfluss ausübt, jedoch in den vergangenen Jahren steten Zuwachs verzeichnen konnte. Interessierten soll dieser Einblick durch die umfangreiche Bibliographie eine Hilfe bei der Recherche zu diesem Thema bieten. / With this short introduction the author tries to provide an overview about the status of research about a theme that has not been sufficiently taken into consideration by researchers yet: the out-of-school, privately organized remedial education or private tutoring, the so called shadow education. Hereby this work focuses on the countries Japan and Germany. While in Japan a system of shadow education exists for decades, which shall lead the Japanese youth to superior results compared to compulsory school education, a comparable influence of institutionalized private tutoring can’t be found in Germany so far. This work shall provide a help to those who want to research about this theme, especially through its comprehensive bibliography.

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.