Contents Volume 47 2001

Volume Contents

Contents Volume 47 2001     

Mathematik — ein polarisierendes Schulfach

Zusammenfassung Mathematik ist ein polarisierendes Fach, ein Fach, das entweder geliebt oder abgelehnt wird. Der Beitrag fragt nach den Ursachen für eine derartige Polarisierung und beschreibt dabei die Stellung des Fachs Mathematik in der Schule. In einem ersten Teil werden unter Bezug auf die historische Entwicklung des Faches Mathematik die Zielsetzungen des Mathematikunterrichts beschrieben. Dabei wird deutlich, dass im Mathematikunterricht über die historische Entwicklung hinweg für die gymnasiale Bildung st?rker formale Ziele von Mathematik als Geistesbildung formuliert wurden, w?hrend für die Volks-und Realschulbildung st?rker materiale Bildung der Bef?higung zur Umweltbew?ltigung gefordert wurden. In einem zweiten Teil werden Probleme und Defizite des Mathematikunterrichts beschrieben wie die Dominanz von Regeln und Kalkülen und die einseitige Orientierung an einer deduktiv aufgebauten Fachsystematik. In einem dritten Teil werden Konsequenzen und Ma?nahmen zur Behebung der Defizite vorgeschlagen wie die Orientierung an fundamentalen Ideen. Auf der Ebene der Lehr-Lern-Formen wird die Bedeutung produktiver Lernumgebungen hervorgehoben sowie die St?rkung von Eigenaktivit?ten und offenen Fragestellungen gefordert.

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Summary Mathematics — a polarizing subject. Mathematics is a polarizing subject, a subject either beloved or condemned. This contribution asks for the reasons for such polarization and, at the same time describes the position of Mathematics as a school subject. In the first part, the aims of mathematics teaching are described in relation with the historical development of mathematics. It becomes obvious that beyond its historical development mathematics teaching at the Gymnasium (higher type secondary school) was laying stronger emphasis on formal goals of mathematics such as the cultivation of the mind, while at the Volksschule (lower type secondary school) and Realschule (intermediate type secondary school) goals related to the ability of mastering daily life were more strongly demanded. In the second part problems and deficits of mathematics teaching are described, such as the prevailing dominance of rules and calculations and the unilateral orientation towards a deductively constructed systematics of the subject. In the third part consequences and measures for remedying the deficits are suggested, for example an orientation on fundamental ideas. At the level of teaching-and-learning-modes productive learning surroundings are demanded and the support of individually initiated activities and open problems is stressed.

     

Stichwort – Formatives Assessment

Formative assessment is considered one of the most effective frameworks to foster learning. It is defined as assessment of student performance aimed at providing diagnostic information to improve teaching and learning. Basic characteristics of formative assessment are the clarification of learning goals, the diagnosis of individual performance, as well as the provision of feedback and individual differentiation based on the diagnostic information. The design of formative assessment varies from spontaneous on-the-fly assessment to planned and formalized curricular-embedded assessment. Studies support the positive effect of formative assessment on learning with its impact varying depending on the concrete implementation. Although there are developments in politics, science, and schools contributing to the implementation of formative assessment, transfer into practice remains challenging. The present paper describes the current state of research by defining and characterizing the construct, presenting empirical results on its efficacy, and by addressing developments and challenges associated with its implementation.     

Language of instruction and student performance: new insights from research in Tanzania and South Africa

This article, drawing on a set of studies conducted in the framework of the Language of Instruction in Tanzania and South Africa (LOITASA) research project, shows how well African students express themselves if they are allowed to use a familiar African language, and conversely the difficulties they have when forced to use a foreign language, a language they hardly hear and never use outside of school, as a language of instruction. A key finding of the research is that when the foreign language, English in this case, is used, there is a much larger spread in test performance between students. This means that a small group of students succeed while the vast majority sinks. The author therefore argues for working towards a goal whereby African children like children in industrialized countries may study in their own language. Pursuing this goal should be a centrepiece in poverty reduction strategies.