Zdm 

About: Zdm is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Curriculum & Teaching method. It has an ISSN identifier of 1863-9690. Over the lifetime, 1374 publications have been published receiving 38677 citations. The journal is also known as: International journal on mathematics education (Internet) & Mathematics education.

Fostering creativity through instruction rich in mathematical problem solving and problem posing

Abstract: Although creativity is often viewed as being associated with the notions of “genius” or exceptional ability, it can be productive for mathematics educators to view creativity instead as an orientation or disposition toward mathematical activity that can be fostered broadly in the general school population In this article, it is argued that inquiry-oriented mathematics instruction which includes problem-solving and problem-posing tasks and activities can assist students to develop more creative approaches to mathematics Through the use of such tasks and activities, teachers can increase their students’ capacity with respect to the core dimensions of creativity, namely, fluency, flexibility, and novelty Because the instructional techniques discussed in this article have been used successfully with students all over the world, there is little reason to believe that creativity-enriched mathematics instruction cannot be used with a broad range of students in order to increase their representational and strategic fluency and flexibility, and their appreciation for novel problems, solution methods, or solutions

A global survey of international perspectives on modelling in mathematics education

Abstract: In this article we survey the current debate on modelling and, describe different perspectives on this debate. We relate these perspectives with earlier perspectives and show similarities and differences between these different approaches.

What are modelling competencies

Abstract: Modelling and application are seen as a highly important topic for maths lessons But so far the concept «modelling competencies» has not been described in a comprehensive manner: The aim of this paper is to supplement former descriptions of modelling competencies based on empirical data An empirical study was carried out which aimed at showing the effects of the integration of modelling tasks into day-to-day math classes Central questions of this study were—among others: How far do math lessons with focus on modelling enable students to carry out modelling processes on their own? What are modelling competencies? Within the theoretical approach, definitions of modelling processes as a basis for definitions of modelling competencies and important views of modelling competencies are discussed Based on this theoretical approach the transfer into practice is described Finally we will look at the results of the study An analysis of the students' abilities and their mistakes lead to more insight concerning the concept of modelling competencies

The onto-semiotic approach to research in mathematics education

Abstract: In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.

Theoretical and empirical differentiations of phases in the modelling process

Abstract: The reconstruction of pupils modelling processes can be found in many empirical studies within the literature on modelling. The empirical differentiations of the phases, which includes putting statements and actions of the pupils in the right phase, has not been reconstructed from a cognitive psychological point of view on a micro level thus far. In this article different modelling cycles are discussed with attention to distinctions in the various phases. The "modelling cycle under cognitive psychological aspects" is specifically emphasized in contrast to the other cycles. On the basis of the results of the COM²-project (Cognitive psychological analysis of modelling processes in mathematics lessons, Borromeo Ferri) the phases of the modelling process are described empirically. Some difficulties in the process of distinguishing the various phases are also pointed out. Kurzreferat: Die Rekonstruktion von Modellie- rungsprozessen bei Lernenden ist in vielen empirischen Studien innerhalb der Literatur zum Modellieren zu finden. Die empirische Unterscheidung der Phasen, was die Einordnung von Aussagen und Handlungen der Lernenden miteinbezieht, wurde bisher noch nicht aus kognitionspsychologischer Sicht auf einer Mikro- ebene rekonstruiert. In diesem Artikel wird nach einer Ubersicht ausgewahlter Modellierungs- kreislaufe der "Modellierungskreislauf unter kognitionspsychologischen Aspekten im Vergleich hervorgehoben. Somit liegt der Fokus auf einer kognitionspsychologischen Perspektive hinsichtlich des Modellierungskreislaufes. Auf der Basis von Ergebnissen des KOM²-Projekt (Kognitionspsycho- logische Analysen von Modellierungsprozessen im Mathematikunterricht, Borromeo Ferri) werden die Phasen empirisch beschrieben und auch Schwierigkeiten bei der Einordnung in diese Phasen verdeutlicht. ZDM-Classification: C30, D10 1. Different modelling cycles - different approaches and aims Looking at the literature on modelling and applications one can find different modelling cycles. These cycles are different, because they are dependent on various directions and approaches of