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Proceedings of the 13th International Congress on Mathematical Education
This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German...
Traditions in German-Speaking Mathematics Education Research
This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community? These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 185...
The Relationship between Language and Spatial Ability
This work investigates how different fifth-grade students solve spatial-verbal tasks and the role of language in this process. Based on a synthesis of theoretical foundations and methodological issues for supporting the relationship between spatial ability and language, this present study examines and classifies strategies used by students as well as the obstacles they encounter when solving spatial tasks in the reconstruction method.
Technology-Assisted Guided Discovery to Support Learning
Technology is becoming more and more integrated in mathematics teaching and the use of technology is explicitly demanded by the curricula. Technology can be for example integrated while conceptualizing parameters of quadratic functions. In this thesis three technical visualizations (classic function plotter, drag mode, and sliders) for the manipulation of parameters of quadratic functions shall be compared with an access without the possibility of technical visualization. For this purpose, a Guided Discovery environment was developed, which was conducted in an intervention study with 14 classes of grade 9 (N=383). Different strengths and weaknesses of the individual visualizations in favor o...
The Impact of Scale on Children’s Spatial Thought
In this book, Cathleen Heil addresses the question of how to conceptually understand children’s spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps. In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children’s spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children’s spatial thought in those two settings both at a manifest and latent level.
Mathematical Modelling
This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research
Zusammenhänge zwischen Sprachkompetenz und Bearbeitung mathematischer Textaufgaben
Nadine Wilhelm untersucht empirisch, wie sich Sprachkompetenz auf die Bearbeitung mathematischer Textaufgaben auswirkt. Aufbauend auf der grundlegenden Unterscheidung von kommunikativer und kognitiver Funktion von Sprache analysiert sie nicht nur Leseschwierigkeiten, sondern zieht vielschichtige kognitionspsychologische und mathematikdidaktische Beschreibungsansätze für Bearbeitungsprozesse von Textaufgaben heran. Dadurch entsteht ein umfassender und theoretisch abgesicherter Überblick über sprachbedingte Hürden, der einfache Erklärungsansätze relativiert, indem er die komplexen Zusammenhänge zwischen sprachlichen und konzeptuellen Hürden aufzeigt.
Fermi-Aufgaben - Mathematik kompetenzorientiert 78
Wie viele Klavierstimmer gibt es in Chicago? Diese Frage konnte Enrico Fermi recht genau beantworten. Dabei waren seine einzigen Hinweise recherchierbare Daten sowie sinnvolle Schätzwerte und Modellrechnungen. Aufgaben dieser Art haben auf den ersten Blick nur wenig mit Mathematik zu tun. Dennoch sind sie in den letzten Jahren immer bekannter geworden. Mit diesen Fermi-Aufgaben schulen Sie wichtige Kompetenzen, wie Problemlösen und Modellieren. Genau diese Fähigkeiten benötigen die Schüler im Alltag bei offenen Fragestellungen, für deren Beantwortung meist lediglich grobe Schätzungen zur Verfügung stehen: Wie groß ist die Würfelwahrscheinlichkeit für eine bestimmte Zahl bei den ve...
Fermi-Aufgaben - Mathematik kompetenzorientiert 56
Kopiervorlagen mit komplexen Schätzaufgaben oder mathematischen Problemsituationen, die Selbstständigkeit und Kompetenzen wie Modellieren und Problemlösen fördern. Mit Extra-Übungen zur Einführung der Fermi-Methode. Alle Aufgaben mit Tipps und weiterführenden Aufgaben zur Differenzierung. Problemorientierung im Fach Mathematik Die Fermi-Aufgaben, die ihren Namen nach dem begabten Kernphysiker Enrico Fermi erhielten, sind in der letzten Zeit immer populärer geworden. Und das, obwohl sie zunächst nicht viel mit Mathematik zu tun zu haben scheinen - geht es bei ihnen doch eher um Schätzungen, Modellrechnungen und Problemlösungen. Doch im Alltag ist diese problemorientierte Herangehen...
