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• Design guidelines for dynamic mathematics worksheets

  311-323

  Markus Hohenwarter

  Judtih Preiner

  Views:

  21

  In a Math and Science Partnership project in Florida, middle school teachers are using the dynamic mathematics software GeoGebra to create interactive online worksheets for mathematics learning. Formative evaluation of these materials based on design principles of multimedia learning has lead to a list of specific design guidelines for such dynamic worksheets that we present in this article. These design guidelines can give advice both for the creation of new dynamic worksheets and the evaluation of existing material on the Internet.

• Kompetenzstreben und Kompetenzerwerb: Funktionale didaktische Fördermöglichkeiten durch Differenzierung und Individualisierung

  1-52

  Hans-Jörg Herber

  Éva Vásárhelyi

  Views:

  32

  As a first glimpse of specific research endeavours the most important components of competence motivation are discussed in relation to didactical questions of gaining competence by inner differentiation and individualization: self-efficacy, optimal challenge, intrinsic motivation, exploration needs, internal attribution, self-determination motivation, defense of self-worth, self-concept, and achievement motivation. In this sense "competence" means ever changing standards of self-regulation of an individual interacting with the various cognitive and emotional demands of his/her environment.
  In fulfilling these requirements a prototypical example of inner differentiation in mathematics instruction is given. This didactical elaboration is available as a selfinstructing unit in Hungarian and German language within the "Electronic periodical of the Department of Methodology of Mathematics" which can be reached under http://mathdid.inhun.com.

• Experimentieren um einen Satz zu finden - vollständig separierbare Mosaike auf der Kugel und ihre Anwendungen

  297-319

  Éva Vásárhelyi

  Views:

  25

  This paper reports a case-study which took place within the project named "Inner differentiation and individualization by creating prototypes and analogies under consideration of motivational constraints (taking into account computer-based teaching and learning)" as a part of a pre-service teacher training at the University of Salzburg (Herber, H.-J. & Vásárhelyi, É.).
  The goal of the experiment was to help students to learn the fundamental concepts and basic constructions of spherical geometry using the Lénárt Sphere (a transparent plastic ball with construction-tools) and some self-made interactive worksheets with the Windows version of the dynamical geometry software Cabri.

• Über einen allgemeinen Übungsbegriff bei verschiedenen Unterrichtsmethoden in der Planung des Mathematikunterrichtes

  175-201

  Gabriella Ambrus

  Views:

  37

  Practice is important in the education of mathematics but is neclected in the didactic of mathematics. One of the reasons is that practice is often defined too "narrowly" and the definitions of practice have in most cases an obscure background theory. In the article a general definition of practice is given, which – in contrast to the usual definitions – views practice from the point of the pupils (practice means activity of pupils). By utilising this definition consequences will be drawn. These consequences serve as for the more exact planning of practice in education as for the analysis of the dependency of practice from teachingsmethods.
  In the second part an example will be presented for planning together practice and lesson, in two different teachingsmethods (traditionel, problemsolving). The analysis of both worksheets (one for each method, identical teachingsmaterial) was made on the basis of authors practise in lessons i.e. her own concepts and the experience with pupils at a class 5. On the basis of the expectable solutions is specified – using a criteriacatalog – what was practised.
  The analysis of practice leads further to the examination of above mentioned dependency from teachingsmethods.

• Concept systematization with concept maps in data modelling

  149-166

  Márta Czenky

  János Kormos

  Views:

  40

  An important goal of concept learning is that students can allocate concepts in the hierarchical system of concepts. In the data modelling course, first, we supported concept systematization with worksheets in which the students had to fill in the blank hierarchical figures of classification of the concepts or blank Venn diagrams describing the relationships between concepts. The hierarchical systems, however, are somewhat restricted to the description of connections. The filling in Venn diagrams did not deliver the expected result, so our attention turned to concept maps. In this paper we introduce the concept maps we drew. Then we evaluate the results of concept mapping survey conducted among students. The survey was done in three courses. We compare the results of our survey with the result of an earlier concept systematising survey.

• Development of spatial perception in high school with GeoGebra

  211-230

  László Budai

  Views:

  38

  In everyday life, on numerous occasions we need to project 3D space onto a plane in order to activate our spatial perception. While our ability in this area can be improved, and considering several national and international research results, the development is even necessary on all levels of education. GeoGebra, as a supplement to previously used tools, has proven to be very useful respective to the development. We have many possibilities to display spatial elements in GeoGebra and to apply such kind of worksheets among 15-18 year old students. I show the results of the 2011/2012 school years connected to the development of spatial perception and the results of an input case survey, which also justifies the need for development.

• Teaching graph algorithms with Visage

  35-50

  Andreas Fest

  Ulrich Kortenkamp

  Views:

  27

  Combinatorial optimization is a substantial pool for teaching authentic mathematics. Studying topics in combinatorial optimization practice different mathematical skills, and because of this have been integrated into the new Berlin curriculum for secondary schools. In addition, teachers are encouraged to use adequate teaching software. The presented software package "Visage" is a visualization tool for graph algorithms. Using the intuitive user interface of an interactive geometry system (Cinderella), graphs and networks can be drawn very easily and different textbook algorithms can be visualized on the graphs. An authoring tool for interactive worksheets and the usage of the build-in programming interface offer new ways for teaching graphs and algorithms in a classroom.