Die Habilitationsschrift beschäftigt sich mit der Einbeziehung von Elementen der 3D-Computergrafik in den Unterricht der analytischen Geometrie in der Sekundarstufe II. Vorrangiges Ziel dabei ist, den Unterricht praxisnäher, anschaulicher und attraktiver zu gestalten. Im Bereich des Computereinsatzes im Mathematikunterricht weist die 3D-Computergrafik die Besonderheit auf, dass sie sowohl als Unterrichtsgegenstand als auch als Hilfsmittel für die Visualisierung und für experimentelles Arbeiten von Bedeutung ist. Grundlagen der in der vorliegenden Arbeit angestellten Überlegungen und unterbreiteten Vorschläge bilden einerseits eine Analyse der analytischen Geometrie als schulischer Lerninhalt einschließlich der dabei verfolgten Ziele (Kapitel 1) sowie andererseits die mathematischen Grundlagen der 3D-Computergrafik und ihrer Anwendungen (Kapitel 2). Basierend auf diesen beiden Aspekten werden in Kapitel 3 Potenzen und Ziele des Einsatzes dreidimensionaler Grafiksoftware und der Thematisierung mathematischer Grundlagen der Computergrafik im Stoffgebiet Analytische Geometrie herausgearbeitet. Es wird begründet, dass die Einbeziehung von Elementen der 3D-Computergrafik wesentlich dazu beitragen kann, den Intentionen des Unterrichts in analytischer Geometrie gerecht zu werden und den oft formalen Charakter der Behandlung dieses Themas zu überwinden sowie geometrische Betrachtungsweisen in den Vordergrund zu rücken. In Kapitel 4 erfolgt eine Konkretisierung dieser Überlegungen zu Unterrichtsvorschlägen für die Einbeziehung von Elementen der 3D-Computergrafik in das Stoffgebiet anhand einer Reihe von Gegenstandsbereichen. Erfahrungen aus Unterrichtsprojekten, die auf der Grundlage einiger der in Kapitel 4 entwickelten Konzepte durchgeführt wurden, sind Gegenstand von Kapitel 5. / The book is concerned with possibilities for using the potential of 3D computer graphics in mathematics education in grammar schools, especially in the subject analytic geometry, to improve student''s understanding and motivation. Computer graphics can be used as a tool for visualization of ideas and thoughts and can be also considered as a teaching subject because its mathematical foundations are closely related to the classical contents of mathematics education in grammar schools. Proposals, which are developed in the book, are based both on an analysis of history, aims and problems of teaching analytic geometry (chapter 1) and mathematical foundations of 3D computer graphics and its applications (chapter 2). Based on both aspects potencies and goals of the use of three-dimensional graphics software and the treatment of mathematically based working principles of computer graphics in mathematics education are worked out in chapter 3. It is justified that the inclusion of elements of 3D computer graphics can essentially contribute to the intentions of the instruction in analytic geometry and to overcome the often formal character of the treatment of this topic as well as moving geometrical approaches into the foreground. In chapter 4, these considerations are substantiated and concepts and suggestions for the inclusion of elements of computer graphics into a variety of subject areas are developed. Experiences from instruction projects in analytic geometry classes, that were carried out some of the concepts developed in chapter 4 on the basis, are object of chapter 5.

Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics. The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main attention is paid to localization of learning objects used for teaching and learning mathematics.

School-based professional learning communities (PLCs) have become an important means of “building capacity” among teachers in a wide variety of areas, including those with a subject focus. Very often, these PLCs are mandated by administration, and operate under an established structure. This paper describes an attempt by a mathematics coordinator and school level “lead’ teachers to establish relatively informal PLCs in mathematics in an effort to improve mathematics teaching, and thus student learning, in an environment that focused very much on literacy. The four PLCs created are discussed, as are the opportunities and the challenges that go with the relative freedom offered to the teachers. Sustainability is a central challenge to these groups.

The purpose of this study is to determine the impact on student achievement of elementary school teachers who participated in professional development in the content area of mathematics. Teachers participated in professional development courses and have accumulated a range from three to eighteen total credits from the summers of 1998 through 2007. The impact is measured by student achievement data collected on standardized tests.

Computer Algebra Systems (CAS) have been changing the mathematics instruction requirements for many years. Since the tendency of using CAS in mathematics instruction has been rising for decades and reports have often been positive, the implementation of notebook classes seems to be the consequent next step of mathematics instruction supported by computers. Experiences that have been made with the use of CAS in PC-rooms can be transformed directly into the classroom. Hence the use of CAS is no longer limited to certain rooms. The permanent availability of the notebook with installed CAS offers the chance to realize these concepts that have already been approved with the use of CAS so far. The following speech shall show what these concepts could look like and that the use of notebooks is not only the further development of teaching in PC-classes. Examples from personal experience in teaching will especially show meanders and thought-provoking impulses in order to support teachers finding their way into teaching mathematics instruction in notebook classes successfully. Please allow me to point out two things in the beginning: (1) Yes, I am a vehement supporter of the use of notebooks (and the use of CAS in particular) in mathematics instruction. (2) No, I do not believe that teachers who have chosen another path (or at least partly) are teaching badly.

The network "Developing Quality in Mathematics Education II" is a continuation of the associated project "Developing Quality in Mathematics Education" (http://www.dqime.unidortmund. de). In this project participate universities, teacher education institutions and schools from 11 European countries. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils support developing quality in mathematics education, especially in the area of mathematical modelling. The quality and application of the developed learning materials is also guaranteed by using, comparing and modifying them in eleven different countries. This comparison leads to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus we want to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century. A special feature of this project is the strong connection between theory and practice and between the research and development of mathematics education. In this project our Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava manage testing of translated teaching materials at the high school „Gymnazium Sturovo“. We know that using ICT and didactical software in schools is almost present and wide spread. So we try to focus on several possibilities in solving real-life tasks using this technologies, regard to the fact technologies are hard upon the young generation of students.

Visual modeling concept of integrated constructs (essence) of mathematical objects in teacher training of humanistic area is presented as technology of education in problem solving. The main goal of innovative approach is student’s activity in mathematics on generating of concrete essence manifestations on concepts, methods, theorems, algorithms, procedures and so on. Such student’s activity should be: · Success in an area of actual interests and person’s experience and reached by perception; · Have high level of variability in visual modeling; · Success in domain of reflection process stimulation. Similar creative behavior of persons is typical for actors, dancing, and figure skating and so on. Now we show that such technology will be fruitful for teacher training in mathematics for humanistic specialties.

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This article describes ‘Kidumatica’ – a highly successful project for the promotion of talented students from underprivileged backgrounds. In its 11 year run, Kidumatica has evolved into a way of life for its many students, allowing them opportunities to realize their potential, enter advanced academic studies, and successfully enter a society rich in knowledge and achievement. Kidumatica is based on academic research in the fields of excellence, cognition and mathematics education, and on the social principle of equal opportunity for all and one’s right to self-realization and aspiration, regardless of ethnic background and socio-economic status. Beyond these social/educational purposes, Kidumatica is also a research model and laboratory for testing new programs and teaching methods for gifted students. The following are the basic premises of the Kidumatica model, its goals and how they are achieved, including the recruitment of club members and the mathematical content.