In this article are the results of research of empirical data from two pedagogical experiences using Mathematical Modeling with two groups: one with 28 students from the last period of a course of mathematics teachers, and another with 21 teachers of a course of continuing education. The objectives of the course were: teach Mathematical Modeling, and in sequence, modeling as a method of teaching. The data about the interest for the proposal and the need of the two groups in learning modeling for use in practice was raised from interviews and issues raised and works done by them. Even though the importance of Mathematical Modeling as a method of teaching is not underestimated, some aspects exemplify the difficulties for the participants in changing the concept of teaching and learning: formation of the participants and the need for formation. Key-words: Mathematical Modeling, possibilities and challenges.

Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

In this paper, creative mathematical activities of school pupils in conditions of the differentiated teaching in Russian Federation are described. Various forms of differentiated teaching (internal – level, external – profile) are characterized. Ways of using entertaining problems for detecting and fostering mathematical abilities are revealed. New course of geometry for differentiated teaching is introduced.

This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers) of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples.

Helmut-Schmidt-Univ./Univ. der Bundeswehr, Diss.--Hamburg, 2005.

Univ., Diss.--Oldenburg, 1998. / Auch als: Berichte // Forschungszentrum Terramare ; 9.

Zugl.: Stuttgart, Univ., Diss., 2007.

Stuttgart, Univ., Diplomarbeit, 2007.

Freiburg i. Br., Univ., Dipl.-Arbeit, 2008. / Angefertig am Mathematischen Institut der Albert-Ludwigs-Universität, Stand 4. Oktober 2005. Fehler ausgebessert: 28. Juli 2008.

Stuttgart, Univ., Diss., 2003.