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• Designing a 'modern' abacus for early childhood mathematics

  187-199

  Chrysanthi Skoumpourdi

  Views:

  29

  In this paper, the design of a multi-material, the 'modern' abacus ('modabacus'), for developing early childhood mathematics, is proposed. Presenting the main theories for the design of educational materials as well as similar materials and their educational use, it appears that a new material is needed. The 'modabacus' would be an apparatus which could serve as a multi-material for acting out mathematical tasks as well as a material that could hopefully overcome the limits and restrictions of traditional abacuses and counting boards.

• An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

  13-34

  Róbert Vajda

  Views:

  34

  CreaComp is a project at the University of Linz, which aims at producing computer-supported interactive learning units for several mathematical topics at introductory university level. The units are available as Mathematica notebooks. For student experimentation we provide computational, graphical and reasoning tools as well. This paper focuses on the elementary analysis units.
  The computational and graphical tools of the CreaComp learning environment facilitate the exploration of new mathematical objects and their properties (e.g., boundedness, continuity, limits of real valued functions). Using the provided tools students should be able to collect empirical data systematically and come up with conjectures. A CreaComp component allows the formulation of precise conjectures and the investigatation of their validity. The Theorema system, which has been integrated into the CreaComp learning environment, provides full predicate logic with a user-friendly twodimensional syntax and a couple of automated reasoners that produce proofs in an easy-to-read and natural presentation. We demonstrate the learning situations and the provided tools through several examples.

• Geometry expressions: an interactive constraint based symbolic geometry system

  303-310

  Philip Todd

  Views:

  24

  Dynamic geometry systems such as Geometers' SketchPad or Cabri are productive environments for the exploration of geometric relationships. They are, however, strictly numeric, and this limits their applicability where the interplay between geometry and algebra are being studied. We present Geometry Expressions – a dynamic symbolic geometry environment. While retaining the ease of use of a typical dynamic geometry environment, Geometry Expressions diverges by using constraints rather than constructions as the primary geometry specification mechanism and by working symbolically rather than numerically. Constraints, such as distances and angles, are specified symbolically. Symbolic measurements for quantities such as distances, angles, areas, locus equations, are automatically computed by the system. We outline how these features combine to create a rich dynamic environment for exploring the interplay between geometry and algebra, between induction and proof.

• Das Konzept des Analysisunterrichts von Professor Igor Kluvánek – einige Ergebnisse der qualitativen Forschung

  349-361

  Ján Gunčaga

  Views:

  30

  A renowned Slovak mathematician Professor Igor Kluvanek (1931-1993) during his affiliation with the University of Adelaide in Australia (1968-1990) has worked out a unique course of mathematical analysis for future high school teachers of mathematics. The course has been tested in its conceptual form but, as a whole, it still awaits its publication in the form of a monograph. Along these lines, our aim is to present the way he has introduced some key notions of differential calculus and to discuss its advantages. Central is the continuity of a function via which the limit and the derivative of a function at a point is defined.

• A geometric application to the third-order recurrence relations for sequences

  287-302

  Calin M. Agut

  Ioana E. Agut

  Views:

  31

  Using a third-order linear homogeneous recurrence relation with constant coefficients, it is found a limit-point of a sequence of affixes in plane. Starting from a classic geometric problem, an application is so created and few more nice properties are found and described.