ICME 8 - Topic Group 19

Presentation Summary

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This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8), July 14-21, 1996 in Seville, Spain.

Component-oriented tools for exploratory mathematics

Developments in software engineering tools are allowing us to reconsider the mathematical "elements", processes, representations and interfaces within which teachers and learners could express mathematics, manipulate and experiment with. Within the framework of "YDEES", a project funded by the E.U. and chanelled through the Greek General Secretariat for Research and Technology (project EPET II, number 726), exploratory software for mathematics and geography is being developed and used in five exploratory school cultures nurtured within the project. This contribution is about the new possiblitites which we think arise from the component oriented architercture we are adopting for the development of software.

In the past, end-users were restricted to a relatively narrow span of programming languages where "programmers" had to "model" the target application and its domain by utilising a language's data-constructs and devise "algorithms" that implemented the required behavior. In modern object-oriented systems and frameworks, which are traditionally accompanied with large class-libraries, the user manipulates entities with well-defined "behavior" and the focus of the work now shifts to understanding these behaviors and deciding how objects should "communicate" to achieve the required functionality. In a component-oriented world components to the end-users become what Objects are to programmers.

Confronted with the task of building and using a microworld, end-users need not be concerned with "how" things should work. Instead, provided with prefabricated educationally principled components, they define the necessary inter-component "interactions" that would achieve the desired functionality. In this process they are concerned with "behaviors" instead of data-modeling and algorithms. Development becomes a matter of assemblying a "kit" rather than programming - though a programming language is always present wherever it is desirable for mathematical expression. Components:

  1. Are tangible, visible entities featuring simple or complex, passive or active behavior.
  2. Offer high-level and domain specific functionality wherever it is needed and/or feasible (such as map and graphics-chart components), while they can be designed as general purpose, cross-context tools (like the scripting, slider and calculator components).
  3. Provide the capability for nested "emmbeding" within each other, allowing the interactive construction of active (Boxer like) "compound-documents".
  4. Are reusable to a very high degree.
  5. Closely cooperate in a tight synergy environment. Within the project, we are building a set of components which can be linked together in different combinations to form logo-like programming environments, mathematical simulations, data-handling and representing tools, simulations of geographical situations driven by manipulating mathematical parameters. Our main point is not that we can build these specific examples of exploratory mathematics software but that this architercture allows us to rethink of new functionalitites and objects for techers and pupils to explore with.

M. Koutlis, koutlis@cti.gr, Computer Technology Institute (Patras, Greece)
C. Kynigos, Computer Technology Institute and University of Athens

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