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In fact‚ the “modelling as a bridge to algebra” is a theme cutting across several of the book chapters. Many of the more recent approaches to generational activity‚ that are described in Chapters 2‚ 5‚ 6‚ and 13 use real or pseudo-real situations to stimulate algebraic symbolisation. Particular interest lies in the new possibilities for the use of real data generated in real time with data logging devices in technological environments. ‚ a graphics calculator). As students run in the corridor‚ their motion can be graphed in real time and displayed for class discussion.

Algebra can be used to 40 Chapter 3 express and offer insights into those situations. It is in this emergent expression and consequent empowerment that students can discover a need for algebra. In the illustrative lesson the students are also asking questions and being introduced to tools for answering them without this being seen as prescriptive. 4 Conclusion The crucial point is the power of algebra to gain insight into something that you could not do without it: Algebraic symbolism ... introduced from the very beginning in situations in which students can appreciate how empowering symbols can be in expressing generalities and justifications of arithmetical phenomena ...

4 Epistemic Role of Technique So, in the mid-1990s, in France, when computer algebra systems (CAS) began to make their appearance in high school mathematics classes, research attention shifted to the question of technique, to the development of transformational abilities. A team headed by Michèle Artigue (Artigue, Defouad, Duperier, Juge, & Lagrange, 1998; Trouche, 2000) intensively observed (and questioned and interviewed students on) the use of DERIVE in French classrooms. The researchers found that the teachers were emphasising the conceptual dimensions while neglecting the role of the technical work in algebra learning.

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Algebraic surfaces and golomorphic vector bundles by Friedman.

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