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By Dominique Guin, Kenneth Ruthven, Luc Trouche

An important motive force of modern progress within the use of arithmetic within the professions has been the help introduced through new applied sciences. not just has this facilitated the appliance of tested tools of mathematical and statistical research however it has influenced the improvement of leading edge methods. those alterations have produced a marked evolution within the specialist perform of arithmetic, an evolution which has now not but provoked a corresponding edition in mathematical schooling, really in school point. particularly, even though calculators -- first mathematics and clinical, then photo, now symbolic -- were chanced on compatible in lots of respects to the operating stipulations of scholars and lecturers, and feature even completed a level of respectable reputation, the mixing of recent applied sciences into the mathematical perform of colleges continues to be marginal. it truly is this example which has prompted the examine and improvement paintings to be mentioned during this quantity. the looks of ever extra strong and conveyable computational instruments has definitely given upward push to carrying on with examine and improvement job in any respect degrees of mathematical schooling. among pioneers, such innovation has usually been obvious as a chance to resume the educating and studying of arithmetic. both, in spite of the fact that, the institutionalization of computational instruments inside academic perform has proceeded at a strikingly sluggish speed over decades.

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Nevertheless‚ this shows that a ‘perfect’ CAS‚ able to simplify ‘ideally’ any expression is a pure dream. 2. BASIC COMPUTATIONS AND LIMITS While the main target users of a tool such as DERIVE are at high school level‚ this is quite different for MAPLE and other general CAS‚ which are designed for the engineer‚ the scientist and the researcher. Thus‚ such software is designed with generality in mind‚ and this can have some undesirable side effects for the student. We give a concrete example below: In general, and as seen in the classroom by the author, the student expects to get f(–1) = –1.

Key words: Computation of limits‚ Computer instrumentation‚ Symbolic integration. Algebra System‚ Reasoned Chapter 2 42 1. 1 Foreword Despite the fact that numerous CAS exist‚ we will work mainly in the present paper with MAPLE (version 5) and DERIVE. Our main interest is in symbolic computation. In such a framework‚ the software becomes a kind of ‘personal assistant’ for computations and experimentations‚ for the researcher‚ as well as the teacher. One of the main problem with a CAS is how to interpret the results‚ in particular when the computations seem to have gone wrong.

Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction. But the NCTM emphasizes, nevertheless, the necessary control by teachers of the integration process: Technology cannot replace the mathematics teacher‚ nor can it be used as a replacement for basic understandings and intuitions. The teacher must make prudent decisions about when and how to use technology and should ensure that the technology is enhancing students’ mathematical thinking.

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