By Celia Hoyles (auth.), Christine Keitel, Kenneth Ruthven (eds.)

ISBN-10: 3642785425

ISBN-13: 9783642785429

ISBN-10: 3642785441

ISBN-13: 9783642785443

The NATO complicated learn Workshop on arithmetic schooling and expertise was once held in Villard-de-Lans, France, among may well 6 and eleven, 1993. Organised at the initiative of the BaCoMET (Basic elements of arithmetic schooling for lecturers) team (Christiansen, Howson and Otte 1986; Bishop, Mellin-Olsen and van Dormolen 1991), the workshop shaped a part of a bigger NATO programme on complicated academic expertise. a few workshop participants had already participated in past occasions during this sequence and have been capable of give a contribution insights from them: equally a few individuals have been to participate in later occasions. The difficult for the workshop drew cognizance to big speculative advancements within the functions of complicated details expertise in arithmetic schooling during the last decade, particularly clever tutoring, geometric development, symbolic algebra and statistical research. Over a similar interval, extra undemanding kinds of details expertise had began to have an important impression on instructing methods and curriculum content material: significantly mathematics and picture calculators; average laptop instruments, similar to spreadsheets and databases; and computer-assisted studying programs and computing device microworlds especially designed for academic purposes.

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Writing systems are the prime examples of cognitive technologies, but more specific to mathematics are mathematical notation systems and theories and, more recently, computational devices. Each cognitive technology for mathematics changes the way the subject is done and potentially transforms the practice of mathematical education as well. In some overt and covert ways, it may affect subject matter, curriculum, instruction, learning styles, and the types of cognitive demands made on students. Computer Algebra Systems (CAS)l are the most recent cognitive technologies to create new opportunities as well as dilemmas for mathematics education, particularly at the post-secondary level.

Neither one is satisfactory since these systems do more than manipulate symbols and more than just algebra. The term Computer Mathematics System (CMS) has been suggested (by D. Shumway) but has yet to be adopted. In this chapter we will use the abbreviation CAS to denote either a single system such as MAPLE or the whole family of such systems. 19 In this paper, we begin showing some very simple examples of the power of CAS and then we trace their historical genesis from a limited tool for specialized scientific problems into a cognitive technology for mathematics.

The authors emphasized that the main contribution of computer algebra to scientific work is that it expands the "frontiers of intractability" of a scientific theory. Since exploring the mathematical implications of scientific theories often involves a huge number of algebraic operations, subsequent results, even once they are published in journals, are nearly impossible to follow and verify. However, by using a computer algebra system, verification of such computations is feasible, thus rendering a particular theory more open to scrutiny.

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Learning from Computers: Mathematics Education and Technology by Celia Hoyles (auth.), Christine Keitel, Kenneth Ruthven (eds.)

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