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Titlebook: Approaches to Algebra; Perspectives for Res Nadine Bernarz,Carolyn Kieran,Lesley Lee Book 1996 Kluwer Academic Publishers 1996 algebra.arit

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發(fā)表于 2025-3-21 16:10:25 | 只看該作者 |倒序瀏覽 |閱讀模式
期刊全稱Approaches to Algebra
期刊簡稱Perspectives for Res
影響因子2023Nadine Bernarz,Carolyn Kieran,Lesley Lee
視頻videohttp://file.papertrans.cn/161/160299/160299.mp4
學科分類Mathematics Education Library
圖書封面Titlebook: Approaches to Algebra; Perspectives for Res Nadine Bernarz,Carolyn Kieran,Lesley Lee Book 1996 Kluwer Academic Publishers 1996 algebra.arit
影響因子In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney‘s second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid‘s Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool
Pindex Book 1996
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沙發(fā)
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978-0-7923-4168-0Kluwer Academic Publishers 1996
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Mathematics Education Libraryhttp://image.papertrans.cn/b/image/160299.jpg
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,Einführung in das konsistente Partnering,en reduces algebra), the solving of specific problems or classes of problems (which has played an important role historically in the development of algebra and its teaching), the generalization of laws governing numbers (a very strong focus in certain curricula), the more recent introduction of the
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Hansj?rg Gaus,Christoph Emanuel Müllermetric analysis, as well as the theory of proportions, played an important role in the development of algebra in the Renaissance. Until Viète’s algebraic revolution at the end of the 16th century, geometry was a means to prove algebraic rules, and, likewise, algebra was a means to solve some geometr
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Ergebnisse der empirischen Untersuchung,tremely effective. After a reflection on my own immersion into algebra and the evolution of attitudes toward the teaching of algebra, a teaching experiment using generalization activities is presented. Two generalizing activities are described in some detail, looking at the behavior of adults in the
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