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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Some Reflections on Teaching Algebra through GeneralizationThis brief commentary chapter devoted to issues suggested by the Mason and Lee chapters raises a number of fundamental questions concerning generalization: the epistemological status of generalization and the nature and complexities of generalization as it is manifested in the didactic context of the algebra classroom.

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The Role of Problems and Problem Solving in the Development of Algebrain an educational approach based on an oversimplified vision of algebra, which hides the semantic background of its grammar. In this chapter, some decisive factors in the evolution of the constitution of algebraic language are discussed in order to extract lessons from history that have a bearing on the teaching of this language today.

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Book 1996o 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 don

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,Einführung in das konsistente Partnering,concepts of variable and function (which appeared much later historically and which occupy a position of growing importance in some programs), and the study of algebraic structures (which marked the school curriculum in the 1960s under the influence of modern mathematics).

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0924-4921 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 geome

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