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The development of proportional reasoning and the ratio concept Part I — Differentiation of stages

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Abstract

Two related problems have to be solved before we can have a clearer picture of cognitive development:

  1. (i)

    Is development hierarchical, leading to higher-order systems controlling lower-order subsytems?

  2. (ii)

    If so, what are the mechanisms involved in a process of development?

These two problems will be studied here taking as example a concept which finds its achievement only in late adolesence: the concept of proportion. Part I of this article is devoted to the first problem. It will bear on the experiment which was undertaken and the analysis of results leading to a differentiation of stages of development. These stages will be illustrated by typical protocols of each stage.

Part II will be devoted to problem solving strategies at each stage, and finally to a second order analysis leading to an attempt to interpret the passage from one stage to the next in terms of increasing equilibration or adaptive restructuring of the strategies put to use to solve problems.

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  1. Gerald Noelting
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Noelting, G. The development of proportional reasoning and the ratio concept Part I — Differentiation of stages. Educ Stud Math 11, 217–253 (1980). https://doi.org/10.1007/BF00304357

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