CHARACTERIZING THEMATIZED DERIVATIVE SCHEMA BY THE UNDERLYING EMERGENT STRUCTURES

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• 作者：Mercedes Garc铆a (1) mgblanco@us.es
  Salvador Llinares (2) sllinares@ua.es
  Gloria S谩nchez-Matamoros (3) gloriasanchezmg@yahoo.es
• 关键词：KEY WORDS consciousness &#8211 ; derivative schema &#8211 ; reflective abstraction &#8211 ; thematization
• 刊名：International Journal of Science & Math Education
• 出版时间：October 2011
• 出版年：2011
• 期刊代码：94_1571-0068
• 类别：soc
• 卷：9
• 期：5
• 页码：1023-1045
• 数据来源：sp

摘要

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action–process–object–schema). The derivative schema is characterized in terms of the students’ ability to explicitly transfer the relationship between a function and its first derivative to the derivative function and the second derivative. This conscious shift of properties of derivatives is differently manifested by the students in the trans level of development of the derivative schema and can be considered evidence of the different characteristics of the thematization of derivative schema. From here we suggest that there are different underlying structures in the constructed schema due to the consciousness in which students use the relations between a function and its derivative.