This chapter presents the second part of the dissertation’s theoretical framework by unfolding the principle of conceptual focus. Building on a clarified notion of conceptual understanding, it substantiates the generic idea of content-related theorizing for the algebra content in view of the dissertation: variables as generalizers and expressions as descriptions of general relationships. To this end, theoretical elements from algebra education, language-responsive mathematics education, and psychological theories of conceptual learning are integrated into the content-related cognitive engagement framework (introduced in Chapter 2). The chapter concludes by arguing that students’ focus on relevant content-specific processes requires targeted scaffolding through design features aligned with three mid-level design principles that refine the principle of conceptual focus: explicating and connecting relevant concept elements, connecting multiple representations, and enhancing a meaning-related language in rich discourse practices.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Principle of Conceptual Focus for the Case of Understanding Variables and Algebraic Expressions

  • Stefan Korntreff

摘要

This chapter presents the second part of the dissertation’s theoretical framework by unfolding the principle of conceptual focus. Building on a clarified notion of conceptual understanding, it substantiates the generic idea of content-related theorizing for the algebra content in view of the dissertation: variables as generalizers and expressions as descriptions of general relationships. To this end, theoretical elements from algebra education, language-responsive mathematics education, and psychological theories of conceptual learning are integrated into the content-related cognitive engagement framework (introduced in Chapter 2). The chapter concludes by arguing that students’ focus on relevant content-specific processes requires targeted scaffolding through design features aligned with three mid-level design principles that refine the principle of conceptual focus: explicating and connecting relevant concept elements, connecting multiple representations, and enhancing a meaning-related language in rich discourse practices.