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