학술논문
Characterizing the development of a schema for representing and solving algebra word problems by pre-algebraic students engaged in a structured diagrammatic environment.
Document Type
Theses
Author
Source
Dissertation Abstracts International; Dissertation Abstract International; 71-03A.
Subject
Language
English
Abstract
Summary: The tenets of Realistic Mathematics Education's theory of lesson design were employed in choosing the scope and sequencing of the tasks. Using APOS theory (Dubinsky, 1991), Simon and colleagues' (2004) activity-effect theory, and Gray and Tall's (2007) procept theory, the nature and development of students' algebraic understandings were examined. It was found that students developed four overarching understandings. Three of these understandings are prominent in the literature as being prerequisite to a students' algebraic development. Underlying and supporting students' development of these understandings were the following conceptions: an additive quantity can be treated as a process and an object (a procept), a quantitative whole is decomposable, and the parts of a quantitative whole are commutative.