Reinvention of early algebra : developmental research on the transition from arithmetic to algebra

Abstract

In chapter 1 we give our reasons for carrying out this developmental research project on the transition from arithmetic to algebra, which includes the design of an experimental learning strand on solving equations. Chapter 2 describes the theoretical background of the book: current views on the teaching and learning of early school algebra. In particular we discuss the learning difficulties related to obtaining an algebraic mode of thinking - opposed to an arithmetical one - and constructing and solving systems of equations. A brief discourse on the historical development of early algebra and its role in the design of the pre-algebra learning strand constitute chapter 3. In chapter 4 we present the research questions, research method and research plan employed in the study. Chapter 5 contains an account of the design process and learning-teaching experiences with the instructional materials in the first, exploratory phase of the study. The final phase of the study, which includes an overview of the revised learning strand and the overall results, is elaborated in chapter 6. For instance, we argue that symbolizing and reasoning competencies seem to develop independently and that certain errors can be ascribed to arithmetical conventions. Finally, in chapter 7 we conclude with a discussion and a number of recommendations for educational de-signers and teachers. Two sections from one of the the instructional units have been added as an appendix.