Assessment and realistic mathematics education

Abstract

This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals, ideas about teaching and learning mathematics, require new forms of assessment. Within RME this means a preference for observation and individual interviews. However, written tests have not been abandoned within this approach. As this book makes clear, even written tests can give teachers valuable information concerning the learning processes of their students, if these tests are looked at in a new light. The book has two sections. Part I forms the core of the work. Chapter one retraces the early years of the reform of mathematics education in the Netherlands, and provides a survey of how assessment was regarded at that time. Chapter two concentrates on how the MORE research laid the foundation for further development of primary school mathematics assessment within RME. Originally, this research was a comparative study of the implementation and effects of different approaches to mathematics education. Chapter three provides a general orientation of the present state of affairs within RME and presents a further elaboration of the RME theory for assessment. In the second half of the chapter the RME views on assessment are held up to the mirror of international assessment reform. In chapter four, as a supplement to the general orientation, the focus is shifted to written tests. In particular, paper-and-pencil short-task problems and the potential enrichment of such problems through the application of RME theory are discussed. Part II describes three assessment studies in detail. Chapter five focuses on one of the tests that was developed for the MORE research, namely the test for beginning first grade. It provides background information on the development of the test and describes its unexpected results, including some international findings on the test. Chapter six gives an account of a study into the opportunities for RME in special education. The heart of this study is a written test on ratio, similar to MORE tests. Chapter seven covers a developmental research project on assessment that was conducted within the framework of the “Mathematics in Context” project, an American middle school project. The chapter focuses on one particular assessment problem on percentage. The main issue here is the tension between openness and certainty that one meets if one moves to more open-ended problems in assessment.