Low Achievers’ Understanding of Place Value – Materials, Representations and Consequences for Instruction

Abstract

A sound understanding of place value is a crucial competence for successful mathematics learning and the flexible handling of bigger numbers. Firstly, the contribution presents in detail the specific meaning of place value as a fundamental idea as well as results of empirical studies with respect to low achievers. For diagnosing the competencies of low achievers dealing with numbers up to thousand, specific test items were designed that cover different levels of representation and that can be used in interviews or as a paper and pencil test. The contribution presents results of a small case study with fifth- and sixth-graders with special needs using the developed test instrument followed by consequences and indications for classrooms activities. These indications touch aspects like diagnosis with respect to basic competencies, the selection of adequate problems or linking different levels of representation. For low achieving students the topic of place value and its didactical implementation should take a more prominent role for didactical proposals and classroom practice.