Place Value and Regrouping as Helpful Constructs to Diagnose Difficulties in Understanding the Place Value System

Abstract

The understanding of place value systems, especially the base-ten place value system, is one of the most important prerequisites to develop numeracy. The understanding of place value systems can be ascribed to two concepts, which in the tradition of the German subject-matter didactics are called regrouping principle and place value principle. Our study aims at clarifying whether these two principles can be used systematically for an effective identification of the gaps in students’ understanding to give a basis for individual support. We therefore conducted a study with N = 100 third graders (8 to 10 years old). We asked the students to work on 7 tasks on translating named units into written numbers using the place value system, in which the place value principle, the regrouping principle or both principles had to be considered. We analysed the errors qualitatively regarding which principle was violated and developed a typification of solution behaviour. The identified individual difficulties by taking the perspective of the two principles can be a starting point for individual support. Our tasks are shown to be a quick and easy way to diagnose students’ individual problems in understanding the base-ten place value system.