Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Place value, multiplicativity, reunitizing and effective classroom teaching of decimal numeration

Student understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy.