Year 5 Students' Available and Accessible Knowledge of Decimal-number Numeration

This paper reports on a study of the decimal-number numeration knowledge held by 112 Year 5 students who had completed formal instruction in tenths and hundredths. It explores the interaction between available and accessible place-value and regrouping knowledge. Available knowledge was elicited through diagnostic test items; accessible knowledge was elicited through an error analysis of the students' numeration procedures used in addition and subtraction algorithms. The results showed that performance varied markedly between classes (indicating an instructional effect), that regrouping was more difficult than place value, and that there was generally a direct relationship between available and accessible knowledge (although there were many instances of high-available and low-accessible knowledge