Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic…

When children learn to count and acquire a symbolic system for representing numbers, they map these symbols onto a preexisting system involving approximate nonsymbolic representations of quantity. Little is known about this mapping process, how it develops, and its role in the performance of formal mathematics. Using a novel task to assess…

This experimental study explores how 60 primary-age children's (9-11 years old) understanding of rocks was effected by instruction that used the conceptual structure of the rock cycle together with the analogy of aluminium can recycling. Using a combination of probes into children's understanding, including concept maps and semi-structured…

A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on…

This paper describes the methods and outcomes of a 12-year longitudinal study into the effects of an early intervention program, while reflecting back on changes that have occurred in approaches to research, learning and instruction since the preliminary inception stages of the study in the mid 1960s. We began the study to challenge the prevailing…