The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

This paper examines the differences in school (NAPLAN) outcomes between New South Wales and Queensland. It shows that there are pronounced differences in Year 3 NAPLAN results between these states, though these dissipate when later class years are considered. The reasons for these state effects in school outcomes are explored using an empirical…