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.

Information and Communication Technology (ICT) education has been actively implemented around the world recently. ICT curriculum in schools is intended to improve students' programming-oriented thinking rather than to train them as programmers. The core of ICT education is 'computational thinking'. Computational thinking is taking an approach to…

Explaining appears to dominate primary teachers' understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop…

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

Background: A fundamental aim of standardized educational assessment is to achieve reliable discrimination between students differing in the knowledge, skills and abilities assessed. However, questions of the purity with which these tests index students' genuine abilities have arisen. Specifically, literacy and numeracy assessments may also engage…

This paper presents an Early Mathematical Patterning Assessment (EMPA) tool that provides early childhood educators with a valuable opportunity to identify young children's mathematical thinking and patterning skills through a series of hands-on and drawing tasks. EMPA was administered through one-to-one assessment interviews to children aged 4 to…

As classrooms continue to diversify, there is an increasing need to understand children's inclusive behaviours and moral reasoning. Research shows that epistemic beliefs (beliefs about knowing and knowledge) can influence reasoning for adults, but we know little about this relationship in younger children or how classroom contexts relate to…

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…