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.

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

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…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

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…

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…

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the…

Initially differentiating ideas of self-concept, personality, and self-esteem, this paper discusses the development of the self from infancy through adolescence. The discussion of infancy focuses on learning about bodily self and related disruptions and describes the emergence of the social and independent self. The discussion of toddlers and…

This article examines students' ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students…

This document is the fourth volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 42 research reports by presenters with last names beginning between Mul and Wu:…