Background: In learning astronomy, students need to shift between 3D and 2D representations involving complex interactions between the body and material environment. Little attention has been paid to the iconic nature of this astronomical diagramming. Purpose: This research explored the value for students of diagramming to reveal the structural…

Whilst educational goals in recent years for mathematics education are foregrounded the development of mathematical competencies, little is known about mathematics teachers' competencies. In this study, a group of practising teachers were asked to solve an algebra problem, and their solutions were analysed to determine the competencies apparent…

Much recent research and theorizing in the field of reasoning has been concerned with intuitive sensitivity to logical validity, such as the logic-brightness effect, in which logically valid arguments are judged to have a "brighter" typeface than invalid arguments. We propose and test a novel signal competition account of this…

This study investigated how high-ability Australian Aboriginal adolescents reasoned about sources of effort in their transition to secondary schools. High-ability Year 7 Aboriginal adolescents (n = 4) participated in interviews on three occasions: Term 1 Year 6 (primary); Term 1 Year 7 (secondary); and Term 4 Year 7 (post-transition). Parents (n =…

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.

Cosmology presents students with ideas that stimulate their curiosity and brings together various concepts from STEM that call on a variety of reasoning types across multiple representational modes, involving subtleties of spacetime relations, a variety of models and evidence requiring multiple lines of high precision observations. This study…

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…

The goal of this study was to test nonverbal intelligence and neighborhood social capital as protective factors against future delinquency in early adolescent youth placed at risk by virtue of their involvement in childhood conduct problems. Analyzing longitudinal data from 3,028 youth (1,565 boys, 1,463 girls) in one cohort of the Longitudinal…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

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…

A study was conducted to explore the beliefs and practices of 49 New South Wales (NSW) primary school teachers regarding their beliefs and practices concerning the use of concrete materials in the learning and teaching of Number and Algebra. This paper reports on elements of the study regarding why and how teachers use concrete materials. Not only…

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…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…