Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of…

Structural thinking skills should be developed as a prerequisite for a young person's future mathematical understanding and a teachers' understanding of mathematical structure is necessary to develop students' structural thinking skills. In this study, three secondary mathematics pre-service teachers (PSTs) learned to notice structural thinking…

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…

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 article outlines ways that teachers could use the content in Biomes and Food Security unit in the Australian curriculum, and its state and territory versions, to encourage their students to engage with higher order thinking. It first briefly discusses how to describe and classify higher-order thinking and argues that concepts are central to…

Stephens (2008) described structural thinking as an awareness of the way different occurrences of a mathematical property develop into correct generalisations. Many primary pre-service teachers (PSTs) graduate from their tertiary studies without the ability to notice structural thinking. In this study, two primary PSTs learned to notice structural…

Cross-curricula opportunities afforded by STEM education (Science, Technology, Engineering and Mathematics education), supports an environment where students can develop twenty-first century competencies. One approach to addressing cross-curricula opportunities in STEM education is the introduction of computer science (computer…

This paper is a contribution to the debate on powerful knowledge in geography that began in a 2015 issue of IRGEE and was continued by Frances Slater and Norman Graves in 2016. It addresses some of the questions raised by Slater and Graves. First, it suggests an alternative way of describing and identifying powerful knowledge than the one in their…

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

Assessment of general reasoning processes, elementary algebraic understanding, and novel problem solving of (n=147) seventh- and eighth-grade students found that abilities to generalize from patterns and tables of data and understanding variable constructs contributed significantly to application of algebraic concepts and processes. Questions…

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…