This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

This article takes the position that teachers can use simple manipulative materials to model relatively complex situations and in doing so scaffold the development of students' number sense and early algebra skills. While students' early experiences are usually dominated by the cardinal aspect of number (i.e., counting the number of items in a…

Numeracy needs of nursing students are often underestimated by students when they enter university. Even when students are aware of the mathematics required, students underestimate or overestimate the skills they have. Research has highlighted the mathematics and numeracy skills required of nurses and nursing students and numerous studies have…

This research study investigates how pre-service teachers integrate statistical content, students' thinking, and pedagogy as they examine how 11- to 12-year olds develop mathematically. The findings provide insights into: a) how pre-service teachers identify some of the difficulties that students commonly have, and b) what pedagogical approaches…

This study involving 120 Australian and Chinese teachers introduces a construct of teacher capacity to analyse how teachers help students connect arithmetic learning and emerging algebraic thinking. Four criteria formed the basis of our construct of teacher capacity: knowledge of mathematics, interpretation of the intentions of official curriculum…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school…

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

Rhymes are often useful teaching devices for small children, and can even become a creative resource for teaching mathematics. The students and their teachers can change many of them to better fit their environment and/or extend the rhyme so that higher numbers are involved. A number of rhymes and folk tales lend themselves to more detailed…

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

This item bank was compiled by the Australian Council for Educational research (ACER) to help teachers at the secondary school level construct objective tests in arithmetic and algebra. The multiple-choice items were written by teachers who attended ACER writing workshops. The questions are classified according to their subject content and the…

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…

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 contains the second volume of the proceedings of the 30th Annual 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 60 research reports by presenters with last names beginning between Abr…