A cross-sectional study of 132 Australian rural children from grades K-6 assessed children's understanding of the number system. Task-based interview data exhibited lack of understanding of the base ten system, with little progress made during Grades 5 and 6. Few Grade 6 children used holistic strategies or generalised the structure of the number…

One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…

Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

This research report summarises the results of an exploratory teaching program in a primary and secondary school in rural New South Wales, Australia, focused on improving basic mathematics skills. Pupils, aged 11 to 13 years, identified as consistently low-achieving in Mathematics were targeted. The program ran for approximately twenty-five weeks…

The purpose of the study presented in this paper is to investigate how students deal with the concepts of infinity and limit. Based on the communicational approach to cognition, according to which mathematics is a kind of discourse, we try to identify the characteristics of students' discourse on the topic. Four American and four Korean students…

This paper examines the learning needs of 35 Grade 1 children and 60 Grade 2 children who were identified as vulnerable in their number learning on the basis of a clinical interview and reference to a set of research-based growth points. All children were selected for an intervention program that aimed to accelerate learning in four number…

This document contains the fourth volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 64 research report papers: (1) Situated or Abstract: The Effect of…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…

This document contains the third 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 60 research reports by presenters with last names beginning between Ead and Kou:…

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…

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:…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…