This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two…

Background: Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is…

Background: Prior research with adults and children suggests that inhibitory control may have a role to play in learning counterintuitive fractions and decimals that are inconsistent with whole number knowledge. However, there is little research to date with primary school-aged children at the early stages of fraction and decimal instruction that…

This study investigated a highly accomplished third-grade teacher's noticing of students' mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom…

The fourth graders were ready to learn long division; however, their teachers were hesitant to begin the unit--just as they are every year. In a grade-level meeting with the school's math consultant, the teachers voiced their typical concerns. The math consultant was a university mathematics education professor spending a semester of sabbatical…

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better…

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

Background: There is increasing interest in applying neuroscience findings to topics in education. Purpose: This application requires a proper conceptualization of the relation between cognition and brain function. This paper considers two such conceptualizations. The area focus understands each cognitive competency as the product of one (and only…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

The focus of this study was to investigate mental computation conceptual frameworks that Heirdsfield (2001c) formulated to explain the difference between proficient (accurate and flexible) mental computers and accurate (but not flexible) mental computers. A further aim was to explore the potential for students' developing efficient mental…

Recent large scale international studies have indicated that while a gender differential in mathematics performance still exists at secondary school level there are few differences in the primary school years. However there is some indication that differences exist in the use of mental strategies rather than in correctness of responses. In this…

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking…

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…