Fractions remain a challenging area of school mathematics at every stage of education, with impacts that extend far beyond the school years. For this study, researchers engaged in classroom-based design research over a 6-year period to investigate effective strategies for teaching fractions with Canadian students. Participants included 86 teachers…

There is a large body of research that suggests a sound understanding of rational number is vital for success in all areas of mathematics, at school and beyond. In the Australian Curriculum, fractions are formally introduced from Year 1, yet there is evidence to suggest that current approaches are not leading to deep understanding in later years.…

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

Presents a set of activities, in reproducible format, emphasizing geometry. The activities offer experiences in area measure, whole number and fractional computation, and problem solving in spatial relationships. (PK)

Research reports from the annual conference of the International Group for the Psychology of Mathematics Education include: "La construcion algorithmique: niveaux ou stades?" (Mesquita); "For Establishing the Generality of Conjectures" (Miyazaki); "Teachers' Attitudes Towards Mathematics and Mathematics Teaching:…

Research reports from the annual conference of the International Group for the Psychology of Mathematics Education include: "A Comparison of Children's Learning in Two Interactive Computer Environments" (Edwards); "On Building a Self-Confidence in Mathematics" (Eisenberg); "Classroom Discourse and Mathematics…

The third volume of this proceedings contains more of the research reports begun in Volume 2. Papers include: (1) "A Semiotic Model for Analyzing the Relationships between Thought, Language and Context in Mathematics Education" (Juan D. Godino and Angel M. Recio); (2) "Conceptions as Articulated in Different Microworlds Exploring…

The first volume of this proceedings contains an introduction and the plenary, research forum, working group, and discussion group papers. Papers include: (1) "Resources as a Verb: Recontextualizing Resources in and for School Mathematics" (Jill Adler); (2) "Markets and Standards: The Politics of Education in a Conservative Age" (Michael Apple);…

The second volume of this proceedings contains the first portion of the research reports. Papers include: (1) "Learning Algebraic Strategies Using a Computerized Balance Model" (James Aczel); (2) "Children's Perception of Multiplicative Structure in Diagrams" (Bjornar Alseth); (3) "A Discussion of Different Approaches to Arithmetic Teaching"…

The fourth volume of this proceedings contains 29 full research reports continuing on from Volume 3, 84 short oral communications (abstracts only) and 34 poster presentations (abstracts only). The full papers include: (1) "Beliefs, Teacher Education and the History of Mathematics" (George N. Philippou and Constantinos Christou); (2)…