Catherine D. Bruce

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 (representing 12 collaborative research teams spread across 8 school boards) and over 2000 students from Grades 3–10. Quantitative analyses revealed significant pre-post gains in students’ fraction knowledge. Qualitative findings revealed some best practices in fractions instruction, including the importance of focusing on unit fractions and number lines to facilitate student sense-making. These findings lead to a detailed discussion of the benefits of (1) focusing on unit fractions as a central construct that allows students to meaningfully work with fractions and make connections across ideas of increasing complexity; (2) leveraging powerful representations as objects-to-think-with that combine concrete and abstract thinking about fractions; and (3) using a design research methodology in the context of collaborative work with teachers.

The aim of this study was to identify when and how the interactive whiteboard (IWB) functioned as a productive tool that impacted student learning in mathematics. Using video data, field notes, and interview transcripts from 1 school year in two optimal case study classrooms, we were able to examine the unique opportunities afforded by the size of the IWB screen, the manipulation of virtual objects onscreen, and related communication using gestures. We: (i) established criteria for defining “significant learning moments”; (ii) assessed these significant learning moments to determine how the interactive whiteboard was supporting the learning; and (iii) isolated the use of gesture during IWB use to magnify the grain size of our analysis and understanding. The data fell into three types of IWB use: productive (89%), reproductive (2%), and problematic (9%). The study recommends that in order to best support student learning, professional development for teachers should emphasize direct and active student use of the IWB to engage students in inquiry of mathematics.

The purpose of this paper is to report on the nature of collaboration in a multi-year, large-scale collaborative action research project in which a teachers’ federation (in Ontario, Canada), university researchers and teachers partnered to investigate teacher-selected topics for inquiry. Over two years, 14 case studies were generated involving six university researchers and 61 teacher researchers. As teacher researchers collected their topic-specific data, university researchers worked in parallel on case studies at the 14 sites in an attempt to gain insights into the types and value of collaboration in collaborative action research. University researchers gathered 20–30 points of data for each case-study site (including teacher researcher final reports as well as journal entries, focus group interviews, field notes, video footage and questionnaires). Through comprehensive cross-case analysis, researchers were able to examine common traits as well as relationships between the nature of the teams, the nature of the projects and their relative success, to highlight conditions that led to robust collaborations. Through pattern matching, hypothesised events were compared with observations to test the claim that a triad of relationships between the team, the team lead and the researchers functioned as a positive collaborative force that propelled teacher team success in a generative ethos, even when faced with substantial challenges.