This Research Forum proposal arises from a recent focus on spatial reasoning that began with a mu... more This Research Forum proposal arises from a recent focus on spatial reasoning that began with a multi-year collaborative project amongst a diverse group of researchers (mathematicians, psychologists, mathematics educators) from Canada and the US, and continues to expand with the goal of: mapping out the terrain of established research on spatial reasoning; consolidating that research within a nuanced discussion of the actualities and possibilities of spatial reasoning in contemporary school mathematics; offering a critical analysis of the theories and practices that define contemporary curriculum and pedagogy of school mathematics in a range of countries and contexts, and, offer examples of classroom emphases and speculations on research needs that might help to bring a stronger spatial reasoning emphasis into school mathematics.
Previous research suggests that access to technology contributes to the implementation of mathema... more Previous research suggests that access to technology contributes to the implementation of mathematics education reform. This case study of three primary (grade 1–3) teachers investigated how access to computers and math teaching software influenced nine dimensions of reform. Teachers were selected on the basis of their commitment to math reform and their technological literacy. Interviews and observations over five months found that technology had its greatest impact by helping teachers expand the scope of their programs and by promoting positive attitudes toward math. Teachers adapted computer tasks to fit their off-line activities, heightening or depleting the contribution of technology to reform. The computer promoted equity of access to all forms and strands of mathematics but this did not necessarily ensure that all students had access to higher math. None of the teachers realized the potential of the computer to increase student-student construction of mathematical ideas, in p...
Canadian Journal of Science, Mathematics and Technology Education
Fractions remain a challenging area of school mathematics at every stage of education, with impac... more 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 powe...
Students are challenged when learning fractions and problems often persist into adulthood. Teache... more Students are challenged when learning fractions and problems often persist into adulthood. Teachers may find it difficult to remediate student misconceptions in the busy classroom, particularly when the concept is as challenging as fractions has proven to be. We theorized that a technology-based learning resource could provide the sequencing and scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students ex...
This Research Forum proposal arises from a recent focus on spatial reasoning that began with a mu... more This Research Forum proposal arises from a recent focus on spatial reasoning that began with a multi-year collaborative project amongst a diverse group of researchers (mathematicians, psychologists, mathematics educators) from Canada and the US, and continues to expand with the goal of: mapping out the terrain of established research on spatial reasoning; consolidating that research within a nuanced discussion of the actualities and possibilities of spatial reasoning in contemporary school mathematics; offering a critical analysis of the theories and practices that define contemporary curriculum and pedagogy of school mathematics in a range of countries and contexts, and, offer examples of classroom emphases and speculations on research needs that might help to bring a stronger spatial reasoning emphasis into school mathematics.
Previous research suggests that access to technology contributes to the implementation of mathema... more Previous research suggests that access to technology contributes to the implementation of mathematics education reform. This case study of three primary (grade 1–3) teachers investigated how access to computers and math teaching software influenced nine dimensions of reform. Teachers were selected on the basis of their commitment to math reform and their technological literacy. Interviews and observations over five months found that technology had its greatest impact by helping teachers expand the scope of their programs and by promoting positive attitudes toward math. Teachers adapted computer tasks to fit their off-line activities, heightening or depleting the contribution of technology to reform. The computer promoted equity of access to all forms and strands of mathematics but this did not necessarily ensure that all students had access to higher math. None of the teachers realized the potential of the computer to increase student-student construction of mathematical ideas, in p...
Canadian Journal of Science, Mathematics and Technology Education
Fractions remain a challenging area of school mathematics at every stage of education, with impac... more 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 powe...
Students are challenged when learning fractions and problems often persist into adulthood. Teache... more Students are challenged when learning fractions and problems often persist into adulthood. Teachers may find it difficult to remediate student misconceptions in the busy classroom, particularly when the concept is as challenging as fractions has proven to be. We theorized that a technology-based learning resource could provide the sequencing and scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students ex...
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Papers by Cathy Bruce