Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Introduction Over the past 25 years, the research colloquium leaders have individually and in sub... more Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms (e.g., Davis & Simmt, 2006; Martin, McGarvey & Towers, 2011; Martin & Towers, 2011; McGarvey & Thom, 2010; Proulx, Simmt & Towers, 2009; Thom & Glanfield, 2018). While our work has contributed to meaningful insights into mathematical understanding of learners and teachers, we realized that the methodological tools developed and used were limited due to the vast and intricate range of dynamic interactions (Martin, McGarvey & Towers, 2011; Simmt, 2011). This led us to working systemically on the mutual concern: How might we observe, document, display and analyze data from a collective learning systems approach? Building on our previous PME(NA) working group, NCTM research symposium, and PME research forum, in this colloquium we will present our work ...
Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent resea... more Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatial skills that are predictive of success in engineering education and the types of intervention activities that have demonstrated improved performance in STEM subjects. In doing so, we identify parallel assessment measures, skills, and tasks in the development of a spatial skills framework for young engineers that includes physical and mental rotation, symmetry properties, paper folding and unfolding, and cross-cutting objects. These skills are developed through 3D modelling and 2D representational drawings. We illustrate the skills in the framework with samples of work from students in grades 2 and 3 in response to a series of linking-cube tasks in a cube-creature project.
2017 Conference of the Canadian Society for the Study of Education, Feb 7, 2017
The purpose of our pilot study was to identify what Canadian preschool teachers noticed as opport... more The purpose of our pilot study was to identify what Canadian preschool teachers noticed as opportunities for teacher-child mathematical interactions in the classroom and to investigate the value of video as a professional development tool to prompt increased attention to and awareness of different possibilities for mathematical interactions. Using the framework of teacher noticing, we interviewed six preschool teachers to establish an initial baseline of their perspectives and current practices of mathematical interactions. The teachers then participated in three professional development sessions over four-months using collaborative video viewing of classroom routines. Through the sessions the teachers
Knowledge mobilization is becoming increasingly important for research collaborations, but few me... more Knowledge mobilization is becoming increasingly important for research collaborations, but few methodologies support increased knowledge sharing. This study provides insights, using a reflective narrative, into a transdisciplinary knowledge-sharing investigation of the connectivity of educational research to that of other disciplines. As an exemplar for educational research, the study evaluated the use of spatial search terms from mathematics education using: 1) an initial descriptive statistical analysis combined with bi modal network analysis of highly cited articles; and, 2) a second more comprehensive unimodal analysis using bibliographic coupling networks. This iterative analytical process provided a major if surprising insight—although Education is not particularly well connected bidirectionally to many subject areas, it appears to act as a distribution centre for knowledge mobilization, providing a central hub for gathering and analysing knowledge from across disciplines in order to generate the complex system of information that underpins society.
A recent emphasis on mathematics learning in the preschool years has sparked a flurry of research... more A recent emphasis on mathematics learning in the preschool years has sparked a flurry of research in children’s thinking; yet, the same attention has not been paid to teaching mathematics in preschools. This paper examines the reciprocal relationship of teaching|learning mathematics with young children and attempts to move discussions beyond teacher as facilitator or director and learner as explorer or incompetent/incomplete receiver. Through an analysis and discussion of excerpts from two adult/child interactions (one of whom is the researcher), I attend to intentional experiences of teaching and learning through an enactive lens. What is revealed is the shared responsibility for intentional (teaching) acts to disclose intentional (mathematical) objects such that the experiences expand possibilities for acting in a mathematical space.
Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent resea... more Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatial skills that are predictive of success in engineering education and the types of intervention activities that have demonstrated improved performance in STEM subjects. In doing so, we identify parallel assessment measures, skills, and tasks in the development of a spatial skills framework for young engineers that includes physical and mental rotation, symmetry properties, paper folding and unfolding, and cross-cutting objects. These skills are developed through 3D modelling and 2D representational drawings. We illustrate the skills in the framework with samples of work from students in grades 2 and 3 in response to a series of linking-cube...
Many students will struggle with mentally transforming images needed for tessellations, coordinat... more Many students will struggle with mentally transforming images needed for tessellations, coordinate geometry, and motion geometry if they have not had early spatial-visual experiences. The quick-images activity provides a way for young students to develop spatial-visual reasoning, two- and three-dimensional geometry concepts, and geometric vocabulary
This sampler presents assessment tasks that are appropriate for use with students from age 4 to a... more This sampler presents assessment tasks that are appropriate for use with students from age 4 to age 8. The book provides teachers of primary grades mathematics with examples of assessment tasks that reflect the various ways assessments can be used prior to, during and following mathematics instruction. Teachers can then consider the potential of these tasks to uncover the mathematical understandings of their students for the purpose of planning further instruction. Each task can be altered by changing the context, breaking the task into subparts, limiting the scope or complexity of the task, or extending the task to provide more of a challenge or enhance the depth of understanding being assessed.
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Introduction Over the past 25 years, the research colloquium leaders have individually and in sub... more Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms (e.g., Davis & Simmt, 2006; Martin, McGarvey & Towers, 2011; Martin & Towers, 2011; McGarvey & Thom, 2010; Proulx, Simmt & Towers, 2009; Thom & Glanfield, 2018). While our work has contributed to meaningful insights into mathematical understanding of learners and teachers, we realized that the methodological tools developed and used were limited due to the vast and intricate range of dynamic interactions (Martin, McGarvey & Towers, 2011; Simmt, 2011). This led us to working systemically on the mutual concern: How might we observe, document, display and analyze data from a collective learning systems approach? Building on our previous PME(NA) working group, NCTM research symposium, and PME research forum, in this colloquium we will present our work ...
Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent resea... more Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatial skills that are predictive of success in engineering education and the types of intervention activities that have demonstrated improved performance in STEM subjects. In doing so, we identify parallel assessment measures, skills, and tasks in the development of a spatial skills framework for young engineers that includes physical and mental rotation, symmetry properties, paper folding and unfolding, and cross-cutting objects. These skills are developed through 3D modelling and 2D representational drawings. We illustrate the skills in the framework with samples of work from students in grades 2 and 3 in response to a series of linking-cube tasks in a cube-creature project.
2017 Conference of the Canadian Society for the Study of Education, Feb 7, 2017
The purpose of our pilot study was to identify what Canadian preschool teachers noticed as opport... more The purpose of our pilot study was to identify what Canadian preschool teachers noticed as opportunities for teacher-child mathematical interactions in the classroom and to investigate the value of video as a professional development tool to prompt increased attention to and awareness of different possibilities for mathematical interactions. Using the framework of teacher noticing, we interviewed six preschool teachers to establish an initial baseline of their perspectives and current practices of mathematical interactions. The teachers then participated in three professional development sessions over four-months using collaborative video viewing of classroom routines. Through the sessions the teachers
Knowledge mobilization is becoming increasingly important for research collaborations, but few me... more Knowledge mobilization is becoming increasingly important for research collaborations, but few methodologies support increased knowledge sharing. This study provides insights, using a reflective narrative, into a transdisciplinary knowledge-sharing investigation of the connectivity of educational research to that of other disciplines. As an exemplar for educational research, the study evaluated the use of spatial search terms from mathematics education using: 1) an initial descriptive statistical analysis combined with bi modal network analysis of highly cited articles; and, 2) a second more comprehensive unimodal analysis using bibliographic coupling networks. This iterative analytical process provided a major if surprising insight—although Education is not particularly well connected bidirectionally to many subject areas, it appears to act as a distribution centre for knowledge mobilization, providing a central hub for gathering and analysing knowledge from across disciplines in order to generate the complex system of information that underpins society.
A recent emphasis on mathematics learning in the preschool years has sparked a flurry of research... more A recent emphasis on mathematics learning in the preschool years has sparked a flurry of research in children’s thinking; yet, the same attention has not been paid to teaching mathematics in preschools. This paper examines the reciprocal relationship of teaching|learning mathematics with young children and attempts to move discussions beyond teacher as facilitator or director and learner as explorer or incompetent/incomplete receiver. Through an analysis and discussion of excerpts from two adult/child interactions (one of whom is the researcher), I attend to intentional experiences of teaching and learning through an enactive lens. What is revealed is the shared responsibility for intentional (teaching) acts to disclose intentional (mathematical) objects such that the experiences expand possibilities for acting in a mathematical space.
Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent resea... more Engineering is a spatially demanding field. Yet, unlike previously held assumptions, recent research reveals that spatial ability is not innate, but that through experience, education, and intervention, people of all ages can improve their visualization skills—a key component of the engineering habits of mind. In this chapter, we examine the spatial skills that are predictive of success in engineering education and the types of intervention activities that have demonstrated improved performance in STEM subjects. In doing so, we identify parallel assessment measures, skills, and tasks in the development of a spatial skills framework for young engineers that includes physical and mental rotation, symmetry properties, paper folding and unfolding, and cross-cutting objects. These skills are developed through 3D modelling and 2D representational drawings. We illustrate the skills in the framework with samples of work from students in grades 2 and 3 in response to a series of linking-cube...
Many students will struggle with mentally transforming images needed for tessellations, coordinat... more Many students will struggle with mentally transforming images needed for tessellations, coordinate geometry, and motion geometry if they have not had early spatial-visual experiences. The quick-images activity provides a way for young students to develop spatial-visual reasoning, two- and three-dimensional geometry concepts, and geometric vocabulary
This sampler presents assessment tasks that are appropriate for use with students from age 4 to a... more This sampler presents assessment tasks that are appropriate for use with students from age 4 to age 8. The book provides teachers of primary grades mathematics with examples of assessment tasks that reflect the various ways assessments can be used prior to, during and following mathematics instruction. Teachers can then consider the potential of these tasks to uncover the mathematical understandings of their students for the purpose of planning further instruction. Each task can be altered by changing the context, breaking the task into subparts, limiting the scope or complexity of the task, or extending the task to provide more of a challenge or enhance the depth of understanding being assessed.
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Papers by Lynn McGarvey