Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DH... more Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how such knowledge can expand access and conceptual opportunities for both DHH and hearing learners. The article focuses on the spatial reasoning of two grade 1 hard of hearing children as they complete a geometric task with a hearing peer in a mainstream classroom. Informed by research in cognitive science, mathematics, and the fields of deaf and general education, the authors explicate key spatial subcomponent processes of deconstructing and constructing as the children produce 2D and 3D figures. The findings of this qualitative study provide considerations for future research and pedagogy in both deaf and general education.
Early years practitioners need to see learning – particularly in mathematics – not as abstract an... more Early years practitioners need to see learning – particularly in mathematics – not as abstract and ‘disembodied’ but as inherently concrete and ‘embodied’. Dr Jennifer S Thom explains why
Teaching and Learning Secondary School Mathematics, 2018
In this chapter, we consider the images, meanings, and metaphors provoked by the phrase in the ti... more In this chapter, we consider the images, meanings, and metaphors provoked by the phrase in the title of the opening section of the book: The Changing Landscape. Inspired by our Indigenous and ecological sensibilities, we develop new images, meanings, and metaphors that illuminate the collective nature of secondary mathematics classes. We explore the Pirie-Kieren (1989) model in terms of how it relates to the collective level of the class. Using a video based excerpt from a secondary mathematics class, we map the observed ideas onto the Pirie-Kieren model as they emerge and evolve, moment to moment. The results reveal a dynamic ideational topography of the classroom. Through illustrative exemplars and the analyses that accompany these, we reflect on how paying attention to the ideas of the class as live(d) topographies occasion new questions for further investigation into mathematics classroom collectives.
Spatial reasoning skills are critical to early learning, particularly in mathematics, and need to... more Spatial reasoning skills are critical to early learning, particularly in mathematics, and need to be supported by engaging children's entire bodies. Dr Jennifer S Thom explains why
Nowadays, there is a high consensus among educational and psychology researchers, mathematics edu... more Nowadays, there is a high consensus among educational and psychology researchers, mathematics educators and mathematicians that geometry and spatial visualization deserve a prominent role in school mathematics (eg, Lehrer and Chazan, 1998). In contrast to traditional approaches in which these topics were pushed into the very background, today their importance is understood to be absolutely central. Curriculum writers from many countries have also acknowledged the relevance of geometry within reform ...
This thesis reports on a qualitative study in which three fifth grade children were presented wit... more This thesis reports on a qualitative study in which three fifth grade children were presented with six nonroutine mathematical problems involving six different 3-D pyramids, constructed out of multi-link cubes1. The children were videotaped while they worked without any adult help as a cooperative group to solve the pyramid problems. During these sessions, the students produced various 3-D cube models, 2-D drawings, and written records of arithmetic calculations as their solutions to the six problems. Through the lens of enactivism, this study describes and interprets the coevolutionary processes of the group's path of mathematical understandings as it unfolded during the six videotaped sessions. The results revealed building, drawing, and numbering as modes of representation of this group's problem solving work. An analysis of these three modes of representation explored the co-emergence of the children's individual and collective understandings, as well as the interrel...
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 ...
The article focuses on the ideas and meanings that emerge for the author as she experiences the d... more The article focuses on the ideas and meanings that emerge for the author as she experiences the death of her father. Here, through a series of vignettes which expose curricula as live(d) by herself, her father, and others, the author explores multiple conceptions of the live(d) curriculum. As a result, ideas and meanings of (in)visibility, last(ing) rituals, and life feeling itself surface and in significant ways occasion the author’s new awareness and deeper understanding of the live(d) curriculum.
Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DH... more Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how such knowledge can expand access and conceptual opportunities for both DHH and hearing learners. The article focuses on the spatial reasoning of two grade 1 hard of hearing children as they complete a geometric task with a hearing peer in a mainstream classroom. Informed by research in cognitive science, mathematics, and the fields of deaf and general education, the authors explicate key spatial subcomponent processes of deconstructing and constructing as the children produce 2D and 3D figures. The findings of this qualitative study provide considerations for future research and pedagogy in both deaf and general education.
Early years practitioners need to see learning – particularly in mathematics – not as abstract an... more Early years practitioners need to see learning – particularly in mathematics – not as abstract and ‘disembodied’ but as inherently concrete and ‘embodied’. Dr Jennifer S Thom explains why
Teaching and Learning Secondary School Mathematics, 2018
In this chapter, we consider the images, meanings, and metaphors provoked by the phrase in the ti... more In this chapter, we consider the images, meanings, and metaphors provoked by the phrase in the title of the opening section of the book: The Changing Landscape. Inspired by our Indigenous and ecological sensibilities, we develop new images, meanings, and metaphors that illuminate the collective nature of secondary mathematics classes. We explore the Pirie-Kieren (1989) model in terms of how it relates to the collective level of the class. Using a video based excerpt from a secondary mathematics class, we map the observed ideas onto the Pirie-Kieren model as they emerge and evolve, moment to moment. The results reveal a dynamic ideational topography of the classroom. Through illustrative exemplars and the analyses that accompany these, we reflect on how paying attention to the ideas of the class as live(d) topographies occasion new questions for further investigation into mathematics classroom collectives.
Spatial reasoning skills are critical to early learning, particularly in mathematics, and need to... more Spatial reasoning skills are critical to early learning, particularly in mathematics, and need to be supported by engaging children's entire bodies. Dr Jennifer S Thom explains why
Nowadays, there is a high consensus among educational and psychology researchers, mathematics edu... more Nowadays, there is a high consensus among educational and psychology researchers, mathematics educators and mathematicians that geometry and spatial visualization deserve a prominent role in school mathematics (eg, Lehrer and Chazan, 1998). In contrast to traditional approaches in which these topics were pushed into the very background, today their importance is understood to be absolutely central. Curriculum writers from many countries have also acknowledged the relevance of geometry within reform ...
This thesis reports on a qualitative study in which three fifth grade children were presented wit... more This thesis reports on a qualitative study in which three fifth grade children were presented with six nonroutine mathematical problems involving six different 3-D pyramids, constructed out of multi-link cubes1. The children were videotaped while they worked without any adult help as a cooperative group to solve the pyramid problems. During these sessions, the students produced various 3-D cube models, 2-D drawings, and written records of arithmetic calculations as their solutions to the six problems. Through the lens of enactivism, this study describes and interprets the coevolutionary processes of the group's path of mathematical understandings as it unfolded during the six videotaped sessions. The results revealed building, drawing, and numbering as modes of representation of this group's problem solving work. An analysis of these three modes of representation explored the co-emergence of the children's individual and collective understandings, as well as the interrel...
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 ...
The article focuses on the ideas and meanings that emerge for the author as she experiences the d... more The article focuses on the ideas and meanings that emerge for the author as she experiences the death of her father. Here, through a series of vignettes which expose curricula as live(d) by herself, her father, and others, the author explores multiple conceptions of the live(d) curriculum. As a result, ideas and meanings of (in)visibility, last(ing) rituals, and life feeling itself surface and in significant ways occasion the author’s new awareness and deeper understanding of the live(d) curriculum.
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