Browsing by Author "Khan, Steven"
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Item Open Access Accumulation of experience in a vast number of cases: enactivism as a fit framework for the study of spatial reasoning in mathematics education(2014-08) Francis, Krista; Khan, Steven; Davis, BrentAs we witness a push toward studying spatial reasoning as a principal component of mathematical competency and instruction in the twenty first century, we argue that enactivism, with its strong and explicit foci on the coupling of organism and environment, action as cognition, and sensory motor coordination provides an inclusive, expansive, apt, and fit framework. We illustrate the fit of enactivism as a theory of learning with data from an ongoing research project involving teachers and elementary-aged children’s engagement in the design and assembly of motorized robots. We offer that spatial reasoning with its considerations of physical context, the dynamics of a body moving through space, sensorimotor coordination, and cognition, appears different from other conceptual competencies in mathematics. Specifically, we argue that learner engagements with diverse types of informationally ‘dense’ visuo-spatial interfaces (e.g., blueprints, programming icons, blocks, maps), as in the research study, afford some of the necessary experiences with/in a vast number of cases described by Varela et al. (1991) that enable the development of other mathematical competencies.Item Open Access Accumulation of experience in a vast number of cases: enactivism as a fit framework for the study of spatial reasoning in mathematics education(Springer, 2015) Khan, Steven; Francis, Krista; Davis, BrentAs we witness a push toward studying spatial reasoning as a principal component of mathematical competency and instruction in the twenty first century, we argue that enactivism, with its strong and explicit foci on the coupling of organism and environment, action as cognition, and sensory motor coordination provides an inclusive, expansive, apt, and fit framework. We illustrate the fit of enactivism as a theory of learning with data from an ongoing research project involving teachers and elementary-aged children’s engagement in the design and assembly of motorized robots. We offer that spatial reasoning with its considerations of physical context, the dynamics of a body moving through space, sensorimotor coordination, and cognition, appears different from other conceptual competencies in mathematics. Specifically, we argue that learner engagements with diverse types of informationally ‘dense’ visuo-spatial interfaces (e.g., blueprints, programming icons, blocks, maps), as in the research study, afford some of the necessary experiences with/in a vast number of cases described by Varela et al. (1991) that enable the development of other mathematical competencies.Item Open Access Enactivism, Spatial Reasoning and Coding(2015) Francis, Krista; Khan, Steven; Davis, BrentDrawing on an enactivist perspective in order to gain insight into how spatial reasoning develops and can be fostered, this article describes a study of how children engaged in spatial reasoning as they learned to program LEGO Mindstorms EV3 robots. Digital technologies afforded multiple opportunities for accumulating experiences for developing spatial reasoning that are difficult to come by in other contexts. Our video-recorded observations of children (aged 9 to 10) suggest that Bruner’s enactive–iconic–symbolic typology of representations develop simultaneously rather than sequentially – the commonly held assumption. Furthermore, these same video observations provided insight into children’s development of spatial reasoning through computer programming. Our findings have implications for how curriculum is designed and implemented in classrooms.Item Open Access Robotics in Mathematics Education(Canadian Mathematics Education Study Group /Groupe Canadien d’Étude en Didactique des Mathématiques, 2019-05) Francis, Krista; Caron, France; Khan, StevenRobots and robotics have spread out of research laboratories, industrial and commercial settings to a variety of new locations including living rooms and classrooms. This incursion has afforded different learning opportunities for children and adults. In the tradition of Papert (1980), who identified educational robots as ‘objects-to-think-with’, our working group set out to explore some of the potential for using robots to think about mathematics and other powerful ideas through engaging with building, programming, testing, mathematising, playing and discussing emergent ethical issues. Participants came with a variety of previous experiences and expertise in mathematics education and coding across diverse settings and with different goals. These included making stronger connections between coding and robotics, or computational thinking and mathematical thinking; examining potential for inclusion in courses for pre-service teachers given jurisdictional pushes or emerging curriculum emphases; seeking active hands-on experiences for applied mathematics courses and modelling; and also because of the ‘that’s cool!’ factor.Item Open Access Syntonic Appropriation for Growth in Mathematical Understanding: An Argument for Curated Robotics Experiences(Springer) Francis, Krista; Khan, StevenIn this paper we argue that a well structured robotics inquiry can lead to what Pirie and Kieren (Educ Stud Math 26:165–190, 1994a; Learn Math 14:39–43, 1994b) called growth in mathematical understanding. In particular we offer that such structuring is a means to encourage processes of syntonic appropriation as introduced by Papert (Mindstorms: children, computers, and powerful ideas. http://worrydream.com/refs/Papert-Mindstorms1st ed.pdf, 1980). We start with the observation that some mathematical concepts are introduced to learners in ways that are disassociated from learners’ bodies, experiences and/or culture(s). In our work students, teachers, researchers, tasks and technologies are dynamically coupled and provide feedback to each other.