PRISM :: Browsing by Author "Davis, Brent"

Browsing by Author "Davis, Brent"

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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, Brent
As 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.
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, Brent
As 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.
Open Access
Addressing the Challenge of Differentiation in Elementary Mathematics Classrooms
(University of Calgary, 2016-05) Babb, Paulino Preciado; Metz, Martina; Sabbaghan, Soroush; Pinchbeck, Geoffrey; Aljarrah, Ayman; Davis, Brent; Werklund School of Education
Addressing students’ diversity of skills and knowledge for mathematics instruction has been a common challenge for teachers. This paper reports results from an innovative partnership of school district, university and curricular material developers aimed at improving mathematics instruction at elementary level. We report successful cases of lessons enacting instructional practices that engage all students in the classroom, ensure they meet expected outcomes, and challenge them with further bonuses. The cases are analyzed based on mastery of learning, with a particular focus on continual assessment during class. We also include challenges we have faced in supporting teachers as they incorporate these practices in their daily teaching.
Open Access
An Examination of Mental Time Travel and Its Role in the Development of Foresightful/Prudential Intellect
(2015-09-24) Parlar, Ugur; Davis, Brent; Shapiro, Bonnie
Mental time travel (MTT) has always been a crucial component of human cognition, but has not always been identified or supported in schooling. Recent advances in psychological science consider MTT to be responsible for future-oriented thought and action, particularly, the formation of foresight. Therefore, an innovative research trajectory for education is to enabling students to harness their MTT abilities and support the development of what could be called foresightful/prudential intellect. By enhancing the flexibility and the reach of MTT ability, education can enable students to develop foresightful/prudential reasoning skills in science, technology, engineering, and mathematics (STEM) domains, including the ability to carry out collaborative MTT. Some of these skills are ecological problem identification and solution, environmental decision-making, root-cause analysis, spatial reasoning, and evolutionary thinking. This thesis first examines the evolution and development of MTT by combining studies in cognitive-developmental science, biological anthropology, and evolutionary neuroscience. A secondary examination reveals that although foresightful/prudential intellect is more closely associated with cognitive self-governance, clear benchmarks for assessing and supporting this intellect via MTT tasks need to be identified. A developmental study that used a dynamic system problem illustrates the ways foresightful/prudential reasoning manifests itself. Quantitative and qualitative differences are found in school-aged children’s and undergraduate students’ episodic memory syntheses when they were asked how to prevent the problem from reoccurring. The results of this study suggest that foresightful/prudential reasoning skills in environmental topics could be extrapolated to entire classrooms by designing MTT-based learning tools or tasks. Two prominent techniques are identified to show what these tools, tasks, or techniques could involve and how they could be designed. Finally, a teacher education agenda is discussed in alignment with the goals of MTT-based learning and fostering the development of foresightful/prudential intellect. This agenda needs to be approached in stages and with a sense of urgency given the current pace of anthropogenic environmental change.
Open Access
Attending and Responding to What Matters: A Protocol to Enhance Mathematics Pedagogy
(University of Calgary, 2017-05) Metz, Martina; Preciado Babb, Paulino; Sabbaghan, Soroush; Davis, Brent; Ashebir, Alemu; Werklund School of Education
For four years we have invested in improving mathematics teaching at the elementary level. By drawing from diverse research emphases in mathematics education and by considering the impact of lessons in terms of student engagement and performance, we have identified four key elements impacting learning in mathematics. Here, we describe the protocol currently used to structure feedback for teachers in the Math Minds Initiative. The key elements that comprise the protocol are: (1) effective variation, (2) continuous assessment, (3) responsive teaching, and (4) engagement.
Open Access
Building Self-Compassion in Adolescents Through a Mindfulness Program
(2017) Wienhold-Leahy, Bernita; Bohac Clarke, Veronika; Davis, Brent; Bosetti, Lynn
Adolescence is a critical time in human life with regards to identity development; adolescents may experience increased emotional turmoil, stress, and susceptibility to mental health problems (O’Connell, Boat, & Warner, 2009). Implementing a mindfulness program within school curriculum may positively influence this crucial time of growth. This case study focused on teaching self-compassion to adolescents through the “Learning to BREATHE” program. Self-compassion involves being kind towards oneself, understanding that we are all part of common humanity, and mindfulness (Neff, 2003a). This multi-methods study was grounded in Integral Theory (Wilber, 2007), which integrates multiple perspectives of self-compassion. In keeping with Integral Methodological Pluralism, self-compassion was examined through multiple lenses with both qualitative and quantitative methodologies. The findings indicated that a mindfulness program teaching self-compassion had many benefits to students, including increased mindful awareness and focused attention; emotional awareness and regulation; self-awareness, self-kindness, and self-acceptance; resiliency and growth mindset; compassion, acceptance, and forgiveness for others; and a belief it could reduce bullying in schools. While school administrators believed that social and emotional learning can benefit students, classroom application and staff buy-in remains a challenge. Mindfulness programs in the school context will need to be introduced slowly over the next several years as students, parents, teachers, and administrators all have to understand the importance of these skills, before they can be implemented into the classroom.
Open Access
Coding Robots as a Source of Instantiations for Arithmetic
(Springer Nature, 2018-09-17) Francis, Krista; Davis, Brent
With louder and more widespread calls to include computer programming as a core element of school curriculum, global efforts to define innovative and distinct coding curricula are underway. We take a different tack in this paper, one oriented by an investigation of the common ground between learning to program and learning mathematics. We observed 9- and 10-year-olds as they learned to build and program Lego Mindstorms EV3 robots over 4 days, attending in particular to the ways that programming robots to move might support the development and integration of powerful instantiations of number, arithmetic and multiplication. Our findings suggest that children’s understanding of number, and their transitions from additive to multiplicative thinking, can be powerfully supported by engaging in practical tasks rather than practice exercises.
Open Access
Computational thinking and experiences of aritimetic
(Mathematics Knowledge Network, 2020) Francis, Krista; Davis, Brent
In this paper, we discuss how students experienced number while learning to program their robot to move. First, we will provide overview of the context and the research by describing a task used to develop conceptions of “number.” Then, we will introduce two discourses from the cognitive sciences that orient the work: Conceptual Metaphor Theory (Lakoff & Nuñez, 2000) and Conceptual Blending Theory (Fauconnier & Turner, 2003). Finally, we will analyze an interaction among two students and their teacher as they tacitly negotiate meanings of number that are appropriate to the task of programming their robot to move forward 100 cm. Our analysis suggests that computational settings may afford rich settings for experiencing and blending distinct instantiations of a range of number concepts in manners that support flexible and transferable understandings.
Open Access
Contextual Interpretations of International Mindedness in International Baccalaureate Diploma Students
(2016) Beek, Avis; Davis, Brent; Bohac-Clarke, Veronika; Tarc, Paul
The purpose of this study was to examine contextual interpretations of international mindedness by International Baccalaureate (IB) Diploma students in a national and an international school in the Czech Republic. Three research questions were addressed in the study: • How is international mindedness actualized by IB Diploma students? • What is the experience of education for international mindedness for IB Diploma students? • What is the role of context in developing international mindedness in IB Diploma students? The conceptual framework was based on Wilber’s (2006) comprehensive integral theory, a novel application in the study of international mindedness. Through integral methodological pluralism, a form of mixed methods research, quantitative and qualitative data was collected and analyzed. Using an empirical methodology, the Global Perspectives Inventory (Braskamp, Braskamp & Engberg, 2014) was administered to IB Diploma students. Descriptive statistical analysis of the results revealed no significant difference between participants from the two schools. Using a hermeneutic phenomenological methodology, interviews were conducted with IB Diploma students and experienced IB Diploma teachers. Findings revealed the experience of international mindedness can be characterized by the development of an intercultural identity, the ability to take alternate perspectives and the capacity to resolve disconnection from important others. Contextual factors of privilege, parent influence and exposure to diversity also characterized the experience of student international mindedness. Implications for improving the education for international mindedness at the level of the school and IB organization are discussed.
Open Access
Cultivating Compassion in the Classroom: Exploring the Phenomenon of Compassion in an Upper Elementary School Classroom Community
(2017) Tebay, Garette; Bohac Clarke, Veronika; Davis, Brent; Leggo, Carl; Brandon, James; Sameshima, Pauline
This research is concerned with “cultivating compassion,” as a means of helping the individual see the interconnectedness of being. This study of the phenomenon of compassion in a classroom community, draws on Wilber’s model of Integral theory for its conceptual framework, development of research questions, methodology, and data analysis. The perspectives of integral methodological pluralism were employed in this mixed-methods research design, where narrative inquiry was complemented with additional methods to tell the story of the grade 4/5 classroom under study. The aim was to provide a comprehensive exploration of the use of mindfulness techniques in this classroom, for supporting the development of compassion in this group of preadolescents. Themes of enhanced self-awareness, increased calm, and happiness were evident, not only in the students, but in their teacher as well. This perceived calm and self-awareness created a shift in the behaviours observed in the classroom—and in the relationships within it. The study explored the classroom, as it is situated within the context of the school and its mandates, as well as within the school district and provincial policies. The analysis of data determined that the impact of the mindfulness program was centered on this classroom, and the teacher. The idea of the positive potential of the inclusion of mindfulness teaching, at the system level also arose from the analysis. A number of implications and recommendations were identified for the implementation of whole-school programming by system leaders, as well as for the integration of meaningful mindfulness activities in classrooms.
Open Access
Designing for a School System that Learns
(2020-09-04) Hill, Joshua T.; Friesen, Sharon; Davis, Brent; Alonso-Yañez, Gabriela; Clark, Douglas B.; Laferrière, Thérèse
In a complex and dynamic world young people need to devise ways of adapting flexibly, they need to be prepared to undertake something unforeseen, to renew our common world. Yet education emphasizes conformity and compliance underpinned by the deeply seated metanarratives of scarcity, standardization, fragmentation, and control. These metanarratives are embedded in the learning, teaching, and leadership in our schools and in the very reform initiatives that seek to change them. In this study I endeavoured to disrupt and replace these ideas. I draw on system thinking, design, and designing learning to reframe school system leadership as designing for a system that learns. From a design-based approach I partnered with school district leaders to redesign a school district’s strategic plan and implementation process. I share the practical design solutions that were developed in response to the needs of the context and chronicle the iterative design process that was driven by the analysis of empirical data. With the aim of opening up possibilities for how system leaders might practice design for a system that learns, I present a theoretical model featuring four interconnected design principles: divergence and convergence to balance autonomy and coordination; feedback cycles to drive iteration; network connectivity to encourage brokerage between and within systems; and design culture to create the conditions for learning to become a collective responsibility. Finally, I reflect on design-based research, complexity, and Indigenous ways of knowing to expand the space of the possible for future research.
Open Access
Dynamic Responsive Pedagogy: Implications of Micro-Level Scaffolding
(University of Calgary, 2015-06) Sabbaghan, Soroush; Preciado Babb, Paulino; Metz, Martina; Davis, Brent; Werklund School of Education
In mathematics education, scaffolding is often viewed as a mechanism to provide temporary aid to learners to enhance mathematical understanding. Micro-level scaffolding is process by which the teacher returns the student(s) to a conceptual point where scaffolding is not needed. Then the teacher creates a series of incrementally more complex tasks leading to the original task. This process is dynamic, as it often requires multiple steps, and it is responsive because involves moment-by-moment assessment, which shapes each increment. In this paper, we present data on how experienced teachers in the Math Minds Initiative employ micro-level scaffolding. Implications of micro-level scaffolding are discussed.
Open Access
Enactivism, Spatial Reasoning and Coding
(2015) Francis, Krista; Khan, Steven; Davis, Brent
Drawing 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.
Open Access
Epiphanies in Mathematics Teaching: The Personal Learning of an Elementary Teacher
(University of Calgary, 2015-06) Preciado Babb, Paulino; McInnis, Vicki; Metz, Martina; Sabbaghan, Soroush; Davis, Brent; Werklund School of Education
The Math Minds partnership strives to increase student engagement, self-esteem and achievement in mathematics and also to deepen teachers’ conceptual understanding of mathematics for instruction. Through this partnership, elementary teachers are changing the way they teach mathematics. By breaking concepts into small steps, continually assessing all children for understanding along the way and giving opportunities for independent “practice” frequently during each lesson, students have shown a significant improvement in mathematics. We present the transformative learning experience of one teacher during one year in this partnership, with surprising results.
Open Access
Exploring Collective Creativity in Elementary Mathematics Classroom Settings
(2018-04) Aljarrah, Ayman; Towers, Jo; Davis, Brent; Sinclair, Nathalie; Francis, Krista; Lock, Jennifer V.
The purposes of this research study were to investigate the nature of collective creativity in mathematics learning, offer needed empirical findings concerning collective creativity in Canadian elementary schools, explore ways in which collective creativity might be fostered in such settings, and generate understandings about the role of teachers in this endeavor. To fulfil the objectives of this study, I adopted a design-based research methodology with(in) which I worked closely with the participant teachers and scholars in the field of mathematics education, co-developing classroom tasks that would prompt collective creativity in mathematics and studying the design, implementation, and re-design of these tasks. I used three data collection methods, selected to gain a deeper understanding of my research questions, including: classroom observations, video records, and interviews. In my analysis and interpretation of the data, the main sources of which were the video recordings of students’ problem-solving sessions and teachers’ interviews, I concentrated on the students’ (co)acting and interacting within the group and how such collaborative practices contribute to the emergence of the new. Based on an extensive review of the literature on creativity, I suggested seven metaphors of creativity. Those were then refined and (re)developed over successive iterations of data analysis and interpretation until I ended up with four metaphors to describe the experience of creativity with(in) the collective: summing forces, expanding possibilities, divergent thinking, and assembling things in new ways. These were embodied in, and a representation of, varied, emergent, yet interwoven and recursive learning acts, thus I used collaborative emergence as an overarching framework for them. Moreover, I determined four categories for features of mathematics learning environments that I believe were critical in the emergence of collective creativity in such environments, including: attendance to inquiry-based learning, cultivation of collaborative problem-solving, an engaging learning environment, and thoughtful, subtle interventions. I believe that my metaphors of creativity, their logical implications and entailments, and the construct of emergence of collective creativity, offer teachers a frame for designing, evaluating, structuring, and restructuring their practices—structured and improvised practices—that include choosing, adopting, amending and/or designing learning activities to prompt and promote effective creative learning.
Open Access
Facing a Changing World, Reinventing Technical Education and Learning Software Innovation 1969-1989: The Assembly of Two Learning Management Systems
(2021-01-14) Stephen, Alan James; Clarke, Veronika Bohac; Clarke, Veronika Bohac; Winchester, Ian; Davis, Brent; Burns, Amy M.; Fidyk, Alexandra L.
Using a sensibility from Actor-Network Theory, this research looks at the social-technical assembly of two early learning management systems from 1969 to approximately 1989. As such, it is more a story of change in post-secondary education rather than a story of software. The research looked at two related cases: Case A – SAIT Reinventing Technical Education: The Southern Alberta Institute of Technology, a polytechnic in Calgary, Canada, faced a changing world in 1969. In response, the President and people across the institution helped reinvent technical education as they created a new learning system by 1977 (competency-based technical education). Out of this assembled a learning management system (heavily influenced by mastery learning), one that was used from Calgary to Melbourne, and places between. Case B – CBTS Reinventing Learning Software Innovation: Facing a stall in innovation of the software at SAIT, key participants in Case A created a company, Computer Based Training Systems Ltd. in Calgary, to design and market a new learning management system. By the early 1990s, this software was being used by Technical Institutes, Colleges, Universities, K-12 education, and industry in Canada, Australia, USA, Ireland, England, South Africa and Zimbabwe. Of note, the users of the software held the first international conference on learning management systems at the University of Limerick, Ireland in 1989. This research makes visible the previously invisible story of the assembly of these two early learning management systems. It may clarify current academic understanding of the history of these systems. More important, this is a first draft of this tale and can act as a foundation for future research—particularly in these cases where there is more to tell. Also, post-secondary leaders and designers of change may find the models of the designers’ thinking (Focus, Flow, Frame and Formative) in Case A useful, with reflective transfer, for projects of designed change today. This design thinking focused on institutional change and contributed to the successful results seen in the two Cases, results that made a difference to students and institutions.
Open Access
Finding a Common Discourse: How do School Psychologists and Teachers Conceptualize Number Sense?
(2024-07-03) Gould, Kelsey Lynn; Drefs, Michelle; LeFevre, Jo-Anne; Davis, Brent
Children’s knowledge of number sense is foundational to their learning of more advanced mathematics. However, the specific conceptual and procedural skills that are assumed to comprise number sense are not necessarily the same across the fields of mathematics education and psychology (Osana & Proulx, 2018). The lack of consistency in how number sense is understood may influence the collaborative work between school psychologists and teachers who work collaboratively to support children’s mathematics learning. The goal of this study was to identify how school psychologists’ and teachers’ conceptualizations of number sense compare. To identify number sense conceptualizations, 16 participants (n = 8 school psychologists; n = 8 teachers) were presented with vignettes designed to elicit understandings of number sense based on Whitacre et al.’s (2020) notions of Approximate Number Sense (ANS), Early Number Sense (ENS), and Mature Number Sense (MNS), as well as the four grounding metaphors of arithmetic proposed by Lakoff and Núñez (2000). Questions associated with each vignette were used to prompt participants to share which aspect(s) of number sense they noticed. A template approach to thematic analysis was used to analyze interview transcripts. Overall, both similarities and differences were observed between groups. Teachers attended more often to MNS constructs whereas school psychologists noticed ANS constructs of number sense (specifically, innate nature of number sense) more often than teachers. Professional groups similarly attended to ENS constructs of number sense and to the four grounding metaphors of number. Taken together, this research provides support for the need to increase effort to promote a coherent, unitary understanding of number sense across the fields of school psychology and education to better support inter-professional collaboration in support of children’s mathematics learning.
Open Access
Integral Exploration of the Engagement of a Scientific Community of Students in a School Conference
(2017) Carlgren, David; Davis, Brent; Renert, Moshe; Bohac-Clarke, Veronika; Yuen, Christopher
There is a difference between the science done and reported in grade-school science classes and that done by scientists conducting research. Participants generally conceptualize the two types of engagement as distinct projects. Grounding in complexity and network theory reveals connections to communities of practice and collaboratories which exist within the environment of professional scientists, but which are lacking from typical grade-school science practices. The lens of Integral Theory reveals that the two realms are further separated in their relative strengths, weaknesses and foci. Combining these facets prompted this exploration of using a sharing conference as a vehicle for building a collaborative community of practice involving both scientists and grade-school students. The research involved creating a community of practice involving scientists and grade-school students that culminated in a school conference and a research paper. Using a framework of Educational Design Research informed by Integral Research principles, information about three main questions was sought: (1) How is it possible to encourage students to participate actively in a community of scientists through the development of a school conference on science? (2) In what ways might this model a direction worthy of inclusion within the evolving science education paradigm? (3) How might engaged participation in a complex community of scientific practice provide benefit to students’ discourse (and participation) as scientists? Data were gathered using mixed methods and presented here as provocative and illustrative case studies that compel and support theory generation. The ultimate purposes were theory generation and the discovery of enhanced meaning of the situation. The lenses of complexity, Integral Theory and network theory were applied to provide context to events as they occurred in a situated fashion. It was observed and reported that the creation of a complex learning environment focused on the research and reporting of a topic in science to be presented at a school conference provided significant motivation and growth opportunities for students and teachers alike. Key elements that contribute to these growths are proposed as are discussions of evolutionary tensions and aspects that could enhance the application of the project for future use.
Open Access
Juxtaposing Mathematical Extensions with Cognitvely Loaded Questions in the Mathematics Classrom
(University of Calgary, 2016-05) Sabbaghan, Soroush; Babb, Paulino Preciado; Metz, Martina; Pinchbeck, Geoffrey; Aljarrah, Ayman; Davis, Brent; Werklund School of Education
Providing mathematical extensions (i.e. bonus questions) intended to evoke deep mathematical thinking after students complete assigned tasks is challenging for teachers. In this paper, we use the Variation Theory of Learning to challenge a common misconception that mathematical extensions should include many interrelated elements and impose a high cognitive load to promote deeper thinking. We present an analysis of observed extensions and provide alternative routes. Pedagogical implications for the design of mathematical extensions are presented.
Open Access
Lego robotics teacher professional learning
(2013-02) Francis-Poscente, Krista; Davis, Brent