PRISM :: Browsing by Author "Francis, Krista"

Browsing by Author "Francis, Krista"

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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
Bridging the gap between evidence-informed and actual teaching practices of engineering educators: an AI-enhanced professional learning system
(2023-09-21) Nelson, Nancy Lynn; Brennan, Robert W.; Male, Sally; Sun, Qiao; Hugo, Ron; Eggermont, Marjan; Francis, Krista
Imagine a classroom where engineering students are challenged to apply what they’re learning, where they interactively explore the complexities of authentic, level-appropriate engineering problems, supported by professors who are aware of and apply evidence-informed teaching practices. Expectations align with the engineering workplace. Learners improve their acquired knowledge and skills through experimentation and deliberate practice. They harness systems thinking as they make connections and see patterns. They are challenged to adapt to whatever scenario they face, to identify problems, think critically, generate and model effective solutions, and to make justifiable decisions. Learners experience the tension between knowing and doing engineering things. They learn firsthand, and in context, what it means to be a practicing engineer. This aspiring approach is very different from the didactic practices reported in most Canadian undergraduate engineering classrooms. The challenge, and the focus of this research, is to encourage and assist engineering educators to stretch their current teaching practices beyond what’s comfortable and customary, to those that are both evidence-informed and truly representative of engineering. This research is a blend of interdisciplinary mixed-methods and design-based research. The interdisciplinary mixed-method research integrates the findings of educational research, learning sciences, professional learning, and systems thinking. Sixteen research studies explore the experiences and practices of educators and students in the Canadian undergraduate engineering system. These findings confirm that a gulf exists between evidence-informed teaching practices and what happens in the typical undergraduate engineering classroom. They clearly establish the need for an educational development model that translates existing educational research into tangible, level-appropriate teaching practices for engineering educators at all levels of experience and skill. This foundational research leads to the design and development of this thesis' first of three contributions, the LENS (Learning Environments Nurture Success) model of engineering faculty development. This model, which is comprised of six lenses that align with an effective learning environment, offers a practical framework to support educational development and planning for all forms of delivery (face-to-face, remote, blended, or hybrid). It can be used independently, in consultation with an educational developer, or in collaboration with colleagues. It threads educator-related threshold concepts associated with learning, pedagogy, assessment, and teaching with technology through each of six lenses, and links myriad interdisciplinary research findings to facilitate the successful education of undergraduate engineering students. The second contribution of this research is a proof-of-concept intelligent Professional Learning System (iPLS). This AI-enhanced learning platform individualizes and guides the development of professional knowledge and skills. The look, feel, and functionality of this proof-of-concept iPLS is shaped by an integration of research findings in professional learning, training and development, technology-based learning, and AI in education. The final contribution of this work is an iPLS application designed to help engineering educators develop their teaching practices. It provides needs-specific recommendations based on an individual's ranking on a novice to expert continuum and achieved teaching-related thresholds. Quantitative and qualitative field test results show the combined LENS, iPLS, and engineering education application (EEA) to be a viable method by which engineering educators can stretch their teaching to include more evidence-informed teaching practices. Using the elements of an elegant design as its measure, the system is determined to be effective and robust with a minimal number of unexpected consequences.
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
Cultivating the Growth of Mathematical Images
(2019-07-05) Plosz, Jennifer A.; Towers, Jo; Francis, Krista; Metz, Martina L.
In this document, I present some of the findings of the study, Cultivating the Growth of Mathematical Images, in which I explore the role that spatial reasoning plays in the growth of mathematical images. This study involved Grade Five students labelled with learning disabilities and their teacher. This study was a microanalysis of a participatory action research study, as it looked at the beginning stages of exploration with students and the impact that a more spatial approach to fractions might have on their growth. Information was gathered from students’ psychoeducational assessment, an informal assessment of spatial reasoning ability, and a pre-assessment task that looked at their understanding of basic number and fractions. There were many layers of complexity surrounding each student’s psychoeducational profile, their performance in the classroom, and the pre-assessment task offered to the students. Certain aspects of these experiences seemed consistent with each other, others contradictory, and still others contained much variability, such as in the area of working memory. During the second week of the study, video data were collected while students engaged with a task that created an interplay between visualizing and building fractions. In analysis of the data, close attention was paid to what sort of offerings the students were given such as signitive (written and oral), imaginative (visualizing), and perceptual (sensory), which are somewhat modified from Husserl (1970). During this task, a pattern of growth began to emerge which is discussed and connected to the Pirie-Kieren (1994) Dynamical Theory for the Growth of Mathematical Understanding. Generally, with the introduction of the signitive only, there was No appearance of movement. Then as the student began either producing or receiving perceptual experiences they progressed into the Image Making phase. The continued engagement with perceptual experiences appeared to create the beginnings of the imaginative, Image Making emergent Image Having phase, and some students were even able to reach the point of being predominately in the Image Having phase. Each participant went through the various phases at varying speeds. Within these various phases, there was found to be much complexity in terms of contributing factors towards growth. The fact that some participants built more than others and therefore had more perceptual offerings seemed a strong contributing factor but other aspects such as their own personal commitment to sense-making as they built, their social interactions, and their own self-belief seemed to also impact growth.
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
Enactivism, spatial reasoning and coding
(Springer, 2015) Francis, Krista
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
Enhancing High School Students’ Spatial Reasoning Through Geometry Transformation Instruction in Ghana
(2023-08) Tay, Mawuli Kofi; Preciado-Babb, Armando Paulino; Koh, Kim Hong; Francis, Krista
Spatial reasoning is a critical skill for learning mathematics, yet efforts to improve high school students' spatial reasoning skills within mathematics classrooms are limited or absent in Ghana. This study aimed to investigate the impact of using dynamic and static visualization approaches within the Experience-Language-Pictorial-Symbolic-Application (ELPSA) pedagogical framework to teach geometry transformation concepts and enhance students’ spatial reasoning skills and geometry transformation knowledge during a four-week intervention. Due to the mixed results regarding the type of visualizations, the study also aimed to compare the effects of dynamic versus static visualization. The study used a one group pretest-post-test design to compare the effects of dynamic versus static visualization instruction. Seventy-seven (77) students from a single school participated in the study and were purposively assigned to either the dynamic (n = 35) or static (n = 42) group. The intervention lasted for four weeks (16 hours), and the dynamic group received dynamic visualization instruction, while the static group received static visualization instruction. The students' spatial reasoning skills and geometry transformation knowledge were assessed using a spatial reasoning instruction and geometry transformation achievement test before and after the intervention. Although there were no significant differences between the groups, both visualization approaches significantly improved students' spatial reasoning skills, including mental rotation, spatial orientation, and spatial visualization, as well as their geometry transformation knowledge. Additionally, the study found a positive relationship between students' geometry transformation scores and their spatial reasoning scores, suggesting that an ELPSA pedagogical approach to visualization instructions can enhance students' spatial reasoning skills within the context of geometry transformation. Overall, these findings have important implications for mathematics educators and curriculum developers, as the findings provide conclusive evidence that targeted geometry transformation instruction within ELPSA pedagogical framework can enhance students' spatial reasoning skills, regardless of the type of visualization used to teach geometry transformation.
Open Access
Enhancing student’s spatial reasoning skills with a robotics intervention
(North American Chapter of the International Group for the Physchology of Mathematics Education, 2021-12-20) Francis, Krista; Rothschuh, S.; Davis, B.
Spatial reasoning is a high-impact topic as it strongly predicts interest in, appreciation of, and success in STEM domains and careers. Yet, spatial reasoning is often under-used, underdeveloped, and ignored in current grade-school curriculum and teaching. Framed by the perspective of embodied cognition, our study explores changes in elementary students’ spatial reasoning skills after participation in either a short-term or a long-term robotics intervention. We administered measures of spatial reasoning elements before and after two differently structured robotics interventions to students aged 9-10 years: a short-term (N=11) and two long-term (N=48). Statistical analysis revealed significant improvements to several different elements of spatial reasoning in both groups. Our findings suggest that programming robots in either the short- or long-term leads to improvements in spatial reasoning.
Open Access
Enhancing Undergraduate Labs for Experiential Learning Can we design labs to better teach employable skills in core mechanical engineering courses?
(2023-08) Love, Mackinley; Egberts, Philip; Wong, Joanna; Nightingale, Miriam; Egberts, Philip; Wong, Joanna; Nightingale, Miriam; Francis, Krista; Hinman, Schuyler
The learning laboratory is a common and important component of contemporary Canadian post-secondary engineering education, intended to relate practice and theory, provide a practical experience in what can be a largely theoretical program, and motivate students. However, a significant minority of mechanical and manufacturing engineering students in a third-year materials science course at the University of Calgary have, across the last decade, reported on their end-of-course surveys that they do not perceive any connections between their laboratories and either their careers or their lectures. Simultaneously, there have been calls from local industry, the provincial government of Alberta that regulates and funds the program, and University administration for more experiential opportunities to be included in undergraduate programs to better prepare students for their future employment. Given that engineering education is directly related to professional engineering practice, it is key that students perceive connections between their program and industrial applications. Therefore, the research question is, how can established educational scholarship be applied to undergraduate engineering laboratories in order to improve students’ perception of their learning experience? Established educational scholarship and expectations from the Government of Alberta and the University of Calgary were reviewed. Qualitative surveys were developed using this scholarship and released to University of Calgary students currently enrolled in the third-year materials science course, asking them to identify and assess learning levels in their laboratories past and present and how course actions affected their assessment. A second series of surveys was released to members of local engineering industry with experience managing students and graduates of the University program, identifying what value they see in engineering learning laboratories. Analysis of results and scholarship provided a set of recommendations for improving the student laboratory learning experience. The core principles of these recommendations are to communicate clearly and explicitly with students, to constructively align all components of the laboratory experience, and to include hands-on participatory experiences whenever possible. Further recommendations targeted implementation of these principles in the laboratory pedagogy, within the laboratory itself as experienced by students, in the laboratory assessment, and in laboratory facilitators such as teaching assistants and technicians.
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
Exploring the Spatial Abilities of Children with Math Learning Disabilities
(2018-12-14) Lenehan, Claire Alice; Drefs, Michelle A.; Wilcox, Gabrielle; Francis, Krista
Individuals with math learning disabilities (MLD) are especially at risk for failing to develop essential math skills. Researchers have established that a relationship exists between spatial abilities and mathematics, but much less is known about the spatial abilities of individuals with MLD. The current study compared the spatial abilities of children aged 8 - 12 with MLD with a comparison group of children with learning disabilities in areas other than math. A spatial assessment battery was administered to measure children’s abilities across five narrow spatial abilities (visualization, closure speed, spatial scanning, flexibility of closure, and visual memory). The children’s environmental spatial abilities were also examined through self-report and parent questionnaires. While no significant group differences were found in any area of spatial ability, the difference in visual memory approached significance. Further examination of the spatial abilities of individuals with MLD is warranted, as a thorough understanding of these abilities may lead targeted spatial interventions with potential to improve the spatial abilities and math skills of students with MLD.
Open Access
Exploring the spatial-math link: The impact of tailored visual memory interventions for children with MLD
(2021-01-08) Donnelly, Emma Leigh Hannah; Drefs, Michelle A.; Makarenko, Erica M.; Francis, Krista
Research has demonstrated that a link exists between spatial abilities and mathematics, with both receiving recognition for their influence on academic and professional achievements. Gaps in the research exist however surrounding narrow spatial abilities and their influence on math difficulties, specifically in children with Math Learning Disorder (MLD), and if spatial deficit remediation is possible. A number of spatial interventions have been shown to improve spatial and mathematics achievement; while promising, the scope of such studies has been largely limited to typically developing populations of children and a narrow range of spatial skills, most notably visualization and mental rotation. The current study implemented a spatial intervention focused on remediating visual memory deficits in three children aged 8-11 with MLD. A novel visual memory intervention was developed with reference to validated visual memory assessment tasks in an attempt to increase participants’ visual memory ability, and in-turn, their math ability. A multiple-baseline single case design technique was used to assess participants’ baseline and intervention performance on visual memory, visualization, and math ability. Follow-up testing also took place to examine any maintenance or generalizability of intervention effects to other spatial or math skills. No significant intervention effects were found on any of the spatial or math abilities. Further examination of the relation between visual memory and mathematics is warranted; a comprehensive understanding of the influence of visual memory on math difficulties may improve education and interventions for children with MLD.
Open Access
Exploring the Synergy Between the Move Steering Input and Turning a Robot
(International Technology and Engineering Educators Association, 2021-05-01) Francis, Krista; Rothschuh, S.; Hamilton, S.; Graham, D.
Open Access
Growth in mathematical understanding and spatial reasoning with programming robots.
(North American Chapter of the International Group for the Physchology of Mathematics Education, 2021-12-20) Francis, Krista; Rothschuh, S.; Davis, B.
This poster describes how programming robots might support both the development of spatial reasoning and growth in mathematical understanding using interpretive video analysis of two Grade 4 students’ attempts to program their robot to follow a pentagon.
Open Access
Identity Development Within Educative Maker Programs
(2019-07-25) Kennedy, Thomas Michael; Lock, Jennifer V.; Redmond, Petrea; Francis, Krista
The purpose of this study was to explore the constructs that influence the development of identity within educative maker programs. As there is no empirical or theoretical model to inform the implementation of maker programs in education, this in-depth exploration was critical in understanding the importance of external constructs on the development of identity within early educative maker experiences. No similar study exists on identity work amid the fragmentation of disciplinary knowledge and application in educational contexts. New knowledge created from this research highlighted intentional constructs in educative maker programs to forge a strong social identity grounded in connectedness, effectiveness, and expansiveness. A qualitative case study design was selected to analyse emergent themes from an in- depth exploration of participant perception and understanding maker identity within the context of a non-curricular educative maker program grounded in robotics and explicit technical skill development. The study gathered data using a three-phased approach which included the use of questionnaire, interviews and observations. Four primary findings which emerged from the research. First, a connected identity, strengthened through the shared histories and experiences with co-participants in the local maker community, did not automatically forge a perceived identity within other parallel communities. Second, environmental and peer relationships were emphasized as critical constructs that offered support and comfort in taking risks in unfamiliar activity and adopting a new social identity in technical activity. Third, the successful performance within the boundary area of maker activity did not alter the need for constructs to offer continued support to forge an effective identity. Fourth, experiences of atypical representation within boundary areas was influential in perceived maker identity. The Conceptual Framework for the Development of Identity Within Educative Maker Programs that emerged from the findings of this qualitative case study offers a foundational understanding of influential constructs to consider for intentionally designing experiences in educative making.
Open Access
Malleability of Spatial Reasoning with Short-Term and Long-Term Robotics Interventions
(Springer, 2021-05-29) Francis, Krista; Rothschuh, S.; Poscente, D.; Davis, B.
Spatial reasoning correlates with academic success in mathematics and science, is highly malleable, and can be learned. Yet, spatial reasoning is often underused, underdeveloped, and ignored in current grade-school curriculum and teaching. This study explores changes in elementary students’ spatial reasoning skills after participation in either a short-term or a long-term robotics intervention. The robotics intervention and the spatial elements within the intervention tasks are described. Measures of spatial reasoning elements were administered before and after each intervention. Two different groups of students ages 9–10 years were tested: a short-term group (N = 11) and a long-term group (N = 48). Statistical analysis revealed significant improvements to several different elements of spatial reasoning in both groups. Findings suggest that programming robots in either the short- or long-term intervention was associated with improvements in spatial reasoning.
Open Access
Multidisciplinary Perspectives on a Video Case of Children Designing and Coding for Robotics
(Taylor & Francis, 2017-05-05) Francis, Krista; Davis, Brent; Hawes, Zachary; Moss, Joan; Okamoto, Yukari; Sinclair, Nathalie; Bruce, Catherine D.; Drefs, Michelle A.; Hallowell, David A.; McGarvey, Lynn M.; Mulligan, Joanne T.; Whiteley, Walter J.; Woolcott, Geoff W.
Spatial reasoning plays a vital role in choice of and success in science, technology, engineering, and mathematics (STEM) careers, yet the topic is scarce in grade school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a video that documented children's progression through 5 days of building and programming robots. Their written opinions on the skills relevant to their careers demonstrated by the children revealed that spatial thinking and design thinking are central to what they see.
Open Access
Pioneering STEM Education for Pre-Service Teachers
(International Journal of Engineering Pedagogy, 2016-11-01) Francis, Krista; Friesen, Sharon; Preciado-Babb, Armando Paulino; Takeuchi, Miwa; Alonso-Yañez, Gabriela; Gereluk, Dianne T.
While there have been numerous initiatives to promote and recruit students into postsecondary studies in science, technology, engineering and mathematics (STEM) around the world, traditional programs of studies for both K to 12 school and teacher education still lack an integrative approach to these disciplines. Addressing this concern, the Werklund School of Education of the University of Calgary started to offer a course in STEM education for the undergraduate Bachelor of Education program. The purpose of this article is to document the first iterations of this course. We draw from narratives of four instructors, including the coordinator of the course, and administrators who were actively involved in creation and approval of the course. We describe the course and its connection to the philosophy of the program, examine the context in which this course was conceived—including both national and provincial policy—and address some challenges and possibilities experienced by administrators, instructors and students during the creation and implementation of the course.