PRISM :: Browsing by Author "Towers, Jo"

Browsing by Author "Towers, Jo"

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Open Access
A metissage of poetry, pedagogy, and writing with children
(2011) Quinn-Hall, Collette; Towers, Jo
Open Access
Creating, understanding and teaching mathematics: complementary processes
(2012) Rapke, Tina; Towers, Jo; Seyffarth, Karen
The purpose of this dissertation is to explore the relationships among understanding, creating and teaching mathematics. It includes two pairs of complementary mathematics and education papers. The papers are complementary in the sense that the education papers draw on the experiences of creating the mathematics that appear in the mathematics papers and in doing so, provide insight into how the mathematical concepts, theorems and proofs are constructed. The education papers not , only provide insight into one mathematician's creating of mathematics, but mine the experiences and insights for their pedagogical implications.
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
Early Years Students’ Relationships with Mathematics
(2016-12-01) Takeuchi, Miwa; Towers, Jo; Plosz, Jennifer
Early years mathematics experiences have been shown to be a significant predictor for students’ school readiness and future mathematics achievement. Previous research also indicates an important connection between emotion and mathematics learning. How do students in early years education in Alberta describe their emotional relationship with mathematics? This article documents the findings of our research focusing on Kindergarten to Grade 2 students. Our analysis showed that many students in the early years, including those at the Kindergarten level, recognized what is considered to be mathematics but mainly associated mathematics with number and numerical operations. The majority reported positive relationships with mathematics, though some described negative relationships with school mathematics learning.
Open Access
Examining Memory States for General Knowledge: A Non-Trivial Pursuit
(2018-01-05) Pereverseff, Rosemary; Bodner, Glen; Protzner, Andrea; Bourdage, Joshua; Towers, Jo
According to the classic distinction between semantic and episodic memory, people answer general-knowledge questions by accessing their semantic memory. However, an appeal of trivia games is the variety of memory and metamemory experiences they arouse—which sometimes include recollection of episodic details. I report an in-depth exploration of subjective memory states for general knowledge. In two experiments, participants classified their answers for general-knowledge questions as learning memory or related memory forms of recollection, or as feels familiar, just know, or guess forms of non-recollection. Surprisingly, participants often reported recollection for their answers. Accuracy of answers assigned to the learning and related memory states, and to the just know state, were equally high. In contrast, accuracy was much lower for the feels familiar state (and was lowest for guesses). The accuracy difference between just know and feels familiar suggests these states are distinct, even though researchers often use them interchangeably. Reports of learning memories increased on an immediate retest. Recollection source judgments on the retest revealed that, in addition to recollecting the answer feedback provided on the initial test, pre-experimental recollections increased. Episodic memory is commonly experienced in semantic memory tasks and is diagnostic of accuracy.
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 metacognition and higher order thinking through digital video creation: a multiple case study
(2013) Bene, Rose Elizabeth; Towers, Jo
Open Access
Exploring Metacognition and Higher Order Thinking Through Digital Video Creation: A Multiple Case Study
(2013-07-12) Bene, Rose Elizabeth; Towers, Jo
Metacognition is the ability to think about and modify or regulate one’s thinking or learning. Since the 1970’s, many studies have investigated the impact of applying metacognitive knowledge, strategies, and self-regulating skills to learning tasks in various disciplines and educational contexts. More often than not, these interventions have resulted in learning gains for the students involved. On a different front, the proliferation of new technologies in the classroom has opened the door for students to discover new ways of acquiring and constructing knowledge, and representing their thinking. The purpose of this qualitative research study was to bring these seemingly divergent research strands together by exploring students’ thinking while they are involved in digital video creation. A multiple case study examining ten high school students’ thinking as they created digital videos was undertaken. The study was informed by a number of theoretical models on metacognition and self-regulated learning as well as literature on constructivist learning, visual research methods, collaborative learning, and the use of digital video in the classroom. A conceptual framework of metacognition was developed from existing models in the literature. Constructs within this framework were used as macro-level coding categories in the data analysis. Both deductive and inductive methods were used to examine the data. Findings revealed many occurrences of high school students’ implicit metacognitive thinking and skills during the process of video creation. When questioned by the researcher, all students were able to explicitly voice their thoughts and explanations about their thinking, feelings, and actions. Students treated DV technology as a full intellectual partner for scaffolding their learning and representations of knowledge. In addition, the collaborative learning involved in video creation became the impetus for shared metacognitions. These findings hold much promise for using DV creation as a tool for stimulating or eliciting metacognitive thinking and skills. As well, the conceptual framework may be useful as an analytical tool in future studies or as the basis for examining the many interrelationships among the different variables that influence metacognition.
Open Access
How Children Signal That They Are Making Mathematical Connections
(2014-04-23) Andrews, Heather J.; Towers, Jo
This study examines how children signal that they are experiencing the interconnectedness of mathematics while working on rich tasks. Based on guidelines recommended by the NCTM (2000), I define the “interconnectedness of mathematics” as how mathematical concepts build on one another; are connected to, and can be used with, other mathematical ideas; and apply in contexts outside of mathematics. A case study of two groups of three, grade-four students is described based on qualitative data from video recorded problem-solving sessions. Three themes emerged from the data gathered. The ways in which children signaled they were making mathematical connections included: 1) using known facts to solve new problems; 2) identifying appropriate strategies to solve a mathematics problem; and 3) making mathematical generalizations. I conclude by discussing the subtlety of some of the signals described in my themes and the implications of such subtle comments including:1) situation awareness; 2) time; and 3) assessment.
Open Access
Images of mathematics learning revealed through students’ experiences of collaboration
(2016-08) Takeuchi, Miwa Aoki; Towers, Jo; Martin, Lyndon
This study focuses on students’ images of mathematics learning and their relationships with mathematics. In this paper we consider how students described collaboration in mathematics classrooms, through the examination of students’ autobiographical interviews and drawings. Our analysis revealed that many students considered mathematics learning mainly as an individualized and isolated process and did not perceive peer talk or collective exploration as meaningful. Our cross-analysis with students’ feelings revealed that those who had positive feelings towards mathematics tended to find group work less helpful. Our findings illuminate a perceived gap between teachers’ widespread use of group work as a teaching strategy and students’ understanding and appreciation of the goals of such instruction.
Open Access
Immigrant students’ mathematics learning experiences in Canadian schools
(2015) Takeuchi, Miwa; Towers, Jo
Open Access
Intellectually honest pedagogy: inviting mathematics in to elementary classrooms
(2010) McLeod, Donna; Towers, Jo
This thesis is an interpretive study that explores the extent to which mathematics pedagogy stands to be influenced by the discipline of mathematics itself in elementary classrooms. In particular, this research focuses on the process of coming to teach mathematics honestly, amid all its natural bounty. This is a journey of narrated moments with students and with mathematics, both remembered and newly experienced. Together these stories deliver both data and method to this hermeneutic study. They are mathematically oriented but set against a metaphor of organic farming. Important conduct on the part of educators emerges and stand as signposts towards an intellectually honest practice. Such conduct includes the cultivation of community, imagination, patience, listening, exchange and play. At the culmination of this thesis, there exists no categorical answer that blueprints reform in math education, but in true inquiry fashion, there has been a deliberate and careful opening up.
Open Access
An Investigation Of Laboratory Activities For Non-STEM-Majors During The COVID-19 Pandemic
(2021-08-04) Gilbert, Brian Christopher Tidbury; Seidel, Jackie; Sullivan, Erin; Alonso-Yanez, Gabriela; Towers, Jo
Laboratory activities have been an aspect of teaching chemistry for the past 200 years. However, their effectiveness in the teaching of chemistry content and skills have, until recently, been largely unexplored. This is especially the case for non-STEM-majors taking introductory and general chemistry courses, who were found in a review of the literature to often be regarded as a lower priority for research efforts due to goals of increasing STEM-major engagement. In an attempt to fill this gap in the literature, this study was designed to investigate if introductory chemistry laboratory activities foster the development of science identity in non-STEM-majors. However, as the COVID-19 pandemic continued into its second wave and people began discussing the future of laboratory activities, the purpose of this study shifted as well. As a result, this study looked at the influence of in-person activities for non-STEM-majors and sought to help support decisions on whether non-STEM-majors should return to in-person laboratory activities in introductory/general chemistry post COVID-19 pandemic. Making use of qualitative research methods, data was collected through a set of interviews with one student and three instructors at the University of Calgary and then analyzed for convergent themes. Results indicated that in-person laboratory activities are beneficial to non-STEM-majors for three primary reasons: 1) The disciplinary skills taught in chemistry laboratory activities are beneficial for daily life beyond laboratory settings; 2) Laboratory activities present students with a toolbox of skills that transfer between disciplines; and 3) Chemistry laboratory activities improve student science identity by showcasing the processes of science. Additionally, participants presented two considerations for returning to in-person laboratory activities following the COVID-19 pandemic: 1) Laboratory activities should change to emphasize student creativity and intrigue in order to improve their accessibility and effectiveness of teaching STEM-majors and non-STEM-majors; and 2) Accessibility of laboratory activities may be improved by implementing remote learning models that have been explored during the COVID-19 pandemic, such as making use of recordings and alternative methods of participation.
Open Access
Literacy Through The Arts: A Phenomenological Inquiry into What it is Like to Experience Literacy within a Theatrical Space
(2019-07-05) Campbell, Harrison Michael; Towers, Jo; Alonso-Yañez, Gabriela; Burwell, Catherine; Lenters, Kimberly A.
Literacy, according to Lindquist and Seitz (2009), “is one of those words, like love, that people use commonly and confidently, as if its meaning were transparent and stable” (p. 8). Literacy in classrooms, however, is inherently complex and the experiences that surround it, especially from the student’s perspective, are often lost. This thesis examines how literacy came to be defined within a specialized arts immersion junior high school in Western Canada and how the unique approach to curriculum was better able to encourage student agency, authorship, and identity within literacy's definition. This research is inspired by the work of the New London Group, which spoke to expanding the scope of literacy pedagogy through a proposed framework of multiliteracies embracing multimodality and contextual responsiveness to the learning environment. (New London Group, 1994). In response to this it was seen that students needed to have spaces in which they can play the role of code breakers, text users and text analysts. Artistic inquiry is a means to create such a space which in addition to teaching applied roles, also allow students to strengthen their social and cultural wellbeing (Wells & Sandretto, 2017). Over the course of a semester eight students created a theatrical space in which they communicated their experiences of literacy with data being collected through interviewing, journaling, monologue writing, and performance. Through the use of Interpretative Phenomenological Analysis students, who were recruited using homogeneous sampling, had their data coded in a way that created a double hermeneutic around literacy as the researcher and students engaged in dialogue and performance as a means of making meaning. This phenomenological process allowed for the development of a flexible open-ended inquiry. The study's findings showed that students within this unique learning environment connected their literacy experiences directly into the fine and performing arts. Students experienced literacy both in a traditional sense and a performative sense, citing that their work within school productions was a way of building upon their literacy skills. For these students, literacy was not a single experience but an interconnected web of experiences that enriched their learning and increased their engagement.
Open Access
Mathematics before teaching: an analysis of the academic transcripts of prospective elementary and secondary mathematics teachers
(2008) Pascuzzo, Tony; Towers, Jo
Open Access
Students' Experiences of Group Work Revealed Through Mathematics Autobiographies
(University of Calgary, 2016-05) Takeuchi, Miwa Aoki; Towers, Jo; Werklund School of Education
Collaboration and collective problem solving have been promoted as essential components of the 21st century skills and can be fostered through group work. Yet we know little about how students are experiencing group work in Canadian mathematics classrooms. Our analysis of Kindergarten to Grade 9 students’ mathematical autobiographies shows that most students perceived group work as a way of offering and/or receiving help for individualized tasks but not necessarily as an opportunity for creative collaboration. Based on our analysis, we discuss the pedagogical implications for designing classrooms that can foster meaningful collaboration.
Open Access
The integration of theory and practice during teaching practica: case studies of mathematics student teachers in Bhutan
(2009) Fricot, Melanie; Towers, Jo
Open Access
The Mentorship Guide for Teaching and Learning
(Taylor Institute for Teaching and Learning, 2019) Barrette-Ng, Isabelle H.; Nowell, Lorelli; Anderson, Sarah J.; Arcellana-Panlilio, Mayi; Brown, Barbara; Chalhoub, Serge; Clancy, Tracey L.; Desjardine, Patricia; Dorland, AnneMarie; Dyjur, Patti; Mueller, Katherine; Reid, Leslie; Squance, Rod T.; Towers, Jo; Wilcox, Gabrielle
Rooted in evidence, this guide will provide you with a unique perspective on supporting mentoring relationships for teaching and learning development. You will explore mentoring relationships, assessing readiness for mentorship, initiating mentorship, developing and sustaining mentoring relationships and mentoring transitions while ultimately improving student learning. You will also reflect on your mentoring relationships as you work through a series of guided questions and practical worksheets. Research on academic mentorship often measures success in terms of mentee research productivity (Feldman, Arean, Marshall, Lovett & O’Sullivan, 2010; Kalet, Fletcher, Ferdman & Bicknell, 2006; Sambunjak, Straus & Marušić, 2006). Teaching mentorship produces different measures of success, including the development of reflective practice and, most importantly, improvements in student learning. Although there are many resources for mentorship in academia (Johnson, 2015; Straus & Sackett, 2014), none of them aim specifically at supporting mentorship for teaching and learning development. Mentorship in teaching and learning differs from research mentorship in terms of aims, approaches and measures of success, which is why we offer this resource.
Open Access
The process of spiritually-inspired lifework
(2007) Mulcair, Deborah Frances; Towers, Jo
Open Access
Understanding Math 10 Students’ Experiences of Struggle to Learn Mathematics
(2017) Smith, Stephanie Ursula; Field, James Colin; Towers, Jo; Francis, Krista
Students have much to tell educators about their experiences of learning mathematics. Their experiences include struggles that may either be productive as they persevere to understand or destructive as they feel that learning is frustrating and painful. The purpose of this study was to gain an understanding and new insights into how students struggle to learn math, the different ways that students struggle, and how this experience shapes how they respond to future encounters of difficulty, as well, as their attitude towards math. Six Math 10 students were interviewed using semi-structured questions. Students’ lived experiences were explored using interpretive methodology. Students spoke about their experiences of confusion, disconnection, encountering hidden rules, not understanding why, freezing on a test, and having to learn concepts that they found were irrelevant to their lives. These experiences may provide new insights and understandings of how teachers may better teach students.