Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

Finding the Open Spaces in Closed Systems: An Exploration of Critical Pedagogy with a Social Justice Directive in an Ontario Secondary School Classroom

This study examines the first experience of students, teachers, and an administrator in implementing a teacher-designed Leadership in Social Justice Program at a large urban Ontario secondary school. The program aimed to infuse a Freirean concept of critical pedagogical praxis (Freire, 1970/1993) in a grade 12 integrated educational experience with a social justice directive. Data were collected through two questionnaires and eight in-depth interviews. The data identified three areas of awareness that described ways in which student participants were impacted most profoundly (a) developing self-awareness, (b) understanding a new educational paradigm, and (c) finding a place in the world. The study found that the program was successful in highlighting the possibility for more meaningful education and engaged many students deeply; however, its success was limited by the lead teacher’s failure to fully grasp and implement tenets of Freirean critical pedagogy that involved the role of the teacher in pedagogical processes.

Improving English as a Second Language (ESL) Pedagogy in One University in Ontario

In this paper, theoretical pedagogical approaches and practical pedagogical approaches are investigated by drawing on English as a Second Language (ESL) teachers’ pedagogical principles and practices, and ESL Chinese students’ second language acquisition and learning needs as they related to improving ESL pedagogy in one university ELP in Ontario. Three experienced ESL teachers were inquired by interviews and 30 ESL Chinese students were surveyed by questionnaires. Based on the mix-method exploratory research design, communicative, task-based, and content-based language teaching approaches are identified and discussed in the light of the interview and questionnaire data.

The Kids Need Hip-Hop: Reengaging Students through Culturally Relevant Pedagogy

My thesis advocates for critically-conscious hip-hop in classrooms to promote student engagement and culturally relevant pedagogical practices. This proposed approach to educating youth offsets the harmful effects of a normalized curriculum that limits students’ creativity and discounts their experiences as lifelong learners. My thesis gathers data from research literature on hip-hop and education, critically-conscious hip-hop lyrics, and also includes my own hip-hop muse to illustrate the positive tenets of critically-conscious hip-hop. The research literature in my thesis is gathered from multiple studies within North American high schools. My hip-hop muse interrelates with critically-conscious hip-hop lyrics because they both address contemporary issues through social commentary and critical awareness. The element of social commentary in my hip-hop muse is displayed through short poems and verses that outline my experiences in a normalized schooling environment. Throughout my thesis, I uncover the causes of student disengagement in classrooms, the ways in which critically-conscious hip-hop music serves as a tool for reengaging youth, and the approaches that must be taken in order to adequately integrate hip-hop into today’s classrooms. My thesis is important within the context of Canadian classrooms because it acts as an agent for social change and cultural relevance through a critical lens. The purpose of this approach, then, is to demonstrate an understanding of the complexity of our society and schooling system through social critique and proposals for change. More importantly, my thesis is grounded in equity; in which critically-conscious hip-hop serves as a bridge for students’ experiences, interests, and independent identities.

A Handbook for Ontario J/I Pre-Service Teachers Developing Inclusive Pedagogy: Understanding Pre-Service Teachers' Thoughts and Feelings About Diversity

This project presents a handbook for Ontario Junior/Intermediate (J/I) pre-service teachers, Ontario J/I teacher education instructors, and J/I associate teachers that facilitates the identification, analysis, and reorganization of J/I pre-service teachers’ thoughts and feelings about diversity characteristics to develop inclusive teaching pedagogy. The handbook outlines collaborative and independent learning activities designed for integration into compulsory J/I Bachelor of Education (B.Ed.) program courses, practicum placements, and independent reflective situations. The handbook is composed of 5 sections: (a) Rationale for Importance; (b) Cross-Curricular Activities for J/I B.Ed. Courses; (c) Course-Specific Activities; (d) Practicum Placement Activities; and (e) Resources for Inclusive Educators. A critical content analysis of a 2011-2012 J/I B.Ed. program in Ontario enabled the creation of the handbook to address specific teacher education programming focused on helping pre-service teachers understand their thoughts and feelings about diversity for the development of inclusive teaching pedagogy. This research contributes to the advancement of theory and practice regarding development of teacher education programming that promotes J/I pre-service teachers’ inclusive pedagogy.

Postsecondary Artist Teachers' Responses to Computer Technology in Their Drawing Pedagogy

While the influence of computer technology has been widely studied in a variety of contexts, the drawing teaching studio is a particularly interesting context because of the juxtaposition of traditional medium and computer technology. For this study, 5 Canadian postsecondary teachers engaged in a 2-round Delphi interview process to discuss their responses to computer technology on their drawing pedagogy. Data sources included transcribed interviews. Findings indicated that artist teachers are both cautious to embrace and curious to explore appropriate use of computer technology on their drawing pedagogy. Artist teachers are both critical and optimistic about the influence of computer technology.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

Affect, ontology, and pedagogy: An autoethnographic study on student-teacher relationships

In studying affect within the realm of student-teacher relationships my thesis project use the concept of “affect” as composed by Baruch Spinoza (1992, 2007). I focus specifically on how Deleuze (1988) interprets and implements the term within his own philosophy, as well as on Antonio Negri’s (2011, 1991) work on Spinoza including his and Michael Hardt’s (2000, 2004, 2009) more recent works. This thesis will explore Spinoza’s affect within the discourse of Affective Pedagogy and Critical Pedagogy while remaining committed to a Spinoizist ontology as outlined by Deleuze (1988). I used artefacts from my past experiences as a student and teacher to produce evocative writing pieces which act as affective continuances of my past experiences as a student, student-teacher, and teacher, and the relationships of affect that composed them. This project used these artefacts and the writings they produced as sites of intensity that are carried through from traces, to evocative thresholds, to concepts, and finally into analysis.

Investigating Formative Assessment: Exploring the Impact on the Self-Efficacy and Motivation of Mathematics Students

This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Embracing the Crisis in the Foundations of Mathematics

The crisis in the foundations of mathematics is a conceptual crisis. I suggest that we embrace the crisis and adopt a pluralist position towards foundations. There are many foundations in mathematics. However, ‘many foundations’ (for one building) is an oxymoron. Therefore, we shift vocabulary to say that mathematics, as one discipline, is composed of many different theories. This entails that there are no absolute mathematical truths, only truths within a theory. There is no unified, consistent ontology, only ontology within a theory.

Indian Mathematics Related to Architecture and Other Areas With Special Reference to Kerala

Department of Mathematics, Cochin University of Science and Technology

Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.