- Ontario, Canada
Joyce Mgombelo
Brock University, Faculty of Education, Faculty Member
Research Interests: Sociology, Metaphysics, Epistemology, Education, Play, and 4 moreMindfulness, Wisdom, Doctrine, and Gautama Buddha
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The paper argues for the significance of complexity science and its role in the ethics of teaching that is not based on moral codes. Through the work of Varela on human consciousness, and the work of Newburg and his colleagues on... more
The paper argues for the significance of complexity science and its role in the ethics of teaching that is not based on moral codes. Through the work of Varela on human consciousness, and the work of Newburg and his colleagues on neurotheology, the paper explores the elements of human consciousness that are relevant for characterising an ethical act. Varela’s concepts of emergent self and autopoiesis as well as Newburg’s concept of Absolute Unitary Being provide the necessary conditions for characterizing an ethical act as essentially unconscious. Finally the paper discusses the implication of these contentions for ethics in teaching. There are indeed among propositions, proposals, problems, questions, those that are decidable, and those that are in principle undecidable. … Only those questions that are in principle undecidable, we can decide. (Heinz
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Recess is often a topic overlooked in pedagogical theory due to its presumed simplicity. The essence of recess connects with play as a physical counterpart to a well-rounded education. In this article we explore the relationship play has... more
Recess is often a topic overlooked in pedagogical theory due to its presumed simplicity. The essence of recess connects with play as a physical counterpart to a well-rounded education. In this article we explore the relationship play has with recess and well-being and explore its pragmatikos (systematic usefulness) as regards schooling in lieu of deep ecological frameworks of systems (wholism) theory and systemic, nonlinear dynamics. We argue that recess in its current conceptualisation—in contradistinction to work or study—is a counterfeit to metaphysical play based on the writings of Ananda K. Coomaraswamy who sheds light on its spiritual premise. By bringing to the forefront metaphysical Ideas of play we encounter similitudes between the Platonic doctrine of ēdūcere and anamnesis with Buddhist phenomenology, especially regarding the practice of Mindfulness (sati); both extol a “recollection” as opposed to a “memorisation” which arguably occupies much of Westernised curriculum. Fi...
Research Interests: Sociology, Metaphysics, Epistemology, Education, Play, and 4 moreMindfulness, Wisdom, Doctrine, and Gautama Buddha
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George Richardson: One of Ted Aoki's most important contributions to the field of curriculum scholarship is the insight that curriculum is much more process than product. For Aoki, curriculum is best imagined as a negotiatory act... more
George Richardson: One of Ted Aoki's most important contributions to the field of curriculum scholarship is the insight that curriculum is much more process than product. For Aoki, curriculum is best imagined as a negotiatory act that takes place between curriculum understood as formal plan and curriculum understood as lived experience (Aoki, 1988, 1989, 1992). In a broad sense, it is in this complex negotiatory space that we all craft our professional identities and “overcome mere correctness, so that we can see and hear our ...
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In our on-going five-year naturalistic research, we analyze how math majors and future math teachers learn to use programming for mathematics investigation. Using the instrumental approach (Trouche, 2004) as a framework, we present some... more
In our on-going five-year naturalistic research, we analyze how math majors and future math teachers learn to use programming for mathematics investigation. Using the instrumental approach (Trouche, 2004) as a framework, we present some exploratory results on how the instrumental orchestration of an instructor (Bill) supports the activity of his students.
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... DOI: 10.1080/00207390903236459 Joyce R. Mgombelo a * & Chantal Buteau b pages 1051-1068. ... In the twentieth century, the education philosopher-pragmatic John Dewey articulated what continues to be a challenge in regard to... more
... DOI: 10.1080/00207390903236459 Joyce R. Mgombelo a * & Chantal Buteau b pages 1051-1068. ... In the twentieth century, the education philosopher-pragmatic John Dewey articulated what continues to be a challenge in regard to teachers' knowledge of subject matter. ...
Research Interests: Mathematics, Computer Science, Instructional Design, Educational Technology, Mathematics Education, and 11 moreMathematical Programming, Planning, Teaching Methods, Teacher Learning, Learning Object, Conceptual Framework, Mathematical, Computer Program, Curriculum and Pedagogy, Large Scale, and Learning Experience
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The paper draws from a hermeneutic phenomenological research study, which aimed at exploring the meaning of teachable moments from the lived experiences of grades 6–8 mathematics teachers. A primary and important stage of hermeneutic... more
The paper draws from a hermeneutic phenomenological research study, which aimed at exploring the meaning of teachable moments from the lived experiences of grades 6–8 mathematics teachers. A primary and important stage of hermeneutic phenomenological study is for researchers to begin their research with a personal story. This paper presents the results of this primary stage, which focused on one of author's experiences of storytell-ing in a grade 6 to 8 mathematics classes for the purpose of humanizing mathematics as a way of engaging both the 'being' of mathematics students and their cognitive faculties. Data was collected from personal teaching stories of one of the researcher/author. The paper argues that teacher's storytelling humanizes mathematics in ways that engages both the 'being' and cognitive faculties of a student.
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The collected works of English mathematics educator, Mary Boole, might be invaluable for education and curriculum research that attempts to understand the question: “what counts as knowing?” Even though it was written before 1916, Boole’s... more
The collected works of English mathematics educator, Mary Boole, might be invaluable for education and curriculum research that attempts to understand the question: “what counts as knowing?” Even though it was written before 1916, Boole’s work allows curriculum researchers and teacher educators interested in the question to experience a significant shift in thinking. For example, in the following excerpt from the collected works, Mary Boole informs our view of education and provides us with an initial, though not so clear, orienting statement:
In this chapter the authors discuss a development project conducted in Tanzania which became known as “hisabati ni maisha”—mathematics is living/life. The goal of the project was to build capacity for mathematics teaching and learning in... more
In this chapter the authors discuss a development project conducted in Tanzania which became known as “hisabati ni maisha”—mathematics is living/life. The goal of the project was to build capacity for mathematics teaching and learning in rural and remote communities. The work was based on lessons learned from research conducted in Tanzania prior to the project, Canadian indigenous perspectives and complexity thinking. Of critical importance was the building and nourishing of relationships between the team and participants and among participants, and ongoing openness to emergent ideas and strategies. This openness led to constant tinkering with the design and activities of the project which we believe led to a project that had better and unexpected outcomes. We pay particular attention to some of the ways in which we tinkered with the design of the project in light of interactions among the project team and participants in the project.
Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms... more
Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms (e.g., Davis & Simmt, 2006; Martin, McGarvey & Towers, 2011; Martin & Towers, 2011; McGarvey & Thom, 2010; Proulx, Simmt & Towers, 2009; Thom & Glanfield, 2018). While our work has contributed to meaningful insights into mathematical understanding of learners and teachers, we realized that the methodological tools developed and used were limited due to the vast and intricate range of dynamic interactions (Martin, McGarvey & Towers, 2011; Simmt, 2011). This led us to working systemically on the mutual concern: How might we observe, document, display and analyze data from a collective learning systems approach? Building on our previous PME(NA) working group, NCTM research symposium, and PME research forum, in this colloquium we will present our work ...
This paper focuses on the process of university mathematics students engaging in a sequence of programming-based mathematical project tasks as part of a course. Data of this naturalistic research was collected mainly through four student... more
This paper focuses on the process of university mathematics students engaging in a sequence of programming-based mathematical project tasks as part of a course. Data of this naturalistic research was collected mainly through four student projects and semi-structured individual interviews. The analysis led to narratives of students’ development process (instrumental genesis) in which enacted strategies (instrumented actions) are highlighted. In this paper we discuss a participant’s development process. Results suggest that the student, after 1 course, has appropriated programming as instrument for creating a tool for pragmatic purposes; however, not yet as instrument for mathematics investigations and applications, i.e., as an object-to-think-with (Papert, 1980).
The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument... more
The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for computer programming technology use in the context of pure or applied mathematical investigation. We illustrate it by examining the engagement (scheme development) of an undergraduate student engaged in ‘authentic’ programming-based mathematical inquiry work, i.e. complete inquiry work as mathematicians would do. Two schemes are elaborated, namely the scheme of validating the programmed mathematics and the scheme of articulating in the programming language a mathematical process. Our discussion evidences some specific features of the programming language as artefact associated with a general aim of mathematical inquiry, in particular in terms of articulation between mathematics and programming.
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This paper discusses the results of a pilot study that explored how prospective secondary school teachers are shaped by learning experiences during their undergraduate mathematics education. The collaborative study, which was conducted by... more
This paper discusses the results of a pilot study that explored how prospective secondary school teachers are shaped by learning experiences during their undergraduate mathematics education. The collaborative study, which was conducted by a mathematician and a mathematics educator, drew from the experiences of prospective teachers in a non-traditional undergraduate mathematics program that makes extensive use of technology. Analysis of data collected from detailed questionnaires, journals, and focus group discussions strongly suggests that designing, implementing, and testing Learning Objects promotes prospective teachers’ learning of the mathematics needed for teaching. Furthermore, the analysis shows that prospective teachers’ experiences of ownership, engagement, and pride are key to positive learning experiences.
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Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms... more
Introduction Over the past 25 years, the research colloquium leaders have individually and in subgroups, been theorizing about, as well as collecting, analyzing, and reporting on data related to collective action in mathematics classrooms (e.g., Davis & Simmt, 2006; Martin, McGarvey & Towers, 2011; Martin & Towers, 2011; McGarvey & Thom, 2010; Proulx, Simmt & Towers, 2009; Thom & Glanfield, 2018). While our work has contributed to meaningful insights into mathematical understanding of learners and teachers, we realized that the methodological tools developed and used were limited due to the vast and intricate range of dynamic interactions (Martin, McGarvey & Towers, 2011; Simmt, 2011). This led us to working systemically on the mutual concern: How might we observe, document, display and analyze data from a collective learning systems approach? Building on our previous PME(NA) working group, NCTM research symposium, and PME research forum, in this colloquium we will present our work ...
This essay uses an enactive approach to map out the ways Ontario teachers, students, and parents have reimagined online mathematics education at the K-12 level during the COVID-19 pandemic. The essay highlights the importance of education... more
This essay uses an enactive approach to map out the ways Ontario teachers, students, and parents have reimagined online mathematics education at the K-12 level during the COVID-19 pandemic. The essay highlights the importance of education researchers using an appropriate framework in understanding the emerging mathematics education realities. It encourages education researchers to pay attention to this call to action while recognizing that such an action is not without challenges. To address the challenges, education researchers must engage with the evolving mathematics education environment and community by innovating and reimagining their research tools and techniques.
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We investigate how the instrumental orchestration can contribute to our understanding of the teaching to university students of using programming technology for mathematical investigation projects. Our case study highlights a dual role... more
We investigate how the instrumental orchestration can contribute to our understanding of the teaching to university students of using programming technology for mathematical investigation projects. Our case study highlights a dual role the instructors play, as policy maker and as teacher, to orchestrate students' instrumental geneses, and the integration of projects as a key element of the exploitation mode.
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The paper argues for the significance of complexity science and its role in the ethics of teaching that is not based on moral codes. Through the work of Varela on human consciousness, and the work of Newburg and his colleagues on... more
The paper argues for the significance of complexity science and its role in the ethics of teaching that is not based on moral codes. Through the work of Varela on human consciousness, and the work of Newburg and his colleagues on neurotheology, the paper explores the elements of human consciousness that are relevant for charac- terising an ethical act. Varela's concepts of emergent self and autopoiesis as well as Newburg's concept of Absolute Unitary Being provide the necessary conditions for characterizing an ethical act as essentially unconscious. Finally the paper discusses the implication of these contentions for ethics in teaching.