Integrative hypothetical "teaching" trajectory for technologically-culturally sustaining paradidactic praxeologies in mathematics: A critical dialectical pluralism approach

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ID: 287500
2025
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Abstract
In this study, I adapted the term Integrative Hypothetical “Teaching” Trajectory (IHTT), a model designed to develop mathematical teaching pathways that are both technologically and culturally sustaining. This model is grounded in the concept of paradidactic praxeology, which consists of two interconnected blocks: the praxis (i.e., Type of Task [T_pd] and Technique [τ_pd]) and the logos (i.e., Technology [θ_pd] and Theory [Θ_pd]). The IHTT framework was inspired by my previous and ongoing collaborations with indigenous teachers, as well as by recent literature on emerging trends in mathematics education. These influences led me to pose the question: How can teachers adapt to technological innovations while remaining rooted in their cultural identity? Employing a design-based research approach and guided by the methodological principles of critical dialectical pluralism, the development of the IHTT unfolded across three phases with the participation of 11 teachers, 3 ethnomathematicians, 3 educational technology practitioners, and 2 expert teachers. During the design and planning phase, a review of seminal theories, practitioners’ epistemological and ontological beliefs, and teachers’ existing praxeologies informed the initial design of the IHTT. Cultural elements such as batek and laga from the Kalinga province were integrated as exemplars of cultural characteristics, while laptops and projectors served as the technological resources. In the instructional design phase, a series of focus group discussions supported the implementation and refinement of the IHTT, with particular attention given to the evolution of τ_pd and their justifications through θ_pd and Θ_pd, anchored in a clearly defined T_pd. Finally, in the retrospective analysis phase, the IHTT was found to be effective in supporting the design of instruction that is both technologically relevant and culturally sustaining. Significant improvements were observed in teachers’ praxeologies, including the development of more diverse and systematic τ_pd from a defined T_pd, stronger rationale through θ_pd, and deeper alignment with broader educational theory via Θ_pd. These findings further informed the overall structure of the paradidactic praxeology (T_pd, τ_pd, θ_pd, Θ_pd). It is anticipated that the IHTT will continue to serve as a viable framework for supporting teachers as they navigate emerging trends in mathematics education while maintaining their cultural identity and context.
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Authors Hortelano, Julius Ceasar C.
Journal Malay Journal
Year 2025
DOI
DOI not found
URL
https://animorepository.dlsu.edu.ph/etdd_scied/50
Keywords Keywords not found

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