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Towards Recursive Mathematics Curricula: A Complexified Hermeneutic Journey
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- Author / Creator
- Luo, Lixin
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Derived from Doll’s (1993) seminal conceptualization of a post-modern curriculum with the criteria of 4Rs (i.e., richness, relations, recursion and rigor), the present research continues the effort to complexify and theorize recursion and recursive curriculum. This study re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking (Davis & Sumara, 2006), which studies complex systems that are adaptive, such as cognition and knowledge. A mathematics curriculum often seems be designed or delivered as linear: a sequence of predetermined, sometimes unrelated, topics with few chances for learners to revisit them from different perspectives. This suggests learning as accumulation with predictable outcomes. Learning, observed through a complexified world view, is neither linear nor predictable. Learning is a self-organizing process through which a learner and her environment co-evolve, and a recursive elaboration through which a learner transforms her previous understanding (Davis & Sumara, 2002; Davis, Sumara, & Luce-Kapler, 2008). Both learners and school subjects are complex systems with a biological structure (Davis & Sumara, 2002) that emerges. This view demands a recursive curriculum that centers on reviewing previously encountered ideas with an orientation towards newness and changes along its formation. What might such mathematics curriculum be like, particularly at high school level, in theory and practice is my research focus.
The research methodology follows the tradition of hermeneutics (Gadamer, 1989/2013) that attends to language and emphasizes emerging understanding through iterative loops of interpretations. The interpretations in this research are informed by three kinds of entry texts, my personal reflections about recursive curriculum, teaching documents (i.e., programs of studies and textbooks), and conversations with teachers, serving to provoke my thinking and generate further reflection subjected to new rounds of interpretations. Several high school mathematics teaching documents from Canada and China were examined to see in what ways a planned curriculum might afford recursion. Conversations with experienced high school mathematics teachers were conducted in professional development workshops and/or individual meetings. Teachers were invited to reflect on their learning and teaching experiences and comment on several teaching and learning practices (e.g., reviewing), and work with me to revise or generate curriculum materials to promote such practices orientated towards helping students to learn something new from what they have encountered before.
This study aims to make a contribution in the field of mathematics education by addressing the gap between the perceived importance of recursive mathematics curricula and the insufficiency of research about them. I expect that this study speaks to a reinterpretation of reviewing, and potentially provokes learners (both teachers and students) to interpret mathematics and curriculum differently and inspires learners to (re)embark a complexified hermeneutic inquiry on recursive mathematics curricula for the purpose of both learning and teaching. This study has led to a metaphorical and iconic image (see the image on p. v or Figure 9.4.8) of recursive curricula that represents abundant curriculum possibilities rather than a fixed one. Such visualization can provide theoretical and practical references for mathematics educators and education researchers to draw inspirations from when designing towards recursive mathematics curricula. -
- Graduation date
- Fall 2019
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.