The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum ... more The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking. In recognizing the pervasiveness of the phenomenon of a learner encountering something she has previously encountered before and the lack of attention in orientating such reencountering towards transformation in theory and practice, the process of reviewing is reinterpreted as re-viewing and re-encountering. Four forms of re-encountering (re-languaging, re-imaging, re-inbodying, and re-storying) are proposed. Each form is informed by related lived re-viewing experiences, in which a learner learned something new through encountering what s/he had encountered before. Such texts of experiences are generated through autobiographical reflections, teaching documents analysis, conversations with experienced high school mathematics teachers, and iterative reinterpretations of them. This study can provide theoretical and practical references f...
摘要:本文将威廉姆.多尔的后现代课程观应用到作者四岁外甥女的教育中。文章的形式是一封给孩子母亲(作者的姐姐)的信。在信中作者解释了多尔的教育理论在中华人民共和国的适用性。文章开头先介绍了一些对后... more 摘要:本文将威廉姆.多尔的后现代课程观应用到作者四岁外甥女的教育中。文章的形式是一封给孩子母亲(作者的姐姐)的信。在信中作者解释了多尔的教育理论在中华人民共和国的适用性。文章开头先介绍了一些对后现代课程理论化有重要意义的概念,并且比较了现代课程观和后现代课程观的差别。然后作者细致分析了多尔的四个R - 丰富性(Richness)、回归性(Recursion)、关联性(Relations)和严密性(Rigor),同时介绍他们在中国教育的应用以及当把四R视作一个整体时所具有的整体特点(模糊,联网,游戏)。文章最后作者对后现代课程观的理论化给她个人世界观带来的影响进行了反思。
The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum ... more The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking. In recognizing the pervasiveness of the phenomenon of a learner encountering something she has previously encountered before and the lack of attention in orientating such reencountering towards transformation in theory and practice, the process of reviewing is reinterpreted as reviewing and re-encountering. Four forms of re-encountering (re-languaging, re-imaging, re-inbodying, and re-storying) are proposed. Each form is informed by related lived reviewing experiences, in which a learner learned something new through encountering what s/he had encountered before. Such texts of experiences are generated through autobiographical reflections, teaching documents analysis, conversations with experienced high school mathematics teachers, and iterative reinterpretations of them. This study can provide theoretical and practical references for mathematics educators and education researchers to draw inspirations from, when designing towards recursive curricula that center on re-encountering.
Derived from Doll’s (1993) seminal conceptualization of a post-modern curriculum with the criteri... more 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 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.
The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum ... more The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking. In recognizing the pervasiveness of the phenomenon of a learner encountering something she has previously encountered before and the lack of attention in orientating such reencountering towards transformation in theory and practice, the process of reviewing is reinterpreted as re-viewing and re-encountering. Four forms of re-encountering (re-languaging, re-imaging, re-inbodying, and re-storying) are proposed. Each form is informed by related lived re-viewing experiences, in which a learner learned something new through encountering what s/he had encountered before. Such texts of experiences are generated through autobiographical reflections, teaching documents analysis, conversations with experienced high school mathematics teachers, and iterative reinterpretations of them. This study can provide theoretical and practical references f...
摘要:本文将威廉姆.多尔的后现代课程观应用到作者四岁外甥女的教育中。文章的形式是一封给孩子母亲(作者的姐姐)的信。在信中作者解释了多尔的教育理论在中华人民共和国的适用性。文章开头先介绍了一些对后... more 摘要:本文将威廉姆.多尔的后现代课程观应用到作者四岁外甥女的教育中。文章的形式是一封给孩子母亲(作者的姐姐)的信。在信中作者解释了多尔的教育理论在中华人民共和国的适用性。文章开头先介绍了一些对后现代课程理论化有重要意义的概念,并且比较了现代课程观和后现代课程观的差别。然后作者细致分析了多尔的四个R - 丰富性(Richness)、回归性(Recursion)、关联性(Relations)和严密性(Rigor),同时介绍他们在中国教育的应用以及当把四R视作一个整体时所具有的整体特点(模糊,联网,游戏)。文章最后作者对后现代课程观的理论化给她个人世界观带来的影响进行了反思。
The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum ... more The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking. In recognizing the pervasiveness of the phenomenon of a learner encountering something she has previously encountered before and the lack of attention in orientating such reencountering towards transformation in theory and practice, the process of reviewing is reinterpreted as reviewing and re-encountering. Four forms of re-encountering (re-languaging, re-imaging, re-inbodying, and re-storying) are proposed. Each form is informed by related lived reviewing experiences, in which a learner learned something new through encountering what s/he had encountered before. Such texts of experiences are generated through autobiographical reflections, teaching documents analysis, conversations with experienced high school mathematics teachers, and iterative reinterpretations of them. This study can provide theoretical and practical references for mathematics educators and education researchers to draw inspirations from, when designing towards recursive curricula that center on re-encountering.
Derived from Doll’s (1993) seminal conceptualization of a post-modern curriculum with the criteri... more 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 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.
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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 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.
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 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.