The mathematics textbook as a story: A novel approach to the interrogation of mathematics curriculum.

摘要

Both the purpose and overarching goal of this dissertation can be summarized with this quote by Buckminster Fuller: "You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete." That is, to enable substantive positive change in mathematics education, this dissertation builds a new curricular model, tackling the question, "When mathematics textbooks are interpreted as art, what can be learned?" Although unconventional, this approach offers new conceptual tools for teachers and curriculum developers to make sense of the way in which mathematical ideas emerge and develop throughout a curricular sequence and to think anew about mathematics curriculum. Specifically, this work re-conceptualizes a mathematics textbook as a mathematical story with mathematical characters, action, setting, moral, and plot. Built from literary theory, especially the frameworks of Bal (2009) and Barthes (1974), the mathematical story framework supports a vision of mathematics curriculum as a complex narrative able to stimulate the imagination and curiosity of students and teachers alike. In particular, the notion of mathematical plot offers a new opportunity to articulate the sequential dynamics affecting a reader's aesthetic experience, theorized as a tension between questions pursued by a reader and the revelations enabled by the text as the mathematical story unfolds.;Oscillating between the analysis of mathematics textbooks and literary frameworks, the mathematical story constructs were developed and tested. Once stable and consistent, the constructs of mathematical character, action, setting, moral, and plot were carefully defined with examples from written curriculum. In addition, new characteristics of curriculum made visible with this re-conceptualization were explored and articulated through the analysis of multiple textbooks, focusing attention on what can be learned about the manifestation of mathematical characters and mathematical plots in textbooks. In part, these analyses reveal how a mathematical character, such as the number zero, is introduced and temporally evolves throughout a sequence of curriculum. This interpretation of mathematics textbooks also exposes how the development of a mathematical object involves not only the identification of the character but also the reader's identification with the character. A representation using Barthes' hermeneutic codes is also introduced to describe the mathematical plots of different mathematical stories, enabling the different experiences of reading these stories to be recognized and understood.;As mathematics curriculum broadly affects nearly every aspect of mathematics education (from planning to enacting to assessing), this mathematical story framework supports a renaissance of potential opportunities for mathematics teachers and students. It provides a heuristic for the analysis of math textbooks beyond any specific part (such as a task or a definition) in order to recognize the connective tissue of all the parts and the shape and effect of the whole for a reader. It offers teachers new, yet familiar, language for describing and collaborating on mathematics curriculum such as planned lessons or reflections on enacted lessons, further supporting their curricular design work. In addition, this work offers a conceptual foundation on which designers make important choices regarding the introduction and development of mathematical objects, procedures, and representations. In doing so, this work creates the potential to improve the mathematics curriculum offered to students.