Date of Award
Doctor of Philosophy (PhD)
Janine T. Remillard
Mathematics is sometimes described as a “beautiful and interconnected story” (Kaplinsky, 2019, para. 1). Precisely what is meant by the term interconnected—and how interconnectedness relates to instruction—is debatable. Some argue that interconnectedness requires the sequential ordering of mathematical ideas, like the ascending the rungs of a ladder (e.g., Abdussalaam et al., 2015; Fernandez et al., 1992; Kaplinsky, 2019). Additional clarity is warranted, however, to understand the potential influence of non-sequential orderings (Dietiker, 2012, 2013b, 2015a; Lampert, 2001; Zimba, 2011, 2012). I maintain that a better understanding of the nature of interconnectedness or coherence has implications for both instruction and the design of curriculum materials.
In the study presented here, I pursue an investigation of coherence in mathematics instruction. To do so, I apply Dietiker’s (2012, 2013b, 2015a) mathematical story framework. This framework draws on literary theory and narrative analysis, to illuminate underappreciated elements of written lessons. I draw on Dietiker’s work to theorize that mathematical plots involve connected or coherent ideas, deployed in a variety of ways to motivate students’ curiosity. At present, there are no fine-grained studies that analyze mathematical plots of multiple elementary-grades lessons, comparing nuances of sequenced ideas in both written materials and classroom instruction. To better understand ways curriculum materials offer mathematical plots, and how teachers interpret and adapt them, I undertook a case study of two, experienced elementary instructors. I found that both teachers read for mathematical plots, but for different purposes: one reads for plot complexity, to offer scaffolds to students that resequenced ideas; the other reads for moments of suspense, to stimulate students’ problem-solving by purposefully omitting key ideas. Also, curriculum materials framed mathematical plots in varying ways that both supported and undercut their implementation. My findings suggest that curriculum authors should attend carefully to mathematical plots, providing instructors with rationales for sequencing of or omitting ideas. I also situate this work within several broader areas of study, particularly research on the design work of teaching (M. Brown, 2009), teachers’ participation with curriculum materials (e.g., Remillard, 2005), and fidelity of curriculum implementation (e.g., S. Brown, Pitvorek, Ditto, & Kelso, 2009).
Taton, Joshua Aaron, "Complex Numbers: Imagined And Realized Plots & Storylines Of Enacted Mathematics Curricula" (2019). Publicly Accessible Penn Dissertations. 3397.