"Mathematics teacher noticing as a pedagogical practice--attending to, interpreting, and responding to children's mathematical thinking--is growing within mathematics education communities. Much of the research literature primarily focuses on supporting teacher noticing of children's mathematical thinking within classroom contexts, such as analyzing classroom artifacts and video recordings. Recent efforts to support teachers make connections between mathematics and children's funds of knowledge, however, often involve professional work outside of classrooms where teachers learn about children's lived experiences and communities. While there is a growing expectation that teachers draw on children's funds of knowledge to support mathematics learning, this kind of professional work requires an ability to notice mathematics in out-of-school contexts. The bulk of this dissertation is written as a series of three interconnected papers from a single qualitative study where I explored activities of a working group I facilitated to support prospective K-8 teachers to notice children's mathematical practices in out-of-school contexts. A primary thread across this work involves blurring boundaries within mathematics education. In my first article (pp. 51-76), I provided an overview of boundary blurring that prospective teachers in this study engaged--between mathematics and people as well as between mathematics and other disciplines--through early field experiences in out-of-school contexts. I zoomed in to examine a specific boundary, women and mathematics, in my second article (pp. 83-105) and explored intersections of gender, age, and elementary mathematics during an interaction at a science museum site visit. Then, in my third article (pp. 110-133), I zoomed out to focus on broader discourses within mathematics education to challenge overly simplistic allor-nothing type stories about mathematics and people (e.g., 'being a math person'). Across my three articles, I engage an overarching question: What stories do prospective teachers tell about themselves, about children, and about mathematics? This study contributes to a collection of stories about prospective teachers' learning to notice children and their mathematical practices with implications for supporting mathematics teacher education, particularly in contexts outside of school. In closing, I share how my work connects to a broader project in mathematics education, blurring boundaries. I pose an underlying question for my continued work: What would it take to decolonize mathematics education?"--Pages ii-iii.
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