Graduate Thesis Or Dissertation
 

Creating Community: A Case Study of Students’ Experiences in Inquiry-Based Learning

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  • We now have broad consensus in the mathematics education research community that active, inquiry-based classrooms provide a wealth of learning benefits for students (Freeman et al., 2014; Laursen et al., 2014; Theobald et al., 2020). Classrooms that utilize inquiry throughout the entire structure of the course, as opposed to the occasional group activity or unit, fall under the category inquiry-based mathematics education (IBME) (Laursen & Rasmussen, 2019). These classrooms are broadly characterized as consisting of four pillars: (1) students engage deeply with coherent and meaningful mathematical tasks, (2) students collaboratively process mathematical ideas, (3) instructors inquire into student thinking, and (4) instructors foster equity in their design and facilitation choices (p. 138). Given the wide acceptance of inquiry-based methods in undergraduate mathematics, a number of studies have addressed student experiences in these classrooms to provide further insight into the benefits of IBME, the potential downsides of IBME (e.g., Brown, 2018; Johnson et al., 2020; Stone-Johnstone et al., 2019), and to share the “what/when/how/why” of mathematical content as it is taught in these spaces (e.g., Dawkins, 2014a; Kuster et al., 2018; Rasmussen & Kwon, 2007; Wawro et al., 2012). Moreover, there are few studies that combine classroom level observation data with student and professor interview data across the span of an entire term (Dawkins et al. (2019)is a notable exception) in order to capture the interplay between students’ social and mathematical experiences. For my dissertation study, I observed an inquiry-based learning (IBL, which is a particular strand of IBME) undergraduate advanced calculus course. Thus, in addition to the context of being an IBME classroom, my study contributes to research on the teaching and learning of advanced calculus (also known as real analysis), which in turn heavily involves proof-based arguments and reasoning. Real analysis, often introduced as advanced calculus at the undergraduate level is a required course for most mathematics major degrees across the country (Blair et al., 2018). Existing literature shows that proof is not a trivial activity for students to engage in (Stylianides et al., 2016; Stylianides et al., 2017; Stylianou et al., 2015; Weber, 2010) and that advanced calculus is a useful setting in which to study students’ proof activity (Alcock & Simpson, 2002; Alcock & Weber, 2005; Dawkins & Roh, 2016; Weber & Alcock, 2004; Zazkis et al., 2016). In particular, the IBME style of this advanced calculus classroom meant that students were engaging in authentic, student-centered proof activity for the majority of class time. Furthermore, the classroom I observed was run by a highly experienced instructor, who had over 12 years of experience teaching with IBL materials and had spent several years developing this course. Thus, this was an ideal case study for me to observe the full potential of the possibilities of what IBL can offer advanced calculus students, while still emphasizing the difficulties of IBL teaching no matter an instructor’s experience level. My broad research goal for the dissertation was to capture students’ social and mathematical experiences in this classroom setting, and to explore the relation between these experiences and the IBL structure. Additionally, the instructor I observed added several activities to her course that were not prescribed by the IBL structure (such as a reflective essay on personal axioms), and so I also wanted to explore the relation between these activities and students’ experiences. Notably, this class occurred over the Spring 2020 semester, which meant that I inadvertently captured the class’ transition to remote learning and the instructor’s expert facilitation of a safe classroom space throughout that difficult period. My data collection consisted of classroom observations for the entire term, along with a series of individual interviews across the term with the professor and five selected volunteer students. I am broadly motivated to explore the following questions regarding student experiences in inquiry-based learning and how a sense of classroom community was created over the course of a term: 1) In what ways did the IBL structure of the classroom influence and support interplay between the combined social and mathematical experiences of students in this classroom? 2) In what ways did the instructor influence and support interplay between the combined social and mathematical experiences of students in this classroom? 3) How, if at all, did the interplay between these combined social and mathematical experiences work to create an overall sense of classroom community? To answer these questions, I analyzed both classroom and interview data, which enabled me to write three papers that address different aspects of the term. Each paper combines the social and mathematical experiences of the students in a different way (a narrative analysis of the first three days of the term, a thematic analysis of how rehumanizing mathematics occurred and benefited students during the remote transition to online learning due to COVID-19, and an application of a theoretical framework for understanding students’ developing values and norms around proof across the term). In order to address my first two research questions, in each paper I emphasize ways in which the IBL structure and the instructor’s additional activities influenced, or provided opportunity for, these experiences. My third research question is addressed primarily in the second paper in my data regarding classroom community at the end of the term.
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