Scholarship & Research
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Item Two-year community college students' understanding of rational expressions(Montana State University - Bozeman, College of Letters & Science, 2023) Kong, Chor Wan Amy; Chairperson, Graduate Committee: Jennifer Luebeck; Megan Wickstrom (co-chair)This research study investigated the gaps in knowledge held by two-year community college students in simplifying and operating with rational expressions and how these gaps affect their learning. The study employed multiple methods, including completion of a Diagnostic Problem Set, participating in collaborative and exploratory activities, and attending task-based interviews, to elicit and assess students' understanding of rational expressions. The study analyzed and categorized participants' responses based on the participants' different perspectives and learning processes. The research also explored how collaborative and exploratory learning, as well as the use of Knowledge-Eliciting Tasks, can help identify and address students' misconceptions. Qualitative analysis of the findings identified potential causes of the learning gaps and generated recommendations for instructional strategies that can bridge these gaps and improve students' understanding of rational expressions, which is crucial to student success in algebraic subjects and college academic achievement.Item The development of specialized content knowledge in beginning algebra among secondary mathematics pre-service teachers(Montana State University - Bozeman, College of Letters & Science, 2016) Pettry, Danielle Nichole; Chairperson, Graduate Committee: Jennifer LuebeckThe goal of teacher preparation programs is to equip future secondary mathematics teachers for the broad spectrum of mathematical learners they will encounter. Part of that process includes developing their Specialized Content Knowledge, defined by Ball, Hill, and Bass (2005) as a deeper understanding of mathematics that allows teachers to explain new ideas, work problems in multiple ways, and analyze student solutions. This study examined the development of Specialized Content Knowledge among secondary mathematics pre-service teachers. Forty-seven pre-service teachers completed a demographic survey and an assessment measuring Specialized Content Knowledge. Twenty-three of those pre-service teachers were then interviewed to further illuminate experiences that influenced their responses on the assessment, and to elaborate on experiences that they identified as helping them develop Specialized Content Knowledge. Qualitative analysis revealed two broad categories aiding in the development of Specialized Content Knowledge: coursework and interactions with learners. Within the category of coursework, pre-service teachers highlighted course components that were also related to interactions with learners, often in a hypothetical way (e.g., analyzing fictional student work). Findings indicate that the development of Specialized Content Knowledge is strongly influenced by interactions with learners, both face to face and hypothetical. These results are discussed along with recommendations for practice and future research.Item The use of computer algebra systems in a procedural algebra course to facilitate a framework for procedural understanding(Montana State University - Bozeman, College of Letters & Science, 2007) Harper, Jonathan Lee; Chairperson, Graduate Committee: Maurice BurkeThis dissertation study evaluated the implementation and effectiveness of an introductory algebra curriculum designed around a Framework for Procedural Understanding. A Computer Algebra System (CAS) was used as a tool to focus lessons on the Framework and help students gain a deeper, well-connected understanding of algebraic procedures. This research was conducted in response to the prevalence of remedial mathematics and addresses the need for students in remedial mathematics to have a successful learning experience. The curriculum was implemented in the Spring 2007 semester at a western land-grant university. In this quasi-experimental study, one section of introductory algebra was taught using the CAS/Framework curriculum. This treatment section was determined based on a pretest used to judge equivalency of groups. Data sources included procedural understanding assessments with follow-up student interviews, procedural skill exams, classroom observations, and a debriefing interview with the treatment instructor. Qualitative analysis of student and instructor interview transcripts was done to supplement independent observation reports to evaluate the implementation of the curriculum.