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Item Preservice teachers' construction of computational thinking practices through mathematical modeling activities(Montana State University - Bozeman, College of Letters & Science, 2022) Adeolu, Adewale Samson; Chairperson, Graduate Committee: Mary Alice Carlson and Elizabeth Burroughs (co-chair)The importance of learning computational thinking practices in K-12 settings is gaining momentum in the United States and worldwide. As a result, studies have been conducted on integrating these practices in mathematics teaching and learning. However, there is little study that focuses on how to prepare pre-service teachers who will teach the practices in K-12 settings. I investigated how pre-service teachers collaborated to develop computational thinking practices when working on modeling activities with computational tools. To carry out this research, I studied nine pre-service teachers working on modeling tasks for a semester. Five participants recorded their screens and were invited to participate in a stimulated recall interview. Using the interactional analysis procedures, findings showed that the presence of computational tools influenced the positioning (leadership and distributed authority) and collaborative processes (dividing and offloading labor, giving and receiving feedback, accommodation, and refining ideas) pre-service teachers used during modeling. This study found that pre-service teachers used ten computational thinking practices, which are sub-grouped into four broader practices -- data practices, mimicking and mathematizing, model exploration and extension, and model communication. This dissertation also found that pre-service teachers' mathematical knowledge and their ability to code were interdependent. From a research point of view, this study extends our knowledge of the social constructivist theory of doing research in the context of pre-service teachers engaging in modeling activities with computational tools. From the teacher education perspective, this study emphasizes the need to consider the impact of computational tools on the interactions of pre-service teachers during modeling. The study also reveals the need to structure the mathematical modeling curriculum to lead to a better learning experience for pre-service teachers.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 Investigating viable arguments : pre-service mathematics teachers' construction and evaluation of arguments(Montana State University - Bozeman, College of Letters & Science, 2013) Nordby, Kim; Chairperson, Graduate Committee: Jennifer LuebeckThis research investigated pre-service secondary teachers understanding of the term viable argument a new term introduced with the Common Core Standards. The research investigated how they define and understand viable argument, how they construct arguments, and how they evaluate mathematical arguments. The research was conducted using semi-structured interviews with five pre-service teachers that have completed the majority of their mathematical coursework. The results showed that the pre-service teachers compared viable arguments to mathematical proof and they recognized both similarities and differences between these terms. The participants were found to have the understanding of proof, reasoning, and argumentation that will be needed to implement the recommendations of the Common Core Standards.Item A study of the development of technological pedagogical content knowledge (TPACK) in pre-service secondary mathematics teachers(Montana State University - Bozeman, College of Letters & Science, 2012) Mudzimiri, Rejoice; Chairperson, Graduate Committee: Elizabeth Burroughs; Maurice J. Burke (co-chair)The Technological Pedagogical Content Knowledge (TPACK) framework is a relatively new construct that offers a useful perspective from which to understand the development of pre-service teachers' abilities in teaching with technology. It is grounded in the understanding that if teachers are to effectively integrate technology into their instruction, they need to integrate their knowledge of content, pedagogy and technology, instead of viewing these components as separate entities. Current efforts to develop TPACK in pre-service teachers have tended to focus on experiences in either a methods course or an educational technology course. It is admittedly difficult to adequately address technology, pedagogy and content in a single college course. Therefore, this study proposes using three courses that are offered in collaboration, a mathematics teaching methods course, a technology-intensive content-rich mathematical modeling course, and a practicum course, to study the development of connections between technology, content and pedagogy. For this multiple case study, TPACK changes in five pre-service teachers were tracked during a period of about 15 weeks. Data were collected using a TPACK survey, teaching philosophy statements, lesson plans, student teaching episodes, and weekly instructor meeting notes. A detailed analysis of the results demonstrates that the development of pre-service teachers' mathematics TPACK is complex, and there are a number of factors that are at play, such as the pre-service teachers' prior experiences with technology, their mathematical backgrounds and their beliefs about the use of technology in mathematics instruction. Assessing the development of TPACK in pre-service teachers is complicated by the fact that the available model for mathematics teachers' TPACK was developed using observations of in-service mathematics teachers.