Scholarship & Research
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Item The evolution of prospective elementary teachers' competencies : procedural knowledge, mathematical knowledge for teaching, attitudes, and enactment of mathematical practices(Montana State University - Bozeman, College of Letters & Science, 2015) Samuels, Shari Lynne; Chairperson, Graduate Committee: Elizabeth BurroughsThe purpose of this research was to explore the evolution of prospective elementary teachers' competencies (in practices, knowledge, and attitudes); examine the relationships that occur between knowledge, attitudes and practices; and develop an idea of how certain prospective elementary teachers grow and progress in their enactment of two of the Common Core Standards for Mathematical Practice, persevering in problem solving and constructing viable arguments. This was conducted as a case study of the first two of three inquiry-based mathematical content courses for elementary teachers. Both qualitative and quantitative data was collected from a cohort of students moving through the curriculum over the course of a year. Results showed there was an increase in prospective elementary teachers' mathematical knowledge for teaching scores over time, but no change in their procedural knowledge or attitude scores. Positive, linear relationships existed between all of the pair-wise comparisons between mathematical knowledge for teaching, procedural knowledge, and attitudes toward mathematics. Overall, students grew in their ability to problem solve and construct viable arguments in mathematics while moving through the curriculum, with a few exceptions. Three factors contributed to students' learning in the curriculum: the amount of effort made by the student, the atmosphere and attitudes of students in the class, and the nature of the content and questions asked in the curriculum. Another important consideration which arose from the data analysis was the opportunities the curriculum allowed for the practice of written versus verbal explanations, and what was formally assessed. Designers of teacher education programs using a similar curriculum should evaluate the importance of written versus verbal explanations in the goals of the course, and appropriately assess the students.Item Putting professional development into practice : how teachers process, implement, and disseminate specialized knowledge of standards(Montana State University - Bozeman, College of Letters & Science, 2014) Diemert, Kacey Marie; Chairperson, Graduate Committee: Jennifer LuebeckThis study provides a detailed account of how teachers disseminate knowledge of the Common Core State Standards for Mathematics to peers through school-based professional development. The design was a qualitative case study of four school district-based cohorts of middle grades teachers who led professional development in their schools and districts. Data was collected using interviews and school-based observations as each cohort was followed for eight months. The findings lead to a suggested framework for how teachers facilitate school-based professional development after having received professional development themselves, in a "teach the teachers" model. Data analysis produced a variety of results. Among other challenges, a lack of communication among school leaders created a barrier to dissemination. Although challenges were present, every cohort was able to facilitate effective professional development for their peers. The cohort members found that celebration of small successes during the process helped them persevere. The quality and depth of knowledge shared at the school level was diluted compared to the original presentation of the material, especially regarding the Mathematical Practices. This study provides encouraging results for future use of the "teach the teachers" model, which can be improved to maintain the quality of teacher-led, school-based professional development.Item Cognitive presence among mathematics teachers : an analysis of tasks and discussions in an asynchronous online graduate course(Montana State University - Bozeman, College of Letters & Science, 2008) Colt, Diana Lynn; Chairperson, Graduate Committee: Jennifer LuebeckHigher order learning, in terms of both process and outcome, is frequently cited as the goal of higher education (Garrison, Anderson, & Archer, 2000). However, the adoption of computer mediated communication in higher education has far outpaced our understanding of how this medium can best be used to promote higher order learning (Garrison, Anderson, & Archer, 2004). Researchers have examined quantitative components of computer mediated communication, but little work has been done to examine the cognitive aspects of online discussion. Those studies that do exist demonstrate inconsistent evidence of higher order learning in online discussions (Kanuka & Anderson, 1998; Littleton & Whitelock, 2005; McLoughlin & Luca, 2000; Meyer, 2003). Researchers conjecture that this could be due to the nature of the tasks that instructors implement for discussion purposes (Arnold & Ducate, 2006; Meyer, 2004; Murphy, 2004; Vonderwell, 2003). This study explored whether one component of instruction, the tasks assigned to students, had an effect on the level of cognitive presence that existed in the mathematical discussions of practicing mathematics teachers enrolled in an online graduate course. Through the method of content analysis, discussion transcripts were analyzed to look for evidence of higher-order learning based on the cognitive presence coding protocol developed by Garrison, Anderson, and Archer (2001). Seventeen students in a History of Mathematics course form the primary sample for this study. The results of the content analysis were triangulated with qualitative data from a questionnaire on student backgrounds and demographics and a post-course survey assessing student perceptions of their learning experiences. The researcher concluded that the MATH 500 course discussions did provide evidence of higher order learning in terms of cognitive presence. Task type, as defined in this study, was not directly related to the levels of cognitive presence achieved in the course. This finding does not negate the possibility of such a relationship, but in this study the effects of task type could not be isolated from other features of the course structure and assignments.Item Implementing professional development: a case study of mathematics teachers using inquiry in the classroom context(Montana State University - Bozeman, College of Letters & Science, 2011) Mathison, Heather Renee; Chairperson, Graduate Committee: Jennifer LuebeckA body of research supports the use of inquiry-based instruction in science and its use has been advocated in mathematics, but mathematical inquiry remains ill defined and difficult to enact in the mathematics classroom. While helpful, simply valuing inquiry as a learning tool is not sufficient to enable teachers to implement it successfully with their students. In part, the trouble with using inquiry may arise from the fact that teachers received insufficient exposure to inquiry when they were students themselves. The purpose of this case study was to examine how a sample of four teachers who participated in the Middle Grades Mathematics Project (MGM), an inquiry-based professional development opportunity, viewed inquiry and implemented it in their mathematics classrooms. In addition, this research attempted to identify influences that impacted how these teachers used inquiry. The four teachers selected for this study were identified due to interesting contrasts between their districts (urban vs. rural, traditional vs. reform text, level of involvement of fellow school teachers at MGM) and due to potential for comparison between the experience levels of the teachers within each district. Primary data collection occurred during the spring of 2008 and consisted largely of fourteen classroom observations for each teacher and a series of three semi-structured interviews. This data was supplemented by MGM program data and informal interviews. The four teachers in this case study showed that they had distinctly different interpretations of mathematical inquiry. From their different interpretations, a number of consistent features of inquiry were identified. Mathematical inquiry was found to be a student-centered but teacher-guided experience where students built mathematical meaning and collaborated with one another to hone their ideas. Despite their differing interpretations, all of the teachers acknowledged incorporating mathematical inquiry into their teaching after participating in the professional development. While the use of a reform text presented teachers with more lessons that the teachers felt could easily incorporate mathematical inquiry, the teachers that used a standard text were able to incorporate more mathematical inquiry into their lessons through designing lessons of their own or modifying lessons from outside sources.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.Item Action research in mathematics education : a study of a master's program for teachers(Montana State University - Bozeman, College of Letters & Science, 2009) Segal, Sarah Ultan; Chairperson, Graduate Committee: Maurice J. Burke; Jennifer Luebeck (co-chair)Action research is a methodology that has been found to be valuable as a problem-solving tool. It can provide opportunities for reflection, improvement, and transformation of teaching. The purpose of this study is to better understand these claims about the benefits of action research. Several research questions stand out: How is action research experienced by teachers? Is it beneficial and practical for teachers who use it? How are action research findings typically validated? What factors influence whether teachers are able to continue to practice action research? What kind of change has it initiated for teachers? And, how does action research focused on improving student achievement affect high need students? For the past five years, forty-five teachers completing master's degrees in mathematics education at a northern Rocky Mountain land-grant university have been required to conduct an action research project, referred to as their "capstone project." By studying this group of graduates, gathering both qualitative and quantitative data through surveys and interviews, I have examined the effectiveness of action research. This data, combined with graduates' capstone projects, has provided partial answers to the above questions, restricted to faculty-mediated action research within master's programs for mathematics teachers. The extent to which such action research projects impact teachers' practices has not been investigated before. While acknowledging that this research relied primarily upon self-reported data, the results strongly support what the research literature generally asserts about action research. (a) It is beneficial and often transformational for teachers as a professional development tool by allowing them to engage in a focused study of their own practice. (b) When done less formally it becomes more practical. (c) Communicating with others in the field builds confidence in teachers as professionals. (d) It makes teachers more actively reflective and more aware of their teaching and their students' learning. (e) It is effective in understanding and addressing the particular needs of high need students. Continued practice was highly dependent on time and support for action research within the school. Teachers often expressed the importance of having an action research community while conducting their capstones.