Scholarship & Research
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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 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 Environments that encourage mathematics graduate teaching assistants : the effects of institution type and availability of training(Montana State University - Bozeman, College of Letters & Science, 2007) Latulippe, Christine Lynn; Chairperson, Graduate Committee: Linda Simonsen; Dana Longcope (co-chair)This dissertation examined factors which are related to mathematics graduate teaching assistants' (GTAs') teaching attitudes and perceptions of the support for good teaching in their respective math departments. The research questions addressed differences between math GTAs at four groups of universities, categorized using an institution's Carnegie Classification and the availability of teacher-training for GTAs, in regard to math GTA perceptions of the support for good teaching in their department and in regard to math GTA attitudes toward teaching. Additionally, correlations between math GTA perceptions for support and math GTA attitudes toward teaching were examined. Finally, through use of multiple data sources, a qualitative analysis of the primary teaching support structures available to math GTAs at the participating universities in the four groups was conducted.Item The design, implementation, and evaluation of a teacher training workshop for mathematics graduate teaching assistants(Montana State University - Bozeman, College of Letters & Science, 2009) Trouba, Jerome Charles; Chairperson, Graduate Committee: David YoppTo help train new graduate mathematics teaching assistants (GMTAs), a teacher training workshop was designed based on K-12 literature on the components of effective professional development (Garet, et al., 2001). The workshop consisted of six two-hour seminars over a six week period followed by a classroom feedback component of either peer coaching or observation, for a total time commitment of 18 hours. The content of the workshop addressed teaching techniques specifically targeted to GMTAs. These ideas included elements of reflection, techniques for engaging students through active learning, asking good questions, utilizing wait-time, and using formative assessment techniques. The assessment of the workshop was based on Guskey's (1999) work on the five levels of effective professional development evaluation. In the mixed-methods design, 18 GMTAs participated in the workshop. Data collection consisted of three sets of videotapes, two sets of interviews, surveys, and coaching and observation forms. Results indicated that a well-designed workshop can impact teaching practices. Through interviews, GMTAs indicated they were more reflective of their teaching, thought more about the questions they asked, and actively involved their students more during lectures. The workshop was considered effective not only because GMTAs said they changed their teaching but because changes were seen in their teaching. For nine GMTAs strong evidence was collected of their change in teaching: they not only mentioned specific changes to their teaching in the interviews, but these specific changes were observed on videotapes of their classroom. In comparing peer coaching with observation, seven of the ten in the coaching group commented that just watching another's class helped them to improve more than any other part of the coaching process. Only two of the ten coaching participants commented on the helpfulness of the pre and post conference discussions involved with coaching. From the data collected, the possible added benefits of peer coaching may be outweighed by the additional time, organization, and pairing requirements present in a GMTA setting. Five constructs that influenced the effectiveness of the peer coaching experience are discussed. This project contributes to the research base regarding adapting K-12 professional development literature into a collegiate setting.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.