Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item Integrating universal design for learning in online math education: the Desmos experience(Montana State University - Bozeman, College of Education, Health & Human Development, 2023) Wiehe, Blake Skyler; Chairperson, Graduate Committee: Nick LuxThe Universal Design for Learning (UDL) framework is a modern neuroscientific approach to creating learning experiences that are highly accessible and engaging for all students. Despite the growing evidence supporting the theory of UDL, the literature significantly lacks examples of the practical application of UDL principles in curricular resources. This study was designed to investigate an online math learning platform that claims to be developed according to the UDL Guidelines. The purpose of this study is to illustrate the practical application of various UDL Guidelines within the Desmos middle school math platform. The UDL Guidelines served as the basis for this analysis, mapping the data collection and analysis according to the checkpoints that substantiate the nine UDL Guidelines. Through the analysis of six randomly chosen Desmos units from sixth through eighth grade, the results suggest that Desmos substantiates their claim to UDL-alignment through a host of interactive, customizable, and highly relevant learning experiences. The Desmos platform lacks certain features like layout customization, hyperlinked vocabulary support, and activation of background knowledge that could further bolster its alignment to the UDL Guidelines. However, the alignment examples discovered offer a window into UDL-aligned design thinking that can serve as inspiration for external curriculum developers and educators looking to create their own UDL learning experiences. This study was a pilot attempt at characterizing UDL design thinking found within an existing curriculum. Future studies analyzing other curricular resources for UDL alignment are warranted, along with further investigations into the impact of those platforms on student achievement.Item Exploring the impact of standards-based learning on lesson planning in an undergraduate math methods course(Montana State University - Bozeman, College of Education, Health & Human Development, 2022) Day, Corinne Thatcher; Chairperson, Graduate Committee: Fenqjen LuoThe study examines the performance of pre-service K-8 mathematics teachers on lesson planning assignments using the Association of Mathematics Teacher Educators (AMTE) 2017 Standards for Preparing Teachers of Mathematics as a reference for evaluation. In addition to contributing to the literature on pre-service mathematics teachers' pedagogical content knowledge, the study aims to evaluate the impact of standards-based learning (SBL) on student growth in a higher education setting, where SBL has not been widely implemented or studied. A case study research design is utilized to identify strengths and weaknesses in planning for mathematics instruction in a cohort of 21 PSTs enrolled in a math methods course at a small public university, with comparisons made between first and final drafts of two lesson-planning assignments on which PSTs received extensive instructor feedback. Interviews were also conducted with four participants who student taught during the subsequent semester. Findings indicated growth in performance between drafts of the lesson-planning assignments in terms of designing student-centered math lessons but also revealed gaps in PSTs' mathematical content knowledge. Specifically, most PSTs lacked an ability to link procedures to their underlying concepts, resulting in less than proficient performance on mathematics lesson planning. Contributions of the study include the development of an AMTE-aligned tiered rubric for evaluating both PST and mathematics teacher educator (MTE) performance in mathematics instruction and for potential use in framing and evaluating Standards-based practicum experiences in mathematics teacher preparation.Item Hispanic ELL middle-school students and their teachers: perceptions of three mathematics teaching practices(Montana State University - Bozeman, College of Education, Health & Human Development, 2022) Roberts, Christi Szulczewski; Chairperson, Graduate Committee: Jayne DowneyEven though Hispanic English Language Learners (ELL) are one of the fastest growing student demographics in the United States, limited research exists exploring how Hispanic ELLs benefit from mathematics teaching practices that have been determined to be highly effective. The purpose of this qualitative case study was to examine the perceptions of Hispanic ELL middle-school students regarding the efficacy of research-informed instructional practices, as embodied in the Mathematics Teaching Practices described by the National Council of Teachers of Mathematics (NCTM, 2012). Capturing Hispanic ELL student perceptions is of great importance due to the challenging situations that many Hispanic ELL students and their families face (Schneider et al., 2006) in the United States. Additionally, the concerning differences have been observed in achievement data for Hispanic and non-Hispanic students and for ELL and non-ELL students. To address the layered challenges that Hispanic ELL students face daily in school, teachers, school leaders, and researchers can turn to student consultation as one way to gather information to inform teaching practices and develop positive mathematical identities. Findings from this multi-phased qualitative case study suggest that both students and teachers value and find benefit in the use of mathematical discourse, posing of purposeful questions, and attention to multiple representations. Additional insights were uncovered as alignments and divergences between perceptions were analyzed. Recommendations for practice include promoting mathematical discourse, posing purposeful questions for multiple purposes, emphasizing multiple representations, including student voice, building mathematical identity through instruction, and leveraging alignments and divergences in perceptions.Item K-8 preservice teachers's preparedness for technology integration in mathematics: examining perspectives, anticipated practices, and abilities(Montana State University - Bozeman, College of Education, Health & Human Development, 2022) Meyerink, Monte Shane; Chairperson, Graduate Committee: Fenqjen Luo; This is a manuscript style paper that includes co-authored chapters.Research on the use of technological resources--such as virtual manipulatives and mathematical games--in kindergarten through eighth-grade mathematics has highlighted numerous benefits to students' achievement in and attitudes toward mathematics. However, studies have also highlighted preservice teachers' lack of preparedness to integrate technology into their future classrooms. Thus, the purpose of this dissertation is to examine kindergarten through eighth-grade preservice teachers' preparedness to integrate technology into mathematics by analyzing their perspectives on technology integration, their anticipated technology integration practices, and their technology integration abilities. In this three-manuscript dissertation, qualitative analyses employed a social constructivist paradigm and utilized an ethnographic approach to examine preservice teachers' preparedness to integrate technology. By using the PICRAT model as a guiding theoretical framework in each study, preservice teachers' perspectives and abilities were examined in relation to how their anticipated uses of technology would impact mathematics instruction in respect to both students' learning and teachers' pedagogical practices. Findings showed that preservice teachers' tended to report a lack of knowledge in relation to technology integration and both ask questions and express concerns related to how to appropriately integrate technology into mathematics. Nevertheless, preservice teachers also reported an intent to integrate technology into their future classrooms at a relatively frequent basis. When examining preservice teachers' abilities to either evaluate an existing geometry activity or create a geometry activity that utilizes a technological resource, preservice teachers tended to evaluate or create activities that integrated technology in a way that both enabled interactive learning on behalf of the students and amplified teachers' pedagogical practices. Activities that used technological resources to either promote students' passive learning or replace teachers' practices were less frequent, and activities that used technology to either foster students' creative learning or transform teachers' practices were rare. Additionally, preservice teachers' activities tended to align with PICRAT levels that are associated with higher degrees of impact on mathematics instruction when preservice teachers evaluated activities rather than created activities. To conclude, implications for teacher education programs and areas of future research are presented and discussed.Item Does a student's use of self-regulation change in the flipped classroom?(Montana State University - Bozeman, College of Education, Health & Human Development, 2018) Elakovich, Denise Marie; Chairperson, Graduate Committee: Carrie B. MyersMany college freshmen are required to enroll in remedial math every semester as a result of low college placement exams with many of these students failing to succeed in their remedial math courses. Students may fail their remedial math course due to low levels of control of learning, self-efficacy or self-regulation. The purpose of this study was to investigate if the flipped classroom is an effective teaching method for students in a remedial math course and if this method increases a student's control of learning, self-efficacy and self-regulation. This study implemented a quasi-experimental design to compare students in a flipped remedial math class to students in a lecture remedial math class using the Motivated Strategies Learning Questionnaire (MSLQ) designed by Pintrich (1991) to measure control of learning, self-efficacy and self-regulation. Data analyses included frequency data to report the descriptive statistics of students in remedial math; independent t-tests to report significant differences of MSLQ scores and posttest COMPASS math scores; and multiple regressions to report associations among dependent and independent variables in the study. The results found no significant difference for control of learning, self-efficacy, or self-regulation of students in the flipped classroom compared to students in the lecture classroom. A significant difference at rho < .10 was found for math outcomes for students in the flipped classroom compared to students in the lecture classroom. The findings also indicate a small net effect for control of learning, self-efficacy and self-regulation on math placement as well as math outcomes for students in a remedial math course. Also, a student's self-efficacy at the end of the course was predicted by a student's level of self-efficacy and prior academic knowledge at the start of the semester. In conclusion, the findings of this study suggest that the flipped classroom is an effective teaching method to use in a remedial math class. Limitations of this study include a small sample size as well as validity and reliability concerns with the use of the MSLQ survey suggesting further research is needed to investigate the effectiveness of the flipped classroom in a remedial math class.Item Evolving student perceptions of mathematical identity: a case study of mindset shift(Montana State University - Bozeman, College of Education, Health & Human Development, 2017) MacKinder Clyatt, Lori Ann; Chairperson, Graduate Committee: William Ruff.This qualitative study documented the perceptions mathematics students at an alternative high school had during a shift in mindset from fixed to growth in a dual credit math course. The purpose of this study was to capture student perceptions of their own mindset shift and how their perceptions of mathematics changed. The conceptual framework used to interpret the findings was grounded in attribution theory. A case study research design bounded the perceptions of the students and the meanings they gave to these experiences. Data were collected and analyzed from multiple sources: participants' responses to writing prompts, focus group interviews, research field notes, and student artifacts. The grounded narrative that revealed itself from the student perspective over the course of this study was one of growing student trust in self and others as well as a deepening of student mathematical identity. It also showed that student perceptions of mathematics can shift in a short period of time (20 weeks) from a position of fear, shame, apprehension, and defeat to willingness, perseverance, joy, and overcoming challenges into a growth mindset. The recorded focus group discussions and various writing prompts captured the students' perceptions of their mindset shift in relationship to learning and deepening their understanding of mathematics. This study documents the power in individuals to shift out of a truncated learning cycle into a mathematical mindset. If the ability of students to shift from a fixed mindset into a growth mindset is dependent upon an educational environment, an educator's striving for a growth mindset becomes an important component.