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 Improving chemistry pass rates in underachieving algebra students by use of review sessions(Montana State University - Bozeman, Graduate School, 2016) Townley, Linda M.; Chairperson, Graduate Committee: Peggy Taylor.Mount Vernon High School in Alexandria, Virginia struggles to meet state requirements on test scores and student achievement. With over 50% of our students receiving free or reduced lunch and nearly 20% of our students in the English for Speakers of Other Languages program, teachers face many challenges. Pass rates in chemistry and its associated End-of-Course, Standards of Learning exam have missed state and county targets for many years. For this reason I designed a program to provide extra support to a pre-identified group of at-risk students. Algebra 1 is a pre-requisite to be enrolled in chemistry and the class relies heavily on its use. Any student who has trouble in algebra is likely to struggle in chemistry. At the beginning of the school year I identified all of my students who received a D in algebra or failed the corresponding state exam in algebra. I asked these students to participate in a voluntary program for extra review, practice and remediation. This was accomplished during a non-academic study period and was available for one hour, once a week, for the duration of the school year. Pre- and post-assessment data was collected to analyze the effectiveness of the program. In addition students' attitudes were investigated as being a large part of student's success in the classroom. Surveys, interviews and journals were used to track student changes in attitude over the year. What developed throughout the program was a strong student-teacher relationship in the small number of students who participated. Results indicated that students were able to perform near the level of their peers with a stronger algebra background if they participated in the treatment. More than half of the students who met the criterion for inclusion in the program chose to participate. These students' normalized gains were far above the non-treatment group giving strong support to the success of the program. Students also showed gains in their attitudes about school in general.Item Predicting performance in ninth grade algebra through the use of Piagetian tasks, achievement test scores, and previous performance(Montana State University - Bozeman, 1976) Olsen, Gary AlbertItem An analysis of the predictive validity of eight predictors of success in first-year algebra(Montana State University - Bozeman, 1971) Bauer, Gary WallaceItem Developing basic concepts in ninth grade algebra(Montana State University - Bozeman, 1956) Hemmy, DarleItem Presentation of algebra by programmed textbook or teaching machines(Montana State University - Bozeman, 1962) Booth, William J.Item An investigation of two approaches in teaching elementary algebra(Montana State University - Bozeman, 1967) Tripp, Merrill LaVereItem Instructional problems revealed through use of standardized tests administered to students in sub-college algebra at Montana State College(Montana State University - Bozeman, 1958) Terwilliger, Homer LewisItem The effects of project-based learning on student acheivement and motivation in remedial high school algebra(Montana State University - Bozeman, Graduate School, 2014) Konrad, Terina Frances; Chairperson, Graduate Committee: Peggy Taylor.Research was conducted to look into the effects of project-based learning on student achievement and motivation in a remedial high school algebra classroom. Throughout the 12 week research period, 13 projects or activities were included in the algebra curriculum. Projects included card games to help reinforce integer operations, order of operations puzzles, equation bingo, and six teleconferences with NASA engineers about applications of mathematics outside of the classroom. Through student surveys, interviews, and summative assessment scores, in addition to a classroom observation journal by the teacher, data was collected on the effects of project-based learning. The data showed an improvement in pre and post test results. The increase was a positive outcome of the research, but was not substantial enough to prove project-based learning in high school algebra is the most successful way to teach the material. It was found students who have extrovert personalities are more receptive and benefit more from project-based learning. Introvert personalities struggle with project-based activities due to social anxiety preventing them from fully participating in the activity. The results of the data analysis did show a substantial increase in students' attitudes towards math. By the end of the treatment students made positive comments concerning math and wrote about how math is important for their futures. The students who made the positive comments were more likely to complete assignments and study to understand the material. Overall, the research showed project-based learning as being a good teaching tool to help motivate students to learn.