Scholarship & Research
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Item The mathematics in mathematical modeling(Montana State University - Bozeman, College of Letters & Science, 2017) Fulton, Elizabeth Anne White; Chairperson, Graduate Committee: Elizabeth BurroughsThe purpose of this research was to investigate how teachers interact with mathematics while teaching mathematical modeling to elementary students. To conduct this study, I used a case study approach with four elementary teachers. Each teacher participated in professional development on mathematical modeling prior to the study and incorporated mathematical modeling into their classroom. Modeling task lessons were observed and teachers participated in interviews before and after each lesson. I qualitatively explored what mathematical decisions teachers made while teaching mathematical modeling and how students' mathematical contributions influenced the modeling cycle. This analysis took place through three analytical lenses: the mathematics used, the teacher's interactions with their student's mathematical ideas, and as compared to components of the mathematical modeling cycle. Findings indicate that students engaged in meaningful mathematics to explore real-world problems. Across all cases, teachers prepared students to use mathematics by creating tasks with mathematical opportunities and by orienting the students towards using mathematics to investigate the problems. Each teacher allowed their students to introduce most of the mathematical ideas used to investigate the modeling questions. Each task became a mathematical modeling task by the way it was implemented, through teachers' and students' contributions to the activity.Item Preservice elementary teachers' mathematical content knowledge of prerequisite algebra concepts(Montana State University - Bozeman, College of Letters & Science, 2007) Welder, Rachael Mae; Chairperson, Graduate Committee: Linda SimonsenResearch illustrating that student achievement is affected by teachers' knowledge advocates for K-8 teachers to be knowledgeable regarding prerequisite algebra concepts: (1) numbers (numerical operations), (2) ratios/proportions, (3) the order of operations, (4) equality, (5) patterning, (6) algebraic symbolism (including letter usage), (7) algebraic equations, (8) functions, and (9) graphing. The theoretical framework for the knowledge for teaching mathematics built for this study suggests that the mathematical content knowledge needed for teaching consists of specialized content knowledge in addition to common content knowledge. Specialized mathematical content knowledge extends beyond solving mathematical problems to encompass how and why mathematical procedures work and an awareness of structuring and representing mathematical content for learners. The effects of an undergraduate mathematics content course for elementary education students on preservice teachers' common and specialized content knowledge of prerequisite algebra concepts was investigated, using a pre-experimental one-group pretest-posttest design.