Matching Items (4)
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- All Subjects: Mathematics--Study and teaching--Evaluation.
- All Subjects: Student teachers
- Creators: Middleton, James A.
Description
In this mixed-methods study, I examined the relationship between professional development based on the Common Core State Standards for Mathematics and teacher knowledge, classroom practice, and student learning. Participants were randomly assigned to experimental and control groups. The 50-hour professional development treatment was administered to the treatment group during one semester, and then a follow-up replication treatment was administered to the control group during the subsequent semester. Results revealed significant differences in teacher knowledge as a result of the treatment using two instruments. The Learning Mathematics for Teaching scales were used to detect changes in mathematical knowledge for teaching, and an online sorting task was used to detect changes in teachers' knowledge of their standards. Results also indicated differences in classroom practice between pairs of matched teachers selected to participate in classroom observations and interviews. No statistical difference was detected between the groups' student assessment scores using the district's benchmark assessment system. This efficacy study contributes to the literature in two ways. First, it provides an evidence base for a professional development model designed to promote effective implementation of the Common Core State Standards for Mathematics. Second, it addresses ways to impact and measure teachers' knowledge of curriculum in addition to their mathematical content knowledge. The treatment was designed to focus on knowledge of curriculum, but it also successfully impacted teachers' specialized content knowledge, knowledge of content and students, and knowledge of content and teaching.
ContributorsRimbey, Kimberly A (Author) / Middleton, James A. (Thesis advisor) / Sloane, Finbarr (Committee member) / Atkinson, Robert K (Committee member) / Arizona State University (Publisher)
Created2013
Description
Drawing on Lave and Wenger (1991) this study explores how preservice elementary teachers develop themselves as teachers of mathematics, in particular, from the time of their teacher education courses to their field experiences. This study also researches the critical experiences that contributed to the construction of their identities and their roles as student teachers in their identity development. The stories of Jackie, Meg, and Kerry show that they brought different incoming identities to the teacher education program based on their K-12 school experiences. The stories provide the evidence that student teachers' prior experience as learners of mathematics influenced their identities as teachers, especially their confidence levels in teaching mathematics. During the mathematics methods class, student teachers were provided a conceptual understanding of math content and new ways to think about math instruction. Based on student teachers' own experiences, they reconstructed their knowledge and beliefs about what it means to teach mathematics and set their goals to become the mathematics teachers they wanted to be. As they moved through the program through their student teaching periods, their identity development varied depending on the community of practice in which they participated. My study reveals that mentor relationships were critical experiences in shaping their identities as mathematics teachers and in building their initial mathematics teaching practices. Findings suggest that successful mentoring is necessary, and this generally requires sharing common goals, receiving feedback, and having opportunities to practice knowledge, skills, and identities on the part of beginning teachers. Findings from this study highlight that identities are not developed by the individual alone but by engagement with a given community of practice. This study adds to the field of teacher education research by focusing on prospective teachers' identity constructions in relation to the communities of practice, and also by emphasizing the role of mentor in preservice teachers' identity development.
ContributorsKang, Hyun Jung (Author) / Middleton, James A. (Thesis advisor) / Battey, Dan (Committee member) / Sloane, Finbarr (Committee member) / Arizona State University (Publisher)
Created2012
Description
The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using for instruction. Additionally, participants indicated their college major, institution attended, years of experience, and participation in various other learning opportunities. This data was analyzed to look for changes in knowledge, first among those still in college, then among those already in the field, and finally as a whole group to look for a pattern of growth from pre-service through working in the classroom. I compared these results to the theories of learning espoused by the creators of these two tests to see which model the data supports. The results indicate that growth in PCK occurs among college students during their teacher preparation program, with much less change once a teacher enters the field. Growth was not linear, but best modeled by an s-curve, showing slow initial changes, substantial development during the 2nd and 3rd year of college, and then a leveling off during the last year of college and the first few years working in a classroom. Among current teachers' the only group that demonstrated any measurable growth were teachers who majored in a non-education field. Other factors like internships and professional development did not show a meaningful correlation with PCK. Even though some of these models were statistically significant, they did not account for a substantial amount of the variation among individuals, indicating that personal factors and not programmatic ones may be the primary determinant of a teachers' knowledge.
ContributorsJohnson, Jeffrey (Author) / Middleton, James A. (Thesis advisor) / Marsh, Josephine P (Committee member) / Sloane, Finbarr (Committee member) / Arizona State University (Publisher)
Created2016
Description
This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change.
The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development.
The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items.
The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions.
Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change.
The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development.
The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items.
The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions.
Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change.
ContributorsByerley, Cameron (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn P (Committee member) / Middleton, James A. (Committee member) / Saldanha, Luis (Committee member) / Mcnamara, Allen (Committee member) / Arizona State University (Publisher)
Created2016