Thesis (Ph. D.)--Michigan State University. Dept. of Curriculum, Teaching, and Educational Policy, 2008. / Title from PDF t.p. (viewed Aug. 4, 2009). Includes bibliographical references (p. 287-297). Also issued in print.

This thesis is concerned mainly with the interplay between identities involving power series (which are called q-series) and combinatorics, in particular the theory of partitions. The thesis includes new proofs of some q-series identities and some ideas about the generating functions for the rank and crank, a new proof of the triple product identity and a combinatorial proof of a q-elliptic identity.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 149-153).

Thesis advisor: Lillie Albert / Enrollment in a Catholic elementary school has been shown to have a negative impact on student achievement in mathematics (Elder & Jepsen, 2013; Lubienski & Lubienski, 2006; Reardon et al., 2009). A child's mathematics achievement in early elementary school affects on her academic future beyond mathematics alone (CBMS, 2012). The importance of young students' experiences coupled with evidence of a negative impact of Catholic school enrollment on mathematics achievement indicates a need for changes in the mathematical instruction provided in Catholic elementary schools. Professional development can provoke change in mathematical instruction (National Mathematics Advisory Panel, 2008). This study examined the use of the Student Participation in Meaning-Making and Reasoning (SPMMR) domain of the Mathematical Quality of Instruction (MQI) tool as an analysis framework in a video-based professional development for teachers of grades K-3 in an urban Catholic school. First, I designed and delivered a professional development program featuring the MQI SPMMR domain and facilitating connections between the professional learning environment and the elementary classroom. Second, I investigated the experience of teachers in the PD program, as well as its impact on their lesson planning and reflection practices. Findings showed that participants incorporated elements of the SPMMR domain into their work in the classroom with evidence of an increased attention to elements of SPMMR in lesson planning, instruction, and reflective practices. This can be helpful for professional development providers and Catholic school leaders as they plan professional learning opportunities for teachers. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

Thesis (Ed.D.)--East Carolina University, 2009. / Presented to the faculty of the Department of Educational Leadership. Advisor: Marjorie Ringler. Title from PDF t.p. (viewed Apr. 23, 2010). Includes bibliographical references.

This study explores the pedagogical approaches used by fifth grade teachers to introduce division with decimals and the resultant understandings of students in their classrooms. The study is important because of the need for students to gain conceptually-based understandings in mathematics and the limited research on instruction and related learning of the very difficult and complex concept of division with decimals. In particular, there is limited research on strategies teachers use to develop students’ conceptual understanding of division with decimals. Therefore, the research questions are as follows. What strategies do teachers use to introduce division with decimals? When first learning to divide decimal numbers, how do fifth-grade students explain the strategies they use? The study is grounded in social constructivist learning theory and uses a collective case study methodology. Following the study design, three fifth-grade teachers from three schools were interviewed before and after an introductory lesson to division with decimals. They also were observed teaching the study lesson. Following the lesson, one to three students from each class (six in all) were interviewed on their understandings of division with decimals using their classwork from the lesson as a point of entry. The design includes three sources of data: transcriptions from semi-structured interviews of teachers and students, field notes from classroom observations, and artifacts from lessons. Results suggest that instruction of division with decimals varies such that the differences can be captured along a continuum of traditional to reform practices. The placement of the decimal point in the quotient is the focus of the discussion regardless of where the instruction lies on the continuum. Interestingly, as instruction moves towards the traditional end of the continuum, student engagement was a result of interaction with the teacher, whereas closer to the reform end of the spectrum students were engaged with the mathematics.

Thesis (Ph. D.)--University of Toronto, 2005. / Includes bibliographical references (leaves 125-134).

Thesis (Ph. D.)--Michigan State University. Dept. of Teacher Education, 2008. / Title from PDF t.p. (viewed xxx). Includes bibliographical references (p. 268-273). Also issued in print.

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisors: Tonya Bartell and James Hiebert, School of Education. Includes bibliographical references.

The purpose of this study, based on the third year of a three-year research study, was to examine Grade 6 students’ previously developed abilities to integrate their understanding of geometric growing patterns with graphic representations as a means of further developing their conception of linear relationships. In addition, I included an investigation to determine whether the students’ understanding of linear relationships of positive values could be extended to support their understanding of negative numbers. The theoretical approach to the microgenetic analyses I conducted is based on Noss & Hoyles’ notion of situated abstractions, which can be defined as the development of successive approximation of formal mathematical knowledge in individuals. I also looked to Roschelle’s work on collaborative conceptual change, which allowed me to examine and document successive mathematical abstractions at a whole-class level. I documented in detail the development of ten grade 6 students’ understanding of linear relationships as they engaged in seven experimental lessons. The results show that these learners were all able to grasp the connections among multiple representations of linear relationships. The students were also able to use their grasp of pattern sequences, graphs and tables of value to work out how to operate with negative numbers, both as the multiplier and as the additive constant. As a contribution to research methodology, the use of two analytical frameworks provides a model of how frameworks can be used to make sense of data and in particular to pinpoint the interplay between individual and collective actions and understanding.