An understanding of whole number place value is a critical component of second-grade mathematics. This understanding of place value provides the foundational concept for operations with whole numbers. The ability to understand the concept of place value and transfer that understanding to teaching addition and subtraction are often problems associated with teachers’ limited pedagogical content knowledge. Teachers must understand teaching place value does not consist of merely teaching students to name the digit in a particular location. A possible solution to the problem is to provide professional development trainings and implementation support through instructional coaching focused on the teaching of place value in a conceptual manner consistent with best pedagogical practices. Therefore, the purpose of this mixed method study is to describe the pedagogical content knowledge of second-grade teachers in order to answer the research question: What can you expect to see in the classroom teaching of place value from second-grade teachers who have attended 12 hours of professional development and have received instructional coaching? Quantitative data includes the use of the Learning Mathematics for Teaching assessment paired with participant observations, discussions, and interviews in order to gain a deeper understanding of the participants’ thinking. The participants of this study are four second-grade teachers from a rural school district outside of Houston, Texas. Each of the four participants attended 12 hours of professional development and received instructional coaching support through classroom observation with post-observation discussions, a model lesson, and instructional planning. The results of the study show that every participant implemented activities from the professional development, used questioning modeled by the presenter during the sessions, and discussed critical concepts in their classrooms. Additionally, teacher pedagogical content knowledge did improve after 12 hours of professional development and instructional coaching. However, the participants believe that further support should be given through a more detailed scope and sequence, which provides information as to when and how the new concepts and activities need to be incorporated in the classroom.

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.

Theses (Ed.D.)--University of Tulsa, 1987. / Bibliography: leaves 65-66.

Thesis (Ph. D.)--University of Chicago, Department of Education, December 1999. / Includes bibliographical references. Also available on the Internet.

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Measuring Mathematics Instruction in Elementary Classrooms:Comprehensive Mathematics Instruction (CMI) Observation Protocol Development and Validation Sue A. Womack Department of Educational Leadership and Foundations Doctor of Philosophy despite the availability of reform standards in mathematics since 1989 (National Council of Teachers of Mathematics), teachers have not yet aligned instruction with reform ideals on a widespread basis. (Cohen & Hill, 2000; Hiebert, et al., 2005; Spillane & Zeuli, 1999; J. W. Stigler & Hiebert, 1999). Consequently, mathematics education in elementary schools has not produced students with strong mathematical understanding (Hiebert & Grouws, 2007).

A handbook designed for teachers to illustrate how to utilize journaling as an effective teaching practice in the mathematics classroom. This thesis was written to illuminate educators about the powerful research and proper strategies for implementing journaling in mathematics. The handbook provides three lesson plan samples using journaling in the mathematics classroom for grades 3-5, strategies and idea for implementing journaling in mathematics, and tips and activities for mathematical journaling. The goal of this handbook is to give teachers clarity, examples, guidance, and strategies on mathematical journaling.

This design research study explored the potential of Curriculum Support Materials for promoting teaching as design. Conducted over a four-month period, the study traced the design, development, and pilot testing of a web site intended to serve as a professional development resource for teachers. The purpose of this exploratory study was to evaluate the web site's potential for promoting elementary mathematics teachers' understanding of teaching as a design activity and for supporting teachers in engaging in teaching as design. A team of four second grade teachers tested the web site during a two-week pilot unit on introducing the concepts of multiplication and division. Qualitative data were collected from these teachers through a planning and teaching log, a post-unit questionnaire, and a post-unit focus group interview. The findings indicated that the web site had the potential to promote teachers' understanding of teaching as design, but that the web site's potential as a stand-alone resource for supporting teachers in engaging in teaching as design was limited. Two specific features of the web site, the Unit Checklist and the videos addressing the related mathematics content, were identified as potentially valuable resources that could be incorporated into an ongoing professional development experience. Suggestions for revisions to the web site are discussed along with recommendations for further study. / Ed. D.

This sequential explanatory mixed methods study explores elementary mathematics teachers' perceptions regarding their mathematical self-efficacy, how teachers describe their perceptions about their prior mathematical learning experiences and their impact on their instructional practice in the elementary mathematics classroom. In support of this purpose, it is essential also to examine school leaders' role in developing elementary teachers' mathematics self-efficacy. The quantitative data was collected using the Mathematics Teaching and Mathematics Self-Efficacy Scale (MTMSE) online survey. A total of 60 elementary teachers in Grades 3, 4, and 5 were analyzed by descriptive statistics and correlations. A focus group of 6 elementary teachers was conducted, and analysis was explored to provide a more in-depth understanding of the quantitative results about teachers' prior experiences, beliefs, attitudes, and confidence levels around elementary mathematics. The last part of qualitative data collection and analysis was from eight individual campus administrator interviews. These interviews explored how support by campus administrators can increase elementary mathematics teachers' self-efficacy. From the teacher focus group and administrator individual interviews, it is clear that with experience and the correct level of support, teachers' levels of self-efficacy are increased. Experience and available support were shown to positively impact the self-efficacy of elementary mathematics teachers, according to the findings. The data indicated that as elementary mathematics teachers accumulate experience and utilize collaborative support to expand their knowledge of mathematical concepts and ideas, they experience a gradual surge in self-confidence and a heightened sense of assurance when instructing mathematics to their students.

The research for this doctoral study focused on children’s learning in mathematics and its relationship with independent pupil-pupil talk. In particular the interest was in how younger lower attaining children (aged 6-7) exchanged meaning as they talked together within a mathematical task. The data for the doctoral study had been gathered as part of the Talking Counts Project which I directed with colleagues at the University of Exeter. The project developed an intervention to encourage exploratory talk in mathematics with younger lower attaining children. Video material and transcripts of the mathematics lessons from nine classrooms that were part of the TC Project were used as the data set for the doctoral study. The focus of the analysis was on the independent pupil-pupil talk from one pre intervention session and one post intervention session from these nine classrooms. In using an existing data base, analysis was carried out in more depth and from a new perspective. A Vygotskyan sociocultural approach was maintained but analysis of the learning in the doctoral study was refocused in line with theories of situated meaning in discourse and with theories of the emergence of mathematical objects. Hence my examination of the children’s learning for the doctoral study went beyond the original research carried out in the TC Project. Within an interpretivist paradigm the methods of analysis related to the functional use of the children’s language. Interpretations were made of the children’s speech acts and their use of functional grammar. This enabled a study of both social and emotional aspects of shared intentionality as well as personal, social and cultural constructs of mathematical objects. The findings suggested that, where the talk was productive, the children were using deixis in sharing intentions and that this use could be related to the exchange of meaning and objectifying deixis.