This four-month-long qualitative case study looks closely at how one kindergarten teacher tried to help young children have more mathematical discussions. To discover and more deeply understand a kindergarten teacher’s ways of thinking about and facilitating mathematical discussion as part of everyday mathematical instruction, data was collected through classroom observations, semi-structured interviews, and various forms of documentation. Through data analysis in the constant-comparative method, this study found that intensive-discussion mathematics lessons could be accomplished through two pedagogical roles of the teacher. The first was creating a respectful learning environment to motivate children’s participation in mathematical discussion. The second was scaffolding student discussions to construct their own knowledge in the path of their mathematics learning. The analysis detailed here also revealed that successes and failures of discussion-intensive mathematics lessons depend on the teacher’s ability to overcome challenges she encounters while integrating mathematical discussion into her everyday lessons. The presented examples and descriptions in this study offer significant implications for early childhood teachers. This is particularly true for those who care about their young students’ mathematical development, yet either struggle to develop trusting classroom communities or do not know how to facilitate mathematical discussion. This study also provides insights into how teacher educators can help preservice teachers develop a profound understanding of mathematics teaching and learning. This highly influences their moment-by-moment decision-making to appropriately scaffold young children’s talk and learning. It offers implications for administrators about how to support early childhood teachers’ growth, learning, and their practices in teaching mathematics. / text

Thesis advisor: Elida V. Laski / Strategy selection is an essential aspect of problem-solving, particularly within the domain of mathematics. This dissertation examines the mechanisms that guide children’s arithmetic strategy selection in order to advance theoretical understanding of this essential component of cognitive development. Better understanding of arithmetic strategy selection is important because individual differences in children’s arithmetic strategies are predictive of arithmetic accuracy and later math achievement. The current study builds upon prior research that has identified cognitive processes associated with strategy selection by considering the role of metacognitive judgments. The study investigated the direct and indirect effects of cognitive and metacognitive factors on strategy selection in a group of first and second grade students (n = 126). The majority of students generated metacognitive judgments of their competence using decomposition (an advanced strategy at this age) that were consistent with their actual ability. In these cases, their judgments of competence were related to the frequency with which they used decomposition strategies. Additionally, children’s metacognitive judgments of the anticipated amount effort required to execute decomposition mediated the association between children’s cognitive processes/pre-requisite knowledge (working memory and fact fluency) and the frequency with which they used it. Theoretical and practical implications of these findings are discussed. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental and Educational Psychology.

This dissertation investigates the ways in which pre-k teachers understood the math content that they were to teach and their math instruction. To investigate this, a qualitative case study examining five pre-k teachers was conducted. Data sources included observation field notes, teacher interviews, and documents such as state and district pre-k guidelines. The findings from this dissertation suggest that pre-k teachers’ knowledge entails both knowledge of subject matter and pedagogical content knowledge. In addition, this study identified what these pre-k teachers knew about math and teaching/learning math as well as what they still needed to know to provide high quality and effective math instruction. Chapter 1 introduces my research question and important terms, such as mathematical knowledge for teaching (MKT). Chapter 2 synthesizes relevant literature in the area of effective math instruction, theoretical framework of teachers’ mathematical knowledge for teaching and early mathematics education. The literature review seeks to highlight the importance of early childhood teachers’ deep understanding of mathematical content and of their math instruction. Chapter 3 forwards the specific conceptual framework for this study while detailing the methodology that guided this investigation including data gathering and analysis. Chapter 4 presents the findings from this research. It examines pre-k teachers’ understanding of mathematical content that they are to teach and their knowledge of how to teach mathematics. Chapter 5 addresses the significance of these two major findings. First, I discuss the four types of mathematical knowledge and skills that these pre-k teachers possess. I also compare and contrast them with the teacher knowledge examined in the literature. Then, by examining research literature on early math education, I suggest what mathematical knowledge and skills they still need to attain to offer high-quality and effective math instruction. This dissertation concludes with a discussion of implication for teachers, teacher educators, and suggestions for future research. / text