Developing Ambitious Mathematics Instruction Through Number Talks

• Main Author: Woods, Dawn Marie
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2018
• Subjects: Educational Change; Educational Environment; Educational Strategies; Literature Reviews; Mathematics Achievement; Mathematics education; Outcomes of Education; Professional Education; Teacher education; Teacher Educators; Teaching Methods
• ISBN: 9780438864245; 0438864247

Policy and standards documents such as the National Council of Teachers of Mathematics’ Principles to Actions: Ensuring Mathematical Success for All and the National Governors Association’s Common Core State Standards-Mathematics state that students deeply learn mathematics when they socially construct knowledge and are provided with opportunities to talk about their mathematical understandings, both while actively doing mathematics. Yet, it is often unclear how to implement these ambitious instructional practices into the classroom. To investigate this problem, I conducted a 20-week design–based research study with the primary activities being: (1) weekly collaborative teacher meetings focused on implementing Number Talks in the classroom and (2) daily Number Talks in teachers’ classrooms. By using Number Talks – short conversations around purposefully designed computation problems – as a catalyst for change, this study provides teachers with opportunities to investigate, enact, and reflect on how to implement Number Talks with their students as a way to support the development of a math-talk community. To this end, this dissertation addresses three related questions aiming to understand whether and how to assist elementary teachers to develop classroom environments that support students in actively doing and talking about mathematics. These questions are as follows: (1) How does a learning cycle support in-service teachers in learning about Number Talks? (2) How are Number Talks enacted within whole-class discussions during the mathematics instructional block? (3) Does students’ participation in Number Talks affect their attitudes towards math and learning outcomes? Data analysis revealed that as teachers participated in a learning cycle situated within collaborative meetings they began to apply the ambitious instructional practices developed and rehearsed within these meetings as they enacted Number Talks with students. The implementation of these practices, in turn, supported teachers to work towards developing a student-centered learning environment. As students’ contributions became a focal point of discussions, students’ attitudes towards mathematics improved as they became excited about sharing their mathematical thinking within their classroom community. In addition, students developed more sophisticated strategies as they participated in discussions about their mathematical ideas, and over time their mathematical talk shifted from describing the procedure they used to justifying or offering a mathematical reason why a solution is correct. This study contributes to the field of teacher education by expanding current practice-based professional education literature. In particular, this study documents how a cycle of collaborative inquiry supports teachers in developing ambitious instructional practices and, in turn, how students learn about the structure of mathematics as they experience these types of ambitious instructional practices. Further, this study contributes to the field of mathematical argumentation as it provides insight into how young children begin to explain their mathematical ideas as they learn to take another’s point of view, analyze, and revise their thinking. In addition to these research contributions, this study has practical implications for classroom teachers, math teacher educators, district leaders, and other professional development providers both with respect to the design of professional learning for teachers as well as to the potential of using Number Talks as a way to engage students in learning about mathematics.