Graduation Term

2014

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics: Mathematics Education

Committee Chair

Cynthia Langrall

Committee Member

Jae Baek

Abstract

The aims of this study were to investigate how teachers incorporated learning trajectory based research into practice, specifically how they made sense of students' thinking in relation to classroom instruction. To conduct this study, I used an ethno-methodological approach (Garfinkel, 1967) across several months, with three fourth-grade teachers in a diverse, high needs school. Each of the teachers participated in professional development on using learning trajectories (Sarama & Clements, 2009) as a tool to formatively assess individual student's thinking as a means to inform classroom instruction. During the study, the teachers were asked to conduct clinical interviews with students in their classroom and note events during the interviews that revealed students' thinking. They were also asked to note revealing events during their instruction of a month-long mathematics unit. Following student interviews and classroom instruction, the teachers participated in debriefing interviews in which we discussed each of the noted events, what they implied about the students' understanding, and if they provided any implications for instruction. Each of the debriefing interviews was audio recorded and transcribed verbatim resulting in approximately 200 pages of transcribed interviews. Using the construct of mathematics teacher noticing (Jacobs, Lamb, & Philipp, 2010) as

an analytical lens, I qualitatively explored (Miles, Huberman, & Saldana, 2014) what teachers noticed about their students and how they used knowledge of students, gained from task-based interviews and classroom interactions, to inform whole-classroom instruction and planning. I investigated how the teachers referenced learning trajectory based research in their noticing and if and how it surfaced in their practices. I also looked across the three cases to compare and contrast themes.

Findings indicate that the teachers noticed student thinking constantly in their daily work through actions such as students' measurement strategies, counting strategies, language, interactions with other students, and written accounts. However, the actions were not always connected with instructional implications. Across the cases, mathematical tasks and curriculum were critical in helping teachers understand students' thinking and implement it into practice. Interview tasks were relevant in instructional planning when they were similar or connected to future classroom tasks. Within the classroom setting, the teacher's willingness to supplement or modify current curriculum determined how she used knowledge of students' thinking in practice. Teachers unwilling to modify curriculum had difficulty using knowledge of students' thinking in practice. Findings also indicate that knowledge of an individual student's thinking gained from interviews informed teachers of student misconceptions and current understandings of a topic, but much of what informed the teachers' instruction came from a complex framework of past education and daily experiences with students. Lastly, teachers interpreted, redefined, and even rejected learning trajectory research in their own ways depending on how well it agreed with their current practices and belief systems. These findings have implications for the design and conduct of teacher professional development and indicate the need for modifications to current learning trajectories (Sarama & Clements, 2009) to make them more accessible to teachers.

Access Type

Dissertation-Open Access

DOI

http://doi.org/10.30707/ETD2014.Wickstrom.M

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