Date of Award

2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Education

First Advisor

Janine T. Remillard

Abstract

Numerous scholars propose that students can develop deep understandings of mathematical concepts through contextualized problem solving (e.g. Freudenthal, 1991), but little is known about how teachers view contextualized problems [CPs] and whether they implement CPs in ways that align with researchers' recommendations (Chapman, 2006). The limited research available on the topic suggests that teacher beliefs may lead to practices that fail to realize CPs' potential for building conceptual understanding (Gainsburg, 2008, 2009; Pierce & Stacey, 2006) and that teachers may lack a firm understanding of how CPs can support learning (Lee, 2012). This case study sought to characterize the role of contextualized problems in one algebra unit to provide insight into how CPs can support and constrain the learning of mathematics and to provide a better understanding of how teacher beliefs and practices mediate students' experiences with a CP-based curriculum.

Qualitative methods were used to characterize the role of CPs in the written curriculum, the teacher's plans, and the classroom enactment of the curriculum. Teacher interviews provided data on teacher beliefs and factors that influenced her decisions.

The role of CPs changed as the curriculum was transformed from the written page to classroom enactment. The teacher re-sequenced tasks in response to legitimate concerns; this adaptation compromised the progression from CPs to non-contextualized problems present in the written curriculum. As a result, students had fewer opportunities to leverage their experiences with CPs to make sense of analogous non-contextualized tasks, as intended by the curriculum developers. The teacher highlighted the intended mathematics during discussions of CPs by prompting students to reflect across contexts; this type of task was not present in the written curriculum. When the progression from CPs to non-contextualized problems was preserved, students' experiences with CPs were rarely referenced during later work on non-contextualized tasks or during discussions of summative, generalizing tasks.

The analytical framework created to characterize the role of contextualized problems in the curriculum has the potential to guide research, curriculum development, and instruction. Findings around teacher adaptations and recommendations for leveraging the affordances of CPs in instruction have implications for teachers and curriculum developers.

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