AbstractsEducation Research & Administration

In Trinidad and Tobago, there have been substantive efforts to reform mathematics education. Through the implementation of new policies, the reformers have promoted changes in mathematics curriculum and instruction. A focus of the reform has been that of increasing opportunities for students to engage in reasoning and proving. However, little is known about how these policies affect the opportunities for reasoning and proof in the written curriculum, the teaching of proof, and students' learning. Furthermore, we are yet to know how the high-stake assessment measures interact with these new policies to impact the teaching and learning of proof. In this dissertation, my overarching question asks: What are the implications of reform on the teaching and learning of secondary school mathematics in Trinidad and Tobago? To answer this question, I conducted three studies, which examined the content, teaching, and students’ conceptions. All the studies are situated in the teaching reasoning and proof when introducing geometry concepts. In the first study, I conduct a curriculum analysis focused on examining the opportunities for reasoning and proof in the three recommended secondary school textbooks. In the second study, I conduct classroom observations of teachers’ geometry instruction focusing on opportunities for engaging students in reasoning and proof. In the third study, I examine geometry students’ conceptions of proof. The three studies are intended to provide an overview of the impact of reform on instructional issues in relation to the dynamics between teachers, student, and content (Cohen, Raudenbush, & Ball, 2003). For the first study, I adapt a framework developed by Otten, Gilbertson, Males, and Clark (2014) to investigate the quality and quantity of the opportunities for students to engage in or reflect on reasoning and proof. The findings highlight some unique characteristics of the recommended textbooks such as, (a) the promotion of the explanatory role of proof through the affordances of what I define as the Geometric Calculation with Number and Explanation (GCNE) exercises, (b) the necessary scaffolding of proof construction through activities and exercises promoting pattern identification, conjecturing, and developing of informal non-proof arguments, and (c) the varying advocacy for Geometry as an area in the curriculum where students can experience the work of real mathematicians and see the intellectual of proof in their mathematical experiences. All these characteristics align with the reformers’ vision for the teaching and learning of reasoning and proof in secondary school mathematics. In the second study, I examine the nature of the teaching of reasoning and proof in secondary school. I use classroom observations along with pre- and post-observations interview data of three teachers to determine (a) the classroom microculture (i.e., classroom mathematical practices and sociomathematical norms), (b) teachers’ pedagogical decisions, and (c) teachers’ use of the Caribbean Secondary… Advisors/Committee Members: González Rivera, Gloriana (advisor), González Rivera, Gloriana (Committee Chair), McCarthy, Cameron (committee member), Martin, Tami S (committee member), McDermott, Monica (committee member).