What are we really doing here? Exploring aims for school mathematics in curricular systems
Richman, Andrew S.
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The persistence of a 120 year-old mathematics curriculum despite dramatic changes in society (Dossey et al., 2016; NCTM, 2018) and the failure of the US mathematics education system to achieve many of its stated aims, especially for students from traditionally marginalized populations (Attridge & Inglis, 2013; Carnevale & Desrochers, 2003a; Ganter & Barker, 2004; Kastberg et al., 2016; Lei et al., 2015; Mullis et al., 2016) raises the question: “What aims, if any, actually shape the curriculum experienced by students?” This dissertation adds to what is known about curricular systems by building a theory of the role of aims for school mathematics in curriculum development, planning, and enactment. It does so by undertaking a qualitative analysis of ten lessons by four different teachers at two different high schools; tracking how the lessons are transformed from instructional materials into plans by the teacher and then enacted in classrooms and perceived by students. This dissertation analyzes these lessons through the lens of activity theory, enabling a deeper understanding of how aims can be described and how they permeate curricular systems. The data analysis produces a framework for how aims can be described and categorized, how aims permeate an individual stage of curriculum, and how aims permeate across stages of curriculum. It finds that aims can be conceptualized as having two parts, a central activity for which mathematical learning is designed to prepare students and the function that school mathematics plays in preparing students to participate in that central activity. The extent to which and how aims permeate a stage of curriculum can be described as the extent to which the mathematical goals for the lesson are connected to clear central aims. The aims found in particular stages of curriculum and the levels of permeation of those aims in those stages can be tracked across stages to determine whether the stages are reinforcing each other’s support for the achievement of aims or working at cross purposes. The application of this framework to the selected curricular systems reveals many lessons with low levels of aim permeation and extensive changes in the aims of lessons as the curriculum is transformed from intention to plan to enactment. This study suggests that aims are underutilized in curricular planning and provides evidence that the mathematics curriculum may be built following disciplinary logic with aims created to justify what is already in place. Further research must be done to explore this conjecture. If it is supported, then curriculum decision makers who seek to improve the extent to which they achieve their aims and eliminate racial and economic disparities in this achievement must begin by elevating the role of aims in their curricular work.