A primary contributor to facilitating student learning in mathematics includes the mathematics teacher. The design of instructional delivery, presentation of engaging activities and analysis of student feedback are the key responsibilities that mathematics teachers are tasked with in order to present learning opportunities to the students. The approach to satisfying these responsibilities is contingent on the teachers' values and beliefs regarding the various aspects of mathematical proficiency. In this study, I have investigated teachers' valuation of two of these aspects: procedural fluency and conceptual understanding. The literature on these two aspects of mathematical proficiency has focused almost exclusively on elementary teachers. Research studies have uncovered a proclivity of elementary teachers toward procedural learning despite the abstract nature of mathematical processes. Elementary teachers have been found to possess a certain aversion toward a deeper conceptual understanding of mathematics. With regard to secondary teachers, the research is more focused on instructional strategies that emphasize mathematical concepts, but neglect the relationship that these concepts may have to the robust procedures that allow students to process known values as they attempt to discover solutions to both prescribed and unique problems. This study examined the values that secondary teachers place upon two learning constructs within the framework of mathematical proficiency, and how these values influence their approach to teaching. "How do secondary mathematics teachers value procedural fluency and conceptual understanding in their instructional practices?" is the fundamental question of this study. The study reaches beyond this initial question to also examine the root causes of the establishment of these values by asking "how do teachers develop their value-system of procedural fluency and conceptual understanding in their instructional practices?". This study consisted of two phases. In phase one, teachers completed a 27-item survey instrument in order to gather responses about their beliefs regarding conceptual understanding, procedural fluency and a blend of the two constructs. Phase two consisted of a focus group interview of teachers to delve deeper into the source of the various belief systems that serve as the foundation for mathematics instruction in secondary schools in southeastern Pennsylvania.
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