An Investigation of Teachers’ Noticing, Cognitive Demand, and Mathematical Knowledge for Teaching: Video Reflections in an Elementary Mathematics Context

摘要

In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of instruction does not enhance the development of mathematical reasoning and ignores the research on students’ mathematical development (Blanton u26 Kaput, 2005; Stigler u26 Hiebert, 1999). Recommendations by the mathematics community are to broaden and strengthen teacher content knowledge in mathematics and to provide the pedagogical tools needed by teachers to extend their students’ thinking and reasoning (Darling-Hammond, Wei, Andree, Richardson, and Orphanos, 2009; Mewborn, 2003).The purpose of this quantitative study was to investigate the relationship between the teachers’ levels of noticing, the levels of cognitive demand in their enacted tasks, and their levels of mathematical knowledge for teaching in two urban high-need low performing elementary schools. The 54 elementary teachers participated in a long-term mathematics professional development program aimed at developing teachers’ mathematical knowledge for teaching and recognizing and fostering students’ early algebraic reasoning. The data for this dissertation included teachers’ self-selected video segments, written video reflections, and mathematical knowledge for teaching levels from the second year of the professional development. Relationships were explored between mathematical knowledge for teaching, teachers’ levels of noticing, and the levels of cognitive demand represented in mathematics lessons.The findings indicated shifts in teachers’ cognitive demand of enacted tasks and noticing over the course of the second year of professional development. Correlation results indicated significant relationships between teachers’ cognitive demand, teacher noticing, participation, and teachers’ mathematical knowledge for teaching. Moreover, the results showed that the teachers in the K-3 cohort benefited more from the professional development than their 4-6 cohort counterparts when it came to mathematical knowledge for teaching, noticing, and cognitive demand levels.