The purpose of this study was to explore and analyze which fifth-grade teacher inputs were the most important predictors of future outcomes of eighth-grade math students. This quantitative study looked at mathematical achievement through the lens of an education production function. The three inputs that were analyzed were fifth-grade teachers’ background; perception of professional development; and instructional practices and the relationship of those practices to achievement in eighth-grade math. In order to find the relationship between the above variables and student achievement, descriptive statistics, multiple correlations, and multi-variable regression analysis were conducted to examine which predictors had a stronger relationship between eighth-grade math outcomes than others. Taken as a whole, fifth-grade teacher math inputs in this study seemed to explain a small part of the variance regarding eighth-grade math achievement. As a whole, the more frequently students wrote and spoke about math in fifth grade as well as used math tools effectively, the better the outcome in eighth grade.

abstract: This study investigated the current state of the U.S. and Chinese urban middle school math teachers' pedagogical content knowledge (PCK) for the topic of functions. A comparative, descriptive case study was employed to capture the PCK of 23 teachers in Arizona and of 28 teachers in Beijing, regarding their instructional knowledge, understanding of student thinking and curricular knowledge--three key components based on Shulman's conceptualization of PCK--related to functions. Cross-case comparisons were used to analyze the PCK of teacher groups across countries and socio-economic statuses (SES), based on the questionnaire, lesson plan, and interview data. This study finds that despite cultural differences, teachers are likely to share some commonalities with respect to their instructional decisions, understanding of student thinking and curricular knowledge. These similarities may reflect the convergence in teaching practice in the U.S. and China and the dedication the two countries make in improving math education. This study also finds the cross-country differences and cross-SES differences regarding teachers' PCK. On the one hand, the U.S. and Chinese math teachers of this study tend to diverge in valuing different forms of representations, explaining student misconceptions, and relating functions to other math topics. Teachers' own understanding of functions (and mathematics), standards, and high-stakes testing in each country significantly influence their PCK. On the other hand, teachers from the higher SES schools are more likely to show higher expectations for and stronger confidence in their students' mathematical skills compared to their counterparts from the lower SES schools. Teachers' differential beliefs in students' ability levels significantly contribute to their differences between socio-economic statuses. / Dissertation/Thesis / Doctoral Dissertation Educational Leadership and Policy Studies 2014

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