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- Genre: Academic theses
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The research indicated effective mathematics teaching to be more complex than assuming the best predictor of student achievement in mathematics is the mathematical content knowledge of a teacher. This dissertation took a novel approach to addressing the idea of what it means to examine how a teacher's knowledge of mathematics impacts student achievement in elementary schools. Using a multiple case study design, the researcher investigated teacher knowledge as a function of the Mathematics Teaching Cycle (NCTM, 2007). Three cases (of two teachers each) were selected using a compilation of Learning Mathematics for Teaching (LMT) measures (LMT, 2006) and Developing Mathematical Ideas (DMI) measures (Higgins, Bell, Wilson, McCoach, & Oh, 2007; Bell, Wilson, Higgins, & McCoach, 2010) and student scores on the Arizona Assessment Collaborative (AzAC). The cases included teachers with: a) high knowledge & low student achievement v low knowledge & high student achievement, b) high knowledge & average achievement v low knowledge & average achievement, c) average knowledge & high achievement v average knowledge & low achievement, d) two teachers with average achievement & very high student achievement. In the end, my data suggested that MKT was only partially utilized across the contrasting teacher cases during the planning process, the delivery of mathematics instruction, and subsequent reflection. Mathematical Knowledge for Teaching was utilized differently by teachers with high student gains than those with low student gains. Because of this insight, I also found that MKT was not uniformly predictive of student gains across my cases, nor was it predictive of the quality of instruction provided to students in these classrooms.
ContributorsBurke, Margaret Kathleen (Author) / Middleton, James A. (Thesis advisor) / Sloane, Finbarr (Thesis advisor) / Battey, Daniel S (Committee member) / Arizona State University (Publisher)
Created2013
Description
To address the need of scientists and engineers in the United States workforce and ensure that students in higher education become scientifically literate, research and policy has called for improvements in undergraduate education in the sciences. One particular pathway for improving undergraduate education in the science fields is to reform undergraduate teaching. Only a limited number of studies have explored the pedagogical content knowledge of postsecondary level teachers. This study was conducted to characterize the PCK of biology faculty and explore the factors influencing their PCK. Data included semi-structured interviews, classroom observations, documents, and instructional artifacts. A qualitative inquiry was designed to conduct an in-depth investigation focusing on the PCK of six biology instructors, particularly the types of knowledge they used for teaching biology, their perceptions of teaching, and the social interactions and experiences that influenced their PCK. The findings of this study reveal that the PCK of the biology faculty included eight domains of knowledge: (1) content, (2) context, (3) learners and learning, (4) curriculum, (5) instructional strategies, (6) representations of biology, (7) assessment, and (8) building rapport with students. Three categories of faculty PCK emerged: (1) PCK as an expert explainer, (2) PCK as an instructional architect, and (3) a transitional PCK, which fell between the two prior categories. Based on the interpretations of the data, four social interactions and experiences were found to influence biology faculty PCK: (1) teaching experience, (2) models and mentors, (3) collaborations about teaching, and (4) science education research. The varying teaching perspectives of the faculty also influenced their PCK. This study shows that the PCK of biology faculty for teaching large introductory courses at large research institutions is heavily influenced by factors beyond simply years of teaching experience and expert content knowledge. Social interactions and experiences created by the institution play a significant role in developing the PCK of biology faculty.
ContributorsHill, Kathleen M. (Author) / Luft, Julie A. (Thesis advisor) / Baker, Dale (Committee member) / Orchinik, Miles (Committee member) / Arizona State University (Publisher)
Created2013
Description
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.
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.
ContributorsZou, Hui (Author) / Fischman, Gustavo (Thesis advisor) / Berliner, David (Committee member) / Sloane, Finbarr (Committee member) / Arizona State University (Publisher)
Created2014
Description
ABSTRACT Early career science teachers are often assigned to classrooms with high numbers of English language learners (ELL students). As these teachers learn to become effective practitioners, the circumstances surrounding them merit a thorough examination. This study examines the longitudinal changes in Pedagogical Content Knowledge (PCK) and practices of six early career science teachers who taught in urban schools. The teachers participated in the Alternative Support for Induction Science Teachers (ASIST) program during their initial two years of teaching. Our research team followed the participants over a five-year period. This study focuses on data from Years 1, 3, and 5. The data collected included classroom observations and interviews. In addition, classroom artifacts were collected periodically for the purpose of triangulation. The analysis of the data revealed that with the support of the ASIST program, the teachers implemented inquiry lessons and utilized instructional materials that promoted academic language skills and science competencies among their ELL students. Conversely, standardized testing, teaching assignment, and school culture played a role in constraining the implementation of inquiry-based practices. The results of this study call for collaborative efforts among university science educators and school administrators to provide professional development opportunities and support for the implementation of inquiry and language practices among early career science teachers of ELL students.
ContributorsOrtega, Irasema (Author) / Luft, Julie A (Thesis advisor) / Artiles, Alfredo (Committee member) / Baker, Dale R. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT.
ContributorsLage Ramírez, Ana Elisa (Author) / Thompson, Patrick W. (Thesis advisor) / Carlson, Marilyn P. (Committee member) / Castillo-Chavez, Carlos (Committee member) / Saldanha, Luis (Committee member) / Middleton, James A. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Few would argue that teacher effectiveness is a key lever in education reform and improving the overall quality of public education, especially in poor and working class communities. To that end, the importance of supporting and developing beginning teachers is of utmost importance in education, thus requiring deep understandings of the process of learning to teach. Yet, most conceptions of teacher learning struggle to capture the social, cultural, and historical context of teacher learning, particularly in understanding how learning and the production of knowledge is situated, active, and complex. One example of this limitation comes from the field of research on pedagogical content knowledge (PCK) and its importance in developing effective beginning teachers. This study characterizes beginning teachers' production of PCK within a cultural historical activity theory (CHAT) framework. This study finds that the teachers produce PCK mostly based on their own individual experiences and reflections, receiving little assistance from the structures intended to provide them with support. The self-produced PCK is uneven, underdeveloped, and relies on teachers to use their sense of agency and identity to navigate dissonant and unbalanced activity systems. Over time, PCK production remains uneven and underdeveloped, while the individual teachers find it more and more difficult to bring balance to their activity systems, ultimately resulting in their exit from the activity system of teaching in their district and school.
ContributorsDiaz, Victor H (Author) / Fischman, Gustavo E. (Thesis advisor) / Luft, Julie (Committee member) / Artiles, Alfredo (Committee member) / Arizona State University (Publisher)
Created2012
Description
Pedagogical content knowledge (PCK) has been described as the knowledge teachers' use in the process of designing and implementing lessons to a particular group of students. This includes the most effective representations that make the content understandable to students, together with the preconceptions and misconceptions that students hold. For chemistry, students have been found to have difficulty with the discipline due to its reliance upon three levels of representation called the triplet: the macro, the submicro, and the symbolic. This study examines eight beginning chemistry teachers' depiction of the chemistry content through the triplet relationship and modifications as a result of considering students' understanding across the teacher's first three years in the classroom. The data collected included classroom observations, interviews, and artifacts for the purpose of triangulation. The analysis of the data revealed that beginning chemistry teachers utilized the abstract components, submicro and symbolic, primarily in the first year. However, the teachers began to engage more macro representations over time building a more developed instructional repertoire. Additionally, teachers' developed an awareness of and responded to their students' understanding of learning atomic structure during the second and third year teaching. The results of this study call for preservice and induction programs to help novice chemistry teachers build a beginning repertoire that focuses on the triplet relationship. In so doing, the teachers enter the classroom with a repertoire that allows them to address the needs of their students. Finally, the study suggests that the triplet relationship framework should be revisited to include an additional component that frames learning to account for socioscientific issues and historical contributions.
ContributorsAdams, Krista (Author) / Luft, Julie A. (Thesis advisor) / Baker, Dale (Committee member) / Williams, Stanley (Committee member) / Arizona State University (Publisher)
Created2012
Description
The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and about forty percent is English Language Learners (ELLs). The two level Hierarchical Linear Model (HLM) was used to investigate repeated measures of teaching practice measured by Classroom Assessment Scoring System (CLASS) instrument. Also, linear regression and a multiple regression to examine the relationship between teacher knowledge measured by Learning for Mathematics Teaching (LMT) and Developing Mathematical Ideas (DMI) items and teaching practice were employed. In addition, a three level HLM was employed to analyze repeated measures of student mathematics achievement measured by Arizona Assessment Consortium (AzAC) instruments. Results showed that overall teaching practice did not change weekly although teachers' emotional support for their students improved by week. Furthermore, a statistically significant relationship between teacher knowledge and teaching practice was not found. In terms of student learning, ELLs have significantly lower initial status in mathematics achievement than non-ELLs, as were growth rates for these two groups. Lastly, teaching practice significantly predicted students' monthly mathematics achievement growth but teacher knowledge did not. The findings suggest that school systems and education policy makers need to provide teachers with the chance to reflect on their teaching and change it within themselves in order to better support student mathematics learning.
ContributorsKim, Seong Hee (Author) / Sloane, Finbarr (Thesis advisor) / Middleton, James (Committee member) / Flores, Alfinio (Committee member) / Arizona State University (Publisher)
Created2012
Description
The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using for instruction. Additionally, participants indicated their college major, institution attended, years of experience, and participation in various other learning opportunities. This data was analyzed to look for changes in knowledge, first among those still in college, then among those already in the field, and finally as a whole group to look for a pattern of growth from pre-service through working in the classroom. I compared these results to the theories of learning espoused by the creators of these two tests to see which model the data supports. The results indicate that growth in PCK occurs among college students during their teacher preparation program, with much less change once a teacher enters the field. Growth was not linear, but best modeled by an s-curve, showing slow initial changes, substantial development during the 2nd and 3rd year of college, and then a leveling off during the last year of college and the first few years working in a classroom. Among current teachers' the only group that demonstrated any measurable growth were teachers who majored in a non-education field. Other factors like internships and professional development did not show a meaningful correlation with PCK. Even though some of these models were statistically significant, they did not account for a substantial amount of the variation among individuals, indicating that personal factors and not programmatic ones may be the primary determinant of a teachers' knowledge.
ContributorsJohnson, Jeffrey (Author) / Middleton, James A. (Thesis advisor) / Marsh, Josephine P (Committee member) / Sloane, Finbarr (Committee member) / Arizona State University (Publisher)
Created2016