Matching Items (2)
Filtering by
- All Subjects: Mathematics teachers--Training of--Technological innovations.
- Creators: Sloane, Finbarr
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
This study explores teacher educators' personal theories about the instructional practices central to preparing future teachers, how they enact those personal theories in the classroom, how they represent the relationship between content, pedagogy, and technology, and the function of technology in teacher educators' personal theories about the teaching of mathematics and their practices as enacted in the classroom. The conceptual frameworks of knowledge as situated and technology as situated provide a theoretical and analytical lens for examining individual instructor's conceptions and classroom activity as situated in the context of experiences and relationships in the social world. The research design employs a mixed method design to examine data collected from a representative sample of three full-time faculty members teaching methods of teaching mathematics in elementary education at the undergraduate level. Three primary types of data were collected and analyzed:
a) structured interviews using the repertory grid technique to model the mathematics education instructors' schemata regarding the teaching of mathematics methods; b) content analysis of classroom observations to develop models that represent the relationship of pedagogy, content, and technology as enacted in the classrooms; and c) brief retrospective protocols after each observed class session to explore the reasoning and individual choices made by an instructor that underlie their teaching decisions in the classroom. Findings reveal that although digital technology may not appear to be an essential component of an instructor's toolkit, technology can still play an integral role in teaching. This study puts forward the idea of repurposing as technology -- the ability to repurpose items as models, tools, and visual representations and integrate them into the curriculum. The instructors themselves became the technology, or the mediational tool, and introduced students to new meanings for "old" cultural artifacts in the classroom. Knowledge about the relationships between pedagogy, content, and technology and the function of technology in the classroom can be used to inform professional development for teacher educators with the goal of improving teacher preparation in mathematics education.
a) structured interviews using the repertory grid technique to model the mathematics education instructors' schemata regarding the teaching of mathematics methods; b) content analysis of classroom observations to develop models that represent the relationship of pedagogy, content, and technology as enacted in the classrooms; and c) brief retrospective protocols after each observed class session to explore the reasoning and individual choices made by an instructor that underlie their teaching decisions in the classroom. Findings reveal that although digital technology may not appear to be an essential component of an instructor's toolkit, technology can still play an integral role in teaching. This study puts forward the idea of repurposing as technology -- the ability to repurpose items as models, tools, and visual representations and integrate them into the curriculum. The instructors themselves became the technology, or the mediational tool, and introduced students to new meanings for "old" cultural artifacts in the classroom. Knowledge about the relationships between pedagogy, content, and technology and the function of technology in the classroom can be used to inform professional development for teacher educators with the goal of improving teacher preparation in mathematics education.
ContributorsToth, Meredith Jean (Author) / Middleton, James (Thesis advisor) / Sloane, Finbarr (Committee member) / Buss, Ray (Committee member) / Atkinson, Robert (Committee member) / Arizona State University (Publisher)
Created2014