Characterising Features of Secondary Mathematics Teachers’ Classroom Practices with Dynamic Digital Technology: The Case of Geometric Similarity

Much research has shown that mathematics teachers have struggled to integrate dynamic mathematical technologies (DMTs) in everyday classroom practice and their use of technology has thus been limited. Developing a comprehensive understanding of teachers’ practices is important to promote successful integration of DMT into the classroom. Currently, little is known about the complex process of integration of DMT and the associated professional knowledge of practice (PKP) required for teachers, particularly for teaching geometric similarity (GS). This study examines lower secondary mathematics teachers’ integration of DMT into their classroom practices with a particular focus on the topic of GS. The study adopted a multiple case study approach and was situated in an English lower secondary school setting. Participants of the study were three teachers who had different levels of experience and expertise both in teaching and in using DMT. The participants were selected among the Cornerstone Maths (CM) project teachers as they had begun to integrate the DMT, the CM software, in their practices to teach GS. Data collection involved video-recorded classroom observations (including the teacher’s eye view), audio-recorded post-lesson teacher interviews, and teachers’ resources and students’ work. The theoretical lenses of the Structuring Features of Classroom Practice (SFCP) framework along with the Instrumental Orchestration (IO) model guided data collection and analysis. The findings revealed salient differences and some commonalities between the teachers, pointing to key characteristics of classroom practices involving DMT for teaching GS. The findings of this thesis contribute to further appreciation of the complex phenomenon of technology integration into the classroom. This study also makes an original contribution to the literature by adopting the SFCP framework for teaching the topic of GS with DMT. Implications discussed in the thesis could inform practitioners, educators and policy makers about how to facilitate teacher interaction with DMT for productive mathematical learning

The Look Of Pedagogical Content Knowledge In Middle School Statistics

In this study, I attempt to examine the nature of pedagogical content knowledge (Shulman, 1986) that teachers exhibit while observing computer-animated animations that bring up pedagogical issues in the classroom. In-service teachers were asked to view different animations and react to different prompts about the animations. Later, teachers were interviewed to prompt more discussion of pedagogical issues with the intention of clarifying their stance and their knowledge of pedagogy. The computer animations were utilized as a surrogate for classroom teaching, highlighting issues that could be otherwise overlooked during live teaching observation

The relationship between teacher pedagogical content knowledge and student understanding of integer operations

textThe purpose of this study was to determine whether a professional development (PD) for teachers focused on improving teacher pedagogical content knowledge (PCK) related to operations with integers would improve teacher PCK and if there was a relationship between their level of PCK and the change in the understanding of their students as measured by pre- and posttest of teacher and student knowledge. The study was conducted summer 2010 in a large urban school district on two campuses providing a district funded annual summer intervention, called Jumpstart. This program was for grade 8 students who did not pass the state assessment (Texas Assessment of Knowledge and Skills), but would be promoted to high school in the Fall 2010 due to a decision made by the Grade Placement Committee. The Jumpstart program involved 22 teachers and 341 students. For purposes of this study, changes were made to the PD and typical curriculum for a unit on integer operations to promote teacher and student conceptual understanding through a process of mathematical discussion called argumentation. The teachers and students explored a comprehensive representation for integer operations called a vector number line model using the Texas Instruments TI-73 calculator Numln application. During PD, teachers engaged in argumentation to make claims about strategies to use to understand integer operations and to explain their understanding of how different representations are connected. The results showed statistically significant growth in teacher PCK following the professional development and statistically significant growth in student understanding from pre- to posttest compared to the students who participated in the program the previous year. The findings also showed that there was a statistically significant association between teacher posttest PCK and student improvement in understanding even when controlling for years of teaching experience, teacher pretest knowledge, and student pretest score. This adds to the research base additional evidence that professional development focused on teacher pedagogical content knowledge can have a positive effect on student achievement, even with just a short period of PD (6 hours in this case).Science and Mathematics Educatio