Awortwe, Peter Kwamina
(2025)
Understanding the content, pedagogical and technological knowledge of beginning teachers using technology in relation to geometric constructions using dynamic software.
PhD thesis, University of Nottingham.
Abstract
This study explores the content, pedagogical, and technological knowledge (TPACK) of beginning teachers engaging in geometric constructions with dynamic geometry software. It aims to examine how carefully designed tasks can promote productive mathematical talk and dialogic learning among these teachers, improving their TPACK knowledge and deepening their understanding of the knowledge required to teach geometry in technology-rich environments.
To achieve this, the study involved designing effective geometric construction tasks as core components of a dynamic learning ecosystem, within an online platform’s dynamic geometry software environment. These tasks incorporated principles such as scaffolding, collaborative paired learning (via platforms like Microsoft Teams with screen sharing), reflective practices, dynamic manipulation using GeoGebra, instrumental orchestration, Bruner’s (1974) modes of representation, a balance of ostensive and non-ostensive objects, feedback mechanisms, meaningful goals, visible mathematics, and open-ended yet scaffolded tasks. Twelve beginning teachers from Mathematics postgraduate certificate in education (PGCE) programmes across four UK universities participated, with four teachers in phase one and eight in phase two. Data collection methods included video analysis, questionnaires, focus groups, and interviews. Analytical approaches employed interpretive video deductive coding, drawing on dialogic talk and learning principles, and the TPACK framework, with both inductive and deductive thematic analyses providing detailed insights into TPACK development for teaching geometric constructions.
The analysis revealed that certain design principles embedded in the tasks, as set out in the paragraph above, supported productive mathematical talk, dialogic learning and TPACK development among beginning teachers. In addition, participants identified specific features they felt best supported their TPACK knowledge-building, including task complexity, integration of multiple geometric concepts, structured sequencing with progression and scaffolding, alignment with relevant and authentic learning goals, engagement, motivation, and a balance of appropriate challenge and support. Findings also revealed that beginning teachers perceived effective geometry teaching in technology-integrated environments as manifold, requiring a solid understanding of geometric relationships, cross-curricular connections, classroom management in technological settings, software proficiency, and differentiated teaching strategies. This leads to the conclusion that for TPACK development for classroom practice, beginning teachers need a well-rounded skill set that integrates technological fluency, pedagogical strategies, and strong content knowledge.
Analysis of dialogue between beginning teachers in the study confirmed that the carefully designed tasks led to complex interactions of dialogic talk that in turn led to (dialogic and active) learning, critical thinking, and a deep understanding of geometric concepts. The learning ecosystem, within which the designed tasks played a key role, provides proof of concept and an example of how TPACK development for classroom practice of beginning teachers can be achieved.
The thesis concludes with practical recommendations advocating the integration of technology-rich tasks in mathematics teacher training to strengthen beginning teachers’ TPACK knowledge and preparedness. Recommendations for teacher training programmes, educational institutions, researchers, and educational technology developers include embedding technology in training, designing tasks that foster productive mathematics talk, promoting effective TPACK development, and recognising the diverse roles of teachers in technology-centred settings. This research makes a meaningful contribution to the discourse on technology integration in mathematics education, offering valuable insights for educators, researchers, and policymakers.
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