Didactical interactions and tool-task dialectic in mathematics classrooms

  • Ka Hio Lei

Student thesis: Doctoral Thesis


Things make us smart. Tools are made by humans aiming not only at solving technical problem but also developing high-order thinking. In a manner different from traditional mathematics lessons involving direct transmission of knowledge from teachers to students, tool-based mathematics classrooms fabricate an interactive teaching and learning environment. This environment fosters teachers' professional guidance based on students' manipulation of tools. The design of tool-based task aims to formulate students' learning experience via their own acquisition of knowledge through tool manipulations. Mathematics concepts can be visualized and manipulated by students through engaging in activities with tools generating tool-based signs and mathematics signs in a semiotic process. The role of mathematics teachers in tool-based mathematics classrooms is to provide well designed tool-based tasks and implement tool-based lessons in order to orchestrate students' learning, coupled with the endeavour of students' manipulating of tools.;Two new ideas, named didactical interactions and Tool-Task dialectics, were proposed in the study to effectively enforce mathematics teachers' instruction through tool-based pedagogy in interactive classrooms. The main objective of this study was to holistically investigate the implementation processes of tool-based lessons by mathematics teachers based on some theoretical perspectives. A multiple-case study, consisting of three cases with similar and different backgrounds, was conducted. Didactical cycle was one of the main theoretical frameworks, which framed analysis of the study. Based on in-depth analysis within and across cases, didactical interactions and Tool-Task dialectics were empirically developed to enrich tool-based education theories allowing teachers to demystify the cognitive development of students in tool-based lessons. The analysis of flows of the lessons uttered transition directions of critical phases ground on the theory; while pragmatic manipulations of tools operated by students and teachers' orchestration provided strong evidence to illustrate interplay between tools and tasks. Thus, the findings of the study potentially contributed to some aspects of tool-based mathematics education research.;Keywords: tool-based task design, tool of semiotic mediation, didactical cycle, didactical interactions, tool-task dialectic, mathematics classroom.

Date of Award17 May 2018
Original languageEnglish
SupervisorAllen Y L LEUNG (Supervisor)

User-Defined Keywords

  • Educational technology
  • Mathematics
  • Study and teaching
  • Technological innovations.

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