Interpreting the fraction conceptual metaphors of Korean primary students
: A radical constructivist study using scripting

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


How do students understand fraction concepts? How can I gain insight into their understanding of fraction concepts? This study addresses these fundamental questions, motivated by my teaching experiences that brought to light the diverse understandings students possess regarding mathematical concepts. Guided by the perspectives of radical constructivism and conceptual metaphor theory, I investigate students’ metaphors as their thoughts of fraction concepts.
To investigate students’ metaphors, I conduct scripting with 27 sixth-grade Korean students (aged 11-12), as a novel way of exploring their conceptions, and subsequent interviews. Scripting involves the creation of dialogue scripts in response to provided prompts outlining mathematical situations. Prompts ask students to create dialogue scripts and draw fraction images. Scripting and interviews offer me written verbal data (scripts), spoken verbal data (interviews), and non-verbal drawn data (drawing images), providing diverse perspectives on students’ metaphors.
The metaphors and fraction conceptions presented in this study are my interpretations of students’ scripts, interviews, and visual images, as a second-order model. These interpretations lead to the identification of ten distinct fraction metaphors used by students. The insights gained from an in-depth analysis of three students' data through metaphor networks emphasise the significance of both the quantity and quality of metaphors. My interpretation of students’ scripts also introduces a new fraction approach termed “fracturing” and identifies patterns of characters’ actions in scripts as hedging actions.
This study not only contributes new findings related to fractions, but also offers a novel methodology. It demonstrates the applicability of scripting as a research method for young learners and suggests an extended use of scripting as a pedagogical tool.
Date of Award7 May 2024
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAlf T Coles (Supervisor) & Tracy Helliwell (Supervisor)


  • metaphor
  • fraction
  • scripting
  • radical constructivism
  • students' mathematical understanding
  • dialogue writing

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