Using variation theory to enhance the learning of “fitting shapes” of primary four students in Hong Kong

Yujia LIU

Research output: ThesisHonours Projects (HP)


Variation Theory (VT) was first raised by Professor Ference Marton in 1998, stating that learning implies seeing, perceiving, or experiencing critical aspects of the object of learning (OL) (Marton & Booth, 1997). When VT is applied in teaching, teachers can design examples and activities with reference to the patterns of variation to allow students to experience the variation and discern critical features (CFs) of the OL. Previous studies (Driver et al., 2015; Chiu & Bo, 2012; Ting et al., 2017; Leung et al., 2011) demonstrated how to apply VT to support the teaching of one single lesson in various disciplines. However, these studies did not mention how to arrange the teaching of CFs in multiple lessons on the same topic and how teachers guided the students in detail during the whole instruction.
This study aims at exploring the application of VT in enhancing students’ learning of “fitting shapes” of primary four students in Hong Kong. This study adopted an action research approach. A total of 31 students, including 14 boys and 17 girls, participated in this study. With reference to the pre-test results, the author identified two CFs and designed organic lessons on the topic of “fitting shapes”. In addition to showing a series of examples in classroom teaching and the corresponding patterns of variation, the study also demonstrated the interactive teaching process. Apart from collecting the observation data to analyze what VT practices enhanced the students’ learning, the author collected post-test results and compared them with the pre-test results to see which parts of VT practices need to be further improved.
The findings of this study showed that the overall students’ learning of “fitting shapes” had been enhanced. The teaching process with the application of four patterns of variation (contrast, separation, generalization, and fusion), the series of examples matched with CFs, and the appropriate teaching interaction facilitated students’ learning. Nevertheless, to further enhance students’ learning, the teacher may need to add more graphics types (shape, placement) in the examples and counterexamples so as to help students solve more complex situations of “fitting shapes”.
Original languageEnglish
QualificationBachelor of Education (Honours)
  • ZHANG, Yuefeng, Ellen 章月鳳, Supervisor
Publication statusPublished - 2020


  • Variation theory
  • Mathematics in primary schools
  • Fitting shapes
  • Action research
  • Honours Project (HP)
  • Bachelor of Education (Honours) (Primary) – General Studies and Mathematics (Five-year Full-time)
  • Programme code: A5B058
  • Course code: TLS4029


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