Enhancing understanding through the use of structured representations

Chun Yi Lee, Kin Hang Lei*, Ming Jang Chen, Tai Yih Tso, I. Ping Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Mathematical representations are an essential tool in the study of mathematics and problem solving. They are also used in word problems to facilitate the transformation from textual to symbolic information. We proposed a stepwise, blocked, structured state transition graph (STG) based on the principles of instructional message design. In this study, we adopted a posttest-only non-equivalent group design to compare the performance of students who used either STG or matrix-like tables to learn to solve word problems via transition matrices. We also took into account the student's previous learning achievements in mathematics. The participants included four classes of senior students in a vocational high school, with two classes randomly designated as the experiment (STG) group and two designated as the control (Table) group. High-achieving students taught using STG outperformed their counterparts who were taught using matrix-like tables. The performance of low-achieving students appeared to be unaffected by the instructional method. These findings suggest that STG provides a clear representation of the relationships used in matrix calculation, which makes it easier to select and organize information. Nonetheless, alternative methods will be required to improve the performance of low-achieving students.

Original languageEnglish
Pages (from-to)1875-1886
Number of pages12
JournalEurasia Journal of Mathematics, Science and Technology Education
Issue number5
Publication statusPublished - 2018


  • Instructional message design
  • Representation
  • State transition graph
  • Transition matrix

ASJC Scopus subject areas

  • Education
  • Applied Mathematics


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