Bar model method as a problem-solving heuristic: an investigation of two preservice teachers' solution paths in problems involving ratio and percentage

SEVİNÇ Ş., Lizano C.


  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s13394-022-00427-9
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, IBZ Online, EBSCO Education Source, ERIC (Education Resources Information Center)
  • Keywords: Bar model solution, Ratio and percentages, Proportional reasoning, Problem-solving heuristic, Solution paths, Preservice teacher education, PROPORTIONAL RELATIONSHIPS, MATHEMATICS, SENSE
  • Middle East Technical University Affiliated: Yes


This study aimed to explore preservice elementary teachers' use of a bar model as a heuristic for conceptualising relationships between quantities in situations involving ratio and percentages. As a part of a larger project, we focused on two preservice teachers, Maia and Jane, and investigated their solution paths in ratio and percentage problems and the role of the structural representations (i.e., bar model and percent line-bar model) in their solution paths. We analysed these focus participants' written solutions and their think-aloud process during interviews using three coding phases with a constructivist grounded theory approach. We observed that the problem text fed the construction of the structural representations that served to make sense of the quantities and the relationships among them. Furthermore, the structural representations enhanced Maia and Jane's mathematical insights about the problem situations. In addition, we observed that preservice teachers' solution paths were neither linear nor similar, which indicates a mathematical richness in learning. In those solution paths, the model construction played a role in guiding the mathematical operations of constructing and operating on a unit rate in the ratio problem and identifying and operating on a referent whole unit in the percentage problem. We interpreted that variety and nonlinearity in solution paths suggested mathematical richness in learning, the educational implications of which were further discussed.