Patterns and relationships within ratio contexts: Students’ emerging ideas through ratio tables.

Sözen Özdoğan S., Akyüz D., Stephan M.

in: Mathematics as the science of patterns: Making the invisible visible through teaching, Patrick M. Jenlink, Editor, Information Age Publishing, North Carolina, pp.99-125, 2022

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2022
  • Publisher: Information Age Publishing
  • City: North Carolina
  • Page Numbers: pp.99-125
  • Editors: Patrick M. Jenlink, Editor
  • TED University Affiliated: Yes


This study aims to investigate the emerging ideas of the seventh-grade students that are characterized as the number pattern utility while developing ratio tables in the context of teaching ratio and proportion context within a classroom teaching experiment. The study employed a design research and a classroom teaching experiment. The participants were seventh grade-students from a public middle school. The dataset involves artifacts and recordings from a 7-week long classroom teaching experiment. The ratio and proportion instructional sequence developed by Stephan et al. (2015) was used. The teacher supported an inquiry-based environment by using Launch-Explore-Discuss teaching cycles. The data was analyzed using content-analysis from the transcriptions of class sessions and the artifacts of students. The findings revealed that the students discovered several categories of patterns on the ratio table. These included repeating patterns in the early stage of the development of the ratio table, growing patterns with addition, and growing patterns with multiplication. Based on these findings, it could be implied that the pattern relationships within the ratio table developed by the students may support the collective practices of the students for the learning of the ratio and proportion context.