Middle school students' learning difficulties in the ratio-proportion topic and a suggested solution: Envelope technique

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Çalışıcı H.

Universal Journal of Educational Research, vol.6, no.8, pp.1848-1855, 2018 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 8
  • Publication Date: 2018
  • Doi Number: 10.13189/ujer.2018.060830
  • Journal Name: Universal Journal of Educational Research
  • Journal Indexes: Scopus
  • Page Numbers: pp.1848-1855
  • Keywords: Envelope technique, Expanding fractions, Misconception, Ratio-proportion, Reducing fractions
  • Ondokuz Mayıs University Affiliated: Yes


Ratio-proportion is one of the topics that middle school students have difficulty in comprehending. This study aims to determine the learning difficulties that seventh-grade students face while learning about ratio-proportion. Three commonly used strategies to solve ratio-proportion problems are buildup, unit ratio and cross-multiplication. The study also investigated the effect of the envelope technique, which included these three strategies and was developed to improve comprehending and success of students. The study was designed as an experimental study and 34 seventh-grade students participated in the study. The Ratio-Proportion Achievement Test developed by the researcher used to collect the data. The results illustrated that students frequently have misconceptions while solving ratio-proportion problems by confusing the direction of the operation in reducing and expanding the numbers constituting the proportion. It was concluded that the envelope technique is a method that assists students in reaching a rapid, correct solution in ratio-proportion problems, subsequently increasing their mathematical achievements.