Beyond the Across Algorithm: Informal Strategies for Inverse Proportional Problems

The main purpose of this research is to examine the informal strategies of fifth and sixth grade students while solving inverse proportional word problems. Multiple case study was used in this study. The research was carried out in a public middle school from a southern city of Türkiye. The participants of the research consist of three fifth and three sixth grade students. Problem tasks containing inverse proportional word problems were applied as data collection tool. Task-based interviews were used as qualitative data collection method in this study. The data collected from the participants were analyzed using the content analysis method. The findings of the study showed that participating students used eight distinct strategies while solving inverse proportional word problems. It was seen that the fifth and sixth grade students were able to develop their intuitive and informal strategies on inverse proportional problems. It has been observed that in cases where the numerical structures of the problems change, some students failed to notice the inverse proportional relationships and made erroneous direct proportional and additive solutions. The findings of the study indicated that the numerical structures in the problems both affect the difficulty level and the strategies utilized in solving these problems.