Reversibility of thought: An instance in multiplicative tasks

In line with current efforts to understand the piece-by-piece structure and articulation of
children’s mathematical concepts, this case study compares the reversibility schemes of
two eighth-grade students. The aim of the study was to identify the mechanism through
which students reverse their thought processes in a multiplicative situation. Data collected
through clinical interviews depict the precise strategies that the participants used to work
back to find the missing values in an inverse proportional task. This study also illustrates
how a conceptual template generated by one of the participants afforded him considerable
flexibility in the multiplicative task. Another outcome of the study is that it shows how the
numerical characteristics of the parameters in the problem affected the students’ ability to
reverse their thought processes. We infer that there is a need for further research on how
students might represent their reversibility schemes in the form of algebraic equations.