The impact of equal sharing and multiple groups problems on students' understanding of fractions

Abstract

The purpose of this qualitative case study was to examine the impact of division and multiplication word problems, namely Equal Sharing and Multiple Groups problems, on students’ understanding of fractions. Thirteen middle school students, from two different middle schools, participated in this case study. Following a reform oriented approach to instruction, students were introduced to a series of Equal Sharing and Multiple Groups problems to solve and discuss. In addition, each student was given a preassessment, midassessment and postassessment. The data from these assessments along with the recordings of students’ discussions were carefully analysed to determine the impact of Equal Sharing and Multiple Groups problems on students’ understanding of fractions. Students’ understanding of fractions was assessed through their ability to solve word problems related to the five different constructs of fractions: partwhole, measure, ratio, quotient and operator constructs. The results indicated that, for the most part, students’ understanding of fractions did improve through the use of Equal Sharing and Multiple Groups word problems. The study also highlighted the need for further research in the area of naming fractions, in particular, the when and how to introduce the naming of fractions in order for students to have a deeper understanding of the multiplicative relationship between the numerator and denominator.