A Study on fifth grade students' mistakes, difficulties and misconceptions regarding basic fractional concepts and operations

Tarkan Yuırtsever, Nilgün
The purpose of this study was to investigate mistakes made by elementary fifth grade students regarding basic fractional concepts and operations, and difficulties that they encounter. The other purpose was to investigate underlying misconceptions and reasons of those difficulties and mistakes. For this purpose, a mixed-method research combining quantitative and qualitative approach respectively was performed. Data were collected from elementary fifth grade students at the end of the spring semester of 2009-2010. Operation with Fraction Questionnaire (OFQ) was administered to 151 fifth grade students who were chosen from the two public elementary schools in Eskişehir province. By this way, difficulties that elementary fifth grade students encounter and mistakes they make regarding basic fractionalconcepts and operations was analyzed. Afterwards, sixteen of these students participated in a semi-structured interview which was designed to investigate underlying reasons and misconceptions behind those mistakes and difficulties. Results were presented in two phases. In the first phase, common mistakes and difficulties of students were analyzed in detail and representative examples of these errors were introduced. In the second phase, students' mistakes were grouped under five categories as: algorithmically based mistakes, intuitively based mistakes, mistakes based on formal knowledge on fractions, misunderstanding on problem, and missing information in solution. In this phase, misconceptions and underlying reasons of those mistakes and difficulties which students may encounter while learning fractions were described. Results revealed that there was evidence that fifth grade students made various mistakes regarding fractional concepts and operations in the fifth grade elementary mathematics curriculum and they had many misconceptions regarding fraction concepts and operations.