Analysis of Errors in Fractions

Abstract

All investigations that have been made to discover pupil difficulties in the fundamental processes of arithmetic show that pupils make errors for a great variety of reasons. The reasons vary from lack of knowledge of the fundamental facts in the processes to peculiar methods of work due to such psychological difficulties as faulty attention span, roundabout procedure, and lack of power. Several fairly comprehensive studies of pupil difficulties in the fundamental processes with whole numbers have been published. These studies have resulted in the development of diagnostic tests and remedial exercises designed to reveal the difficulties and to provide training to overcome them. This article reports the results of a detailed analysis of errors in solving examples in the processes in fractions made by pupils in Grades V A, VI B, and VI A. The first step in the investigation was to analyze the different types of examples that a pupil might encounter in working with fractions in much the same way that Buswell and John' and the writer' have analyzed the types of examples in the fundamental processes. For example, an analysis of the possible types of examples in the addition of fractions shows that there are forty different types involving the addition of two fractions or mixed numbers, each type different in some respect which might cause specific difficulties. Forty-five different types of examples were revealed in subtraction, forty-five in multiplication, and thirty-seven in division. The first five types in addition are as follows: