Pupils' difficulties in computing fractions: a study of selected secondary schools in Nairobi province
The study investigated the difficulties that pupils face in computing fractions. Fractions were considered vital in this study because they form bulk of pupils' early experience with numbers in secondary school mathematics. Many mathematics topics including decimals, percentages, ratios, proportions, probability, trigonometry, measurements, coordinate geometry and calculus among others, depend on fractions. This is evident from studies in mathematics such as in Algebra (Ogolla 1997, Wanjala, 996), in Ration (Hart, 1984) and Numbers Odanga, 1992), which revealed that pupils faced difficulties in these topics because they lacked knowledge on the basic concepts of fractions. Other studies based on fractions by Landau and Lesh (1983), Hart (1981), Bell et al (1983) and Copeland (1979), classifies fractions among the most dreaded topics of mathematics. Wanjala (1996) advocates for the utilization of pupils misconceptions in mathematics as a basis for minimizing their difficulties in this subject. Landau and Lesh (1983) points out that an investigation into one's understanding and misunderstanding of fractions, provides useful insights which aids in instructional development. Taking these points into consideration, this study investigated pupils difficulties in computing fractions with an objective of determining the various difficulties that pupils face in computing these numbers and, where possible, provide remedial measurements to ease these difficulties. Pupils' difficulties in computing fractions were investigated by administering written tests to 369 pupils from 9 different secondary schools (3 girls, 3 boys and 3 co-education schools). The nine schools were satisfactorily picked from a stratified sample of 44 public secondary schools (Provincial Education Office) in Nairobi province. They, therefore, constituted a representative sample worth investigating. Written tests were used to expose pupils' difficulties in computing fractions. These tests were considered useful since they are the most commonly used learning assessment method and they paved way to access the varied difficulties that pupils face in computing fractions. Pupils' responses to these tests were marked and analyzed to determine the types and magnitudes of difficulties they experienced in computing fractions. Gender differences in computing fractions were also investigated. This study revealed that pupils experience difficulties in computing fractions due to varied reasons. Many of them lack sufficient knowledge on how to determine and use LCM and other common multiplies and factors. They were also found to be unfamiliar with basic definitions and properties of fractions such as the fact that the magnitude of a fraction varies inversely as its denominator and directly as its numerator and that the denominator must not be zero. Many pupils could not successively visualize fractions depicted in diagrams or in number lines. Very few of them were able to interpret correctly problem solving tasks on fractions. Arithmetic incompetence was also common among many pupils under this investigation. The study also found out that girls perform just as well as boys in computation fractions. The study suggests remedial measures that teachers could use to enable more pupils feel successful and confident in computing fractions. The study stresses the need for mathematics teachers to utilize the knowledge of pupils’ difficulties in computing fractions as revealed in this investigation for the benefit of minimizing their pupils misconceptions of fractions. Teachers are also advised to spend more time discussing the definitions and properties of fractions and relating these numbers to other topics of mathematics and in real life.