An investigation of the effect of operational level on the arithmetic performance of grade one children
Creators: name: Davies, Donna Lynn
Publisher: name: University of British Columbia
Year: 2010

description: This study investigated the interactive influence of operational level, type of number sentence, and level of difficulty on grade one arithmetic performance. Of specific interest was the relationship between the child's operational level and his or her accuracy and solution methods when solving addition, subtraction, and missing addend sentences at three levels of difficulty. Subjects of the study were sixty grade one students from a suburb in the lower mainland of British Columbia. Nine types of Piagetian tasks, including seriation, classification, and conservation were administered to a large sample of children. The children were then assigned to three operational levels: transitional, early concrete, and later concrete. Twenty subjects at each of the three operational levels were selected for this study. Subsequently, a nine-item arithmetic test including addition, subtraction, and missing addend sentences at three levels of difficulty was administered individually to the sixty subjects. Both the child's answers to the number sentences and his or her solution procedures were recorded. There was one dependent variable, arithmetic performance, and three independent variables: operational level, type of number sentence, and level of difficulty. Arithmetic performance was analysed by a fixed effects three-way analysis of variance with repeated measures on the last two factors. The solution strategy study was analysed with descriptive statistics. Based on a review of the literature, six hypotheses were formulated and tested. The results of the analysis of variance revealed a second order interaction of operational level, type of number sentence, and level of difficulty; two first order interactions, operational level and type of number sentence and operational level and level of difficulty; and three main effects of operational level, type of number sentence, and level of difficulty (p&lt; .001). An analysis of the solution strategy study results indicated that the children in this study used counting procedures to solve the number sentences. Counting-all, partial counting-on, and counting-with-tally were the implemented strategies for solving addition and missing addend sentences. Counting-all and counting-with-grouping were the procedures used to answer the subtraction items. The partial counting-on and counting-with-tally procedures were designated as intermediate strategies between counting-all and counting-on. The child's operational level influenced his or her choice of solution method. Later concrete children used more advanced strategies than early concrete children who, in turn, used more advanced strategies than transitional children. It was concluded that Piagetian tasks could be included as one assessment to determine the child's readiness for the grade one arithmetic program. Specifically, the conservation of number task may serve to identify whether the child has the cognitive maturity to comprehend the operations of addition and subtraction; and the class inclusion task may indicate the child's readiness for missing addend sentences. It was also recommended that the child be taught solution methods which are appropriate for his or her level of cognitive development. The transitional procedures, partial counting-on and counting-with-tally, that were observed in this study have potential implications for classroom practise and future research.