THE ROLE OF EXAMPLES-USE IN THE UNDERSTANDING OF SIMPLE ADDITION

Abstract

This study is based on Hughes' (1983) proposal for a teaching approach that allows children to achieve an ability to make fluent connections between the "concrete" and the formal codes of arithmetic. An investigation was made to find an effective way of using examples to establish these connections. The examples-use variable was manipulated at two levels, 1) implicit examples-use (hypothetical situation examples used implicitly, without any explanations given), and 2) explicit examples-use (hypothetical situation examples used explicitly, with explanations provided). The children were then tested on two tasks, 1) the target task ( addition problems similar to the hypothetical situations but phrased in the formal-code) and 2) generalisation task (addition problems different from the hypothetical situations phrased in the formal-code). Results of the 2 (examples-use) x 2 (task) analysis of variance (ANOVA) showed that explicit examples-use helped children obtain significantly more correct answers to the formal-code questions in both the target and generalisation tasks. However, an additional formal-to-concrete test showed that children were unable to derive the answer to a hypothetical situation question from the given answer to a same formal-code question. A chi-square test of independence on the number of children who were correct or incorrect in the formal-to-concrete test revealed that performance on the formal-to-concrete test is not related to success in the generalisation task. Hence, the study showed that explicit use of examples helps children make forward linkages but not backward associations.