Relations between children's developmental level in performing Piagetian angle tasks and achievement in learning angle measure, in upper elementary grades

A study of the relations between children's developmental levels in performing selected Piagetian tasks involving angle and angle measure and their achievement in learning angle measure sought information regarding conditions of the child's readiness for instruction in angle measure. The subjects were a randomly chosen sample of 72 predominantly middle-class Anglo students in the fourth, fifth, and sixth grades of a Houston Independent School District elementary school. Three tasks were chosen from Piaget's works; (1) copying a linear pair of angles, (2) copying an obtuse triangle, and (3) sorting triangles into sets of similar triangles. The subjects were observed performing the tasks. They were then Instructed in shgle measure and evaluated in achievement in the instructional unit. Relations between the subjects' angle measure achievement scores and their developmental levels were analysed for the combined tasks and for each task separately. Statistics were limited to rank-order determinations because the levels were at best ordinal. Results indicated that there was a positive correlation between the subjects' achievement in angle measure and (a) their combined ranks for levels in the three tasks and (b) their ranks for levels in each task. The subjects' achievement in learning angle measure was categorized in three ranges (a) good, (b) fair, and (c) poor. The categories were closely related to good, fair, and poor intuitive understanding of angle measure. The relations between the angle measure achievement categories and the task developmental levels seemed to indicate that there was a close relation between (a) Task 1, Level TIB—preoperational—and poor angle measure achievement? (b) Tasks 1 and 2, Levels IIIA-TIIB and IIIB—advanced concrete operational—and gooJ angle measure a achievement. Between Task 3 levels and achievement categories the relations were not well defined. The distribution of subjects by developmental levels was approximately 2.5$ pre-operational, 50X early concrete operational, and 25$ advanced operational. The findings of this study indicate a gap in the predictive power of the angle tasks between pre-operational and advanced concrete operational. Exploration of how children reach the attainment of angle conception—advanced concrete operational level is beyond the scope of this study. However, some suggestions concerning instruction were made. For example, intuitive understanding of angle measure seems to be closely associated with success in learning angle measure, therefore it is suggested that children have varied experiences using angles in applications so that they develop an intuitive understanding of angle measure before they are Instructed in the use of the protractor.