“As soon as the four sides are all equal, then the angles must be 90° each”. Children's misconceptions in geometry

Abstract

This study describes Nigerian and South African students' conceptual understanding in high school geometry based on the van Hiele model of geometric thinking levels. The study further highlights students' misconceptions in school geometry. Concepts of triangles and quadrilaterals were investigated among 36 mathematics learners drawn from grades 10 through 12 who participated in this study. The tasks included identifying and naming shapes, sorting of shapes, stating the properties of shapes, defining of shapes and establishing class inclusions of shapes. The results indicated that many Nigerian and South African high school learners in Grade 10, 11 and 12 hold a number of misconceptions about geometric concepts of triangles and quadrilaterals. The use of imprecise terminology in describing many geometric shapes was common among the learners. The majority of learners in this study were at van Hiele level 0. Although many were able to distinguish between triangles and quadrilaterals, they lacked the appropriate vocabulary to distinguish among shapes in the same class. For many learners, the task of naming shapes was easier than giving a description of their properties. Also many students demonstrated a relatively better understanding of the concept of triangle than that of quadrilaterals. Knowledge of class inclusions of shape was absent among these learners. The results of this study were found to be consistent with those of earlier studies and recommendations are offered.