Students’ misconceptions in geometry and measurement: A study of elementary schools in Gilgit-Baltistan

Date of Award


Document Type


Degree Name

Master of Education (M. Ed.)


Institute for Educational Development, Karachi


Geometry and Measurement (GM) is one of the essential aspects of mathematics that enhances students’ visualization skills, critical thinking, problem-solving, and deductive reasoning. Despite being a crucial content domain of school mathematics, students’ low performance has remained a matter of concern in academia around the globe, with no exception in Pakistan. One of the factors that contribute to students’ low achievement could be their misconceptions which led them to make conceptual errors. This study aimed to explore the elementary school students’ misconceptions in GM using Mathematics Achievement Tests (MATs) data which was collected as part of nationwide study of HEC-NRPU (parent study). The anonymized data of elementary school students’ (n=1,006) achievement in GM of Gilgit-Baltistan were taken from parent study. Altogether, 24 items were used to collect data on geometrical concepts across three target grades (V, VI, VIII) using MATs. The analysis first identified the most difficult items, by computing Difficulty Index (DI), followed by the comparison of students’ performance on these items across gender and school systems.
The findings revealed that of the 24 items, 9 fell in the category of the most difficult items (DI≤0.20). Further analysis of these difficult items uncovered students’ misconceptions in various concepts including; perimeter and area (mixing up the two concepts), angles (misapplication of angle sum property of triangle, unable to differentiating between acute and obtuse angle), line (parallel was considered as perpendicular), and shapes (unable to identify the differences in similar shapes). Bivariate analysis revealed that girls have demonstrated relatively fewer misconceptions; however, the difference was not significant (p>0.05). Moreover, the students of private schools demonstrated significantly fewer misconceptions as compared to their counterparts in public schools (p<0.001) with a small magnitude (r=0.16). Based on the findings, this study has offered recommendations for policy makers, practitioners as well as for future researchers.

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