Enhancing Conceptual Understanding in Mathematics: The Effectiveness of the Square Method for Computing Areas of Irregular Shapes Among Secondary School Students in Tanzania

Abstract

This quantitative study investigates the effectiveness of the square method for teaching secondary school students to compute the area of irregular shapes, integrating mathematics and geography within the context of the school environment. Conducted at KIHONDA and MAFIGA Secondary Schools, the research involved 200 Form Four students selected through simple random sampling. Utilizing a pre-test and post-test design, data were collected to evaluate students’ understanding before and after engaging in practical learning activities. The intervention required students to identify irregular shapes, such as broken windows and cracked tiles, within their school environment, and to compute their area using the square method by counting full and partial squares on a grid overlay. The findings reveal significant improvements in students’ skills: recognition of irregular shapes increased from 22% in the pre-test to 86% in the post-test, indicating enhanced engagement with the material. Furthermore, students demonstrated a marked improvement in selecting appropriate measuring tools and applying estimation techniques. The use of visual aids and hands-on activities facilitated the development of spatial reasoning and provided students with a better grasp of geometric concepts in practical contexts. Group-based exercises further encouraged collaborative learning and problem-solving. Despite these positive outcomes, challenges were noted, including the time-consuming nature of the method when applied to large or complex shapes and a recognized need for additional training and resources among teachers. Overall, the study concludes that the square method is an effective pedagogical strategy for improving students’ understanding of irregular area computation, advocating for its integration across subjects to foster interdisciplinary learning. Future research is encouraged to explore the incorporation of digital tools to complement this method and assess long-term retention of concepts acquired through this approach.