Developing students' conceptual understanding and reasoning skills of geometrical proofs through integrating geogebra software in grade 10 in a private higher secondary school situated in Chitral, Pakistan

Date of Award


Document Type


Degree Name

Master of Education (MEd)


Institute for Educational Development, Karachi


Mathematics is one of the compulsory subjects taught from kindergarten to matriculation level in the schools of Pakistan. Teaching mathematics remained a challenge generally and geometry, particularly due to the abstract nature of the topics. The board and chalk method of teaching is not enough to develop the conceptual understanding and the reasoning skills of students. For this purpose, the integration of the Dynamic Geometry Software's (DGS) are introduced to enrich and enhance the learning of students in classroom teaching, along with the traditional instructional methods. Geogebra is one of the Dynamic Geometry software, which is famous for its freeware, offline use and versatile features to construct analyse and visualize the geometrical objects. An action research based on qualitative approach has been conducted on grade 10 students to develop their understanding of geometrical proofs through integrating the Geogebra software in a private secondary school, Chitral. The data has been collected in two phases and comprises 12 lessons on circle theorems taken from the National Curriculum of Mathematics i.e., NCM (2006). The data collection tools includes focused group discussion of six research participants, interviews of mathematics teacher, feedback from critical friend, students 'work on the software and their written reflections after each phase. The findings revealed that the integration of the software enhanced the understanding of geometrical proofs and their reasoning skills in the students. The students found the software friendly, interactive, and helpful in understanding the abstract topics. The use of the Van Hiele's geometrical thinking model enhanced the understanding of the students in the systematic using of Geogebra. For example, the students visualized the geometrical objects, analysed the properties through dragging and flipping and then informally deduced the relative changes in the figures to formally provide arguments or reasons for their geometrical works in solving problems related to circle theorems. Furthermore, this software helped the teachers to utilize the teaching time effectively through engaging the students individually in the learning process. In addition, the integration of the software filled the gap of conversation between the students and teacher while teaching abstract topics in geometry, making them tangible and visible. Finally, the success of the integration of software in teaching depends on the motivational power and skills of teachers in designing the tasks to scaffold the students' learning vividly.

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