Enhancing grade vii students' conceptual understanding of mathematical content 'Area' by using manipulatives
Date of Award
Master of Education (MEd)
Institute for Educational Development, Karachi
The topic of ‘area’ is one of the challenging topics in curriculum of school mathematics. In most of the cases, conventional teaching methods based on formula, rules and algorithms do not help students to develop sound understanding. This study is an attempt to investigate how students’ conceptual understanding can be enhanced if they are provided with opportunities of using manipulatives. For this purpose, I conducted an action research within qualitative research paradigm with six students of grade VII in a private school of Karachi, Pakistan. The whole class was the secondary participants in the study. However, I selected a group of six students for in-depth analysis of their learning in the classroom. Also, pre and post focus group discussion (FGDs) from participant students and an interview from mathematics teacher were taken. This study consists of three stages, reconnaissance stage, implementation stage and post implementation stage. In reconnaissance stage, I examined students’ current understanding of area and process of teaching and learning of area through classroom observations, interview with mathematics teacher, focus group discussions (FGD) with students and document analysis. In implementation stage the topic was taught using manipulatives. Moreover, the instruction was designed considering hierarchical order of concrete, pictorial and symbolical representations to build students’ concepts. In post implementation stage, the focus was to understand students’ overall experience of using manipulatives and students understanding of area through post FGD. The findings revealed that students’ understanding of area and other concepts associated to it were developed. For example, they develop conceptual understanding of area as two dimensional quantity, use of appropriate unit of measurement, difference between area and perimeter and finding areas of shapes where direct length times breadth formula is not applicable. The contributing factors in developing students’ conceptual understanding were scaffolding as students move from easy to complex concepts, communication among students and with teachers enable students to convey their thoughts to clarify their understanding, simultaneous use of concrete, symbolic and pictorial representations and building connections among different concepts of area. Based on the findings, this study suggests that teachers should first use concrete, pictorial representation and then help students to make its connection with symbolic representations. It is important to understand which manipulative could be appropriate for helping students make transition from one representation to other. Keywords: Conceptual understanding, manipulatives, area.
Begum, K. (2018). Enhancing grade vii students' conceptual understanding of mathematical content 'Area' by using manipulatives (Unpublished master's dissertation). Aga Khan University, Karachi, Pakistan.