Developing proportional reasoning among grade VII students in Karachi, Pakistan

Date of Award


Document Type


Degree Name

Master of Education (M. Ed.)

First Supervisor/Advisor

Dr Nusrat Fatima Rizvi


Institute for Educational Development, Karachi


Proportional reasoning is a core concept in the middle school mathematics curriculum, which helps students connect different concepts in secondary and higher school mathematics. Proportional reasoning also helps students in different disciplines like science, arts, economics, and engineering. Getting mastery in proportional reasoning could be considered a major aim of the secondary school curriculum. A major transition from elementary to secondary school is the expectation from students to seek relationships between the quantities multiplicatively, which is the basis of proportional reasoning.
Students and teachers face challenges in teaching and learning of ratio and proportion. Students misunderstand proportion relations as additive instead of multiplicative relations; they are also unable to identify proportional situations; they often use different methods to solve proportional problems like cross multiplication but are unable to know the reason why they are using this appropriate method. This study is an attempt to develop students' proportional reasoning by engaging them with context-based situations and providing opportunities for using manipulatives. For this purpose, I conducted an action research study using qualitative method with Grade VII students in a private school of Karachi, Pakistan. The study consisted of three stages: reconnaissance stage, intervention stage, and post-intervention stage. The reconnaissance stage aimed to explore the existing practices of teaching and learning ratio and proportion topic through interviews with mathematics teachers, textbook analysis, and lesson plan analysis. In the intervention stage, the topic was taught by using group-based learning and manipulative. In the post-intervention stage, I revisited all the student's work and reflected on all the lessons that I taught.
The study's findings revealed that proportional reasoning skills gradually developed among Grade VII students. Students understood the concept of ratio in terms of multiplicative relations when they develop contextual situations where quantities varied. They also used their knowledge about fractional to solve proportional problems. The factors contributing to developing students’ proportional reasoning skills were discussions on real-world scenarios, the use of manipulatives to have hands-on experience and group-based learning. The findings of the study suggested that teachers should allocate sufficient time to group task and whole class discussion so that students could analyze context-based situations to generate their ideas and share them with their peers. It is also important that a connection between the concept that students learn in primary classes, like addition, multiplication, comparing objects and quantities, and fractions should be built with the concepts that students learn in middle grades like ratio, rate and proportion.

This document is available in the relevant AKU library