Enabling students' in solving non-routine Mathematics problems

Date of Award

2025

Degree Type

Dissertation

Degree Name

Master of Philosophy in Education (MPhil Ed.)

First Advisor

Dr Munira Amirali

Department

Institute for Educational Development, Karachi

Abstract

Mathematics is fundamental to human life, influencing personal, professional, and academic domains. The foundation of mathematics education is to build learners’ capacity to solve non-routine problems along with routine problems as it fosters critical thinking, inventiveness, and perseverance, in both the classroom and in real life. Furthermore, non-routine problems promote flexibility and strategic thinking to connect ideas from different strands of mathematics.  
This study explored how students approach non-routine problems by engaging them in inquiry-based tasks, encouraging them to use multiple strategies, work collaboratively and reflect on the steps undertaken in solving the given task. I used a qualitative approach and conducted action research with group of eight students of Grade VIII at a private school in Karachi, Pakistan. The study consisted of three stages: the reconnaissance stage, the intervention stage, and the post-intervention stage. In the reconnaissance stage, teacher interviews were conducted, textbooks were reviewed and SLOs were analysed. Based on these insights, a supplementary problem-solving booklet was developed. During the intervention stage, iterative cycles were implemented in which a supplementary booklet of non-routine problems was introduced to the classroom, accompanied by inquiry-based and collaborative learning activities. In the post-intervention stage, I revisited all the student's work and reflected on all the lessons that I taught. 
At first, students relied on guess work and procedural fluency. But later, the students began using strategies like spotting patterns, drawing diagrams and justifying. The study further demonstrated the significance of scaffolding, peer collaboration, and productive struggle in fostering persistence and resilience. Learners also demonstrated evidence of metacognitive engagement, particularly in planning, monitoring, and evaluating their strategies while working on non-routine problems. This highlights the role of teachers in fostering classroom environments that value multiple solution pathways and encourage reflective practices, thereby strengthening students’ reasoning in relation to the tasks explored in this study. Therefore, the study's findings showed a gradual yet significant shift in students’ problem-solving approaches. 
The study revealed that engaging students in non-routine tasks fostered greater perseverance, encouraged them to use diverse strategies, and supported metacognitive engagement. Interaction with one of the schoolteachers who observed the researchers and students’ while working on the non-routine tasks highlighted how such opportunities for exploration could shift classroom practices toward reasoning and sense-making.

First Page

1

Last Page

107

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