Examining Grade 9 Students’ Engagement in Mathematical Problem-Solving - When Working as Individuals and in a Small Group Settings

Oct 15, 2026

Problem-solving is central to mathematics education worldwide, and Pakistan’s National Curriculum (Grade I–XII) highlights it as key to building students’ mathematical knowledge and understanding. Guided by Polya’s heuristics, this study investigated Grade 9 students’ mathematical problem-solving when working individually versus in small groups. Data combined semi-structured interviews, observations, written problem responses, and focus group interviews. Results show differences in how students emphasize Polya’s stages and how problem-solving shifts between stages across individual and group contexts, informing instruction in similar settings.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

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Abstract

Introduction

Theoretical background

Examining Grade 9 Students’Engagement in Mathematical Problem-Solving (MPS) When Working as Individuals and in a Small Group Settings Effat Alvi *, and Munaza Nausheen** Abstract Problem-solving is central to mathematics education across the world. The National Curriculum for Mathematics (Grade I-XII) in Pakistan emphasizes the importance of problem-solving in developing students’ mathematical knowledge and understanding. Informed by Polya’s heuristics that guides the problem-solving process, this study examined Grade 9 students’ mathematical problem-solving (MPS) when working asindividuals and in a small groupsetting. Data were triangulated through multiple methods including semi-structured interviews, observations of episodes of students solving problems in a small group, written responses to the problems, and focus group interview. The findings reveal that the participants demonstrated variations in the emphasis given to each stage as well as the manner in which problem-solving was operationalizedat an individual and a group level. Moreover, students both individually and while working in a small group go back and forth among different stages of Polya’s heuristics. These findings have implications for the teaching and learning of MPS in academically less advanced countries similar to Pakistan. Keywords: Polya’s heuristics, Mathematical problem-solving, Word problems, [Individual vs. group](Individual vs. group) *Assistant Professor, Department of Educational Research and Evaluation, IER, University of the Punjab, Lahore. E-mail: [effat.ier@pu.edu.pk](effat.ier@pu.edu.pk) ***Assistant Professor, Department of Educational Research and Evaluation, IER, University of the Punjab, [Lahore. E-mail: munaza.ier@pu.edu.pk](Lahore. E-mail: munaza.ier@pu.edu.pk) Introduction Mathematics is one of the core curriculum subjects taught at all levels of primary, middle and secondary schools in Pakistan (Government of Pakistan, 2006) . Although a range of components and processes are emphasized in mathematics curricula, problem-solving has remained a fundamental constituent in the National Curriculum for Mathematics (Grade I – XII) . Group work, development of relational understanding, mathematical thinking, reasoning, negotiation and communication are major emphases for students outlined in the national curriculum. Consistently, teachers are encouraged to shift their role from ‘dispensing information’ to “planning investigative tasks, managing a cooperative learning environment and supporting students’ creativity in developing relational understanding of the concepts of Mathematics”(p. 2) . Contrary to the expectations of the curriculum (Government of Pakistan, 2006), a detailed analysis of the first national assessment data of middle school students in Pakistan indicates extremely low levels of achievement in mathematics (Tayyaba, 2010) . In particular, students performed poorly on demanding items that required them to use complex cognitive skills such as reasoning and problem solving. Overall, the results displayed marked disparities between the expectations of the curriculum and the actual achievement of students. Given the emphases in the national curriculum, and the huge deficits demonstrated in students’ performance in mathematics and problem-solving, researchers have paid close attention to the effectiveness of teaching problem-solving skills (Ali, Hukamdad, Akhter, & Khan, 2010; Perveen, 2010) . For example, Perveen examined the effect of heuristics oriented problem-solving instruction on secondary school students’mathematical achievement and problem-solving skills by conducting an experimental study. The results of the study demonstrated that students who were taught by the problem-solving heuristics outscored students who were taught by expository instruction on a mathematics achievement test. Ali et al. (2010) reported similar trends with elementary and high school students. While the effectiveness of teac

FAQs

What problem-solving framework guides the study?

The study uses Polya’s four-stage problem-solving heuristics. It examines how students apply these stages during mathematical problem-solving.

How does the study compare individual work with small-group work?

It investigates how Grade 9 students employ Polya’s heuristics while working alone versus while working in a small group, focusing on variations in stage emphasis and how students move across stages.

What data sources support the study’s findings?

The study triangulates data using semi-structured interviews, observations of students solving problems in a small group, written responses, and focus group interviews.

Oct 15, 2026

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