Why Do Middle School Students Struggle with Large-Number Word Problems? A Qualitative Study of Conceptual, Procedural, and Place-Value Difficulties in Social Arithmetic
DOI:
https://doi.org/10.64780/jole.v2i1.173Keywords:
Conceptual difficulties, large-number word problems, place-value reasoning, procedural errors, social arithmeticAbstract
Background: Persistent difficulties in solving large-number word problems remain a central challenge in middle school mathematics learning, particularly in social arithmetic where students must integrate conceptual understanding, procedural fluency, and accurate place-value reasoning. Previous studies have documented frequent computational errors, yet limited attention has been given to the underlying cognitive and representational mechanisms that shape these difficulties.
Aims: This study aims to examine the nature of students’ conceptual, procedural, and place-value difficulties in solving large-number social arithmetic word problems and to identify patterns that hinder effective problem solving.
Method: A qualitative descriptive design was employed involving 65 seventh-grade students from two middle school classes. Data were collected through participant observation and systematic analysis of students’ written responses. The data were coded thematically across conceptual understanding, procedural execution, and place-value representation to capture recurring error patterns and learning barriers.
Results: The findings reveal three dominant forms of difficulty: misconceptions in selecting appropriate operations, unstable sequencing of computational procedures, and persistent misplacement of digits in thousands and millions. These difficulties frequently co-occur, resulting in fragmented problem comprehension, inaccurate numerical representation, and ineffective solution strategies.
Conclusion: The results indicate that students’ struggles extend beyond procedural weakness and reflect deeper breakdowns in conceptual integration and representational reasoning. Addressing these difficulties requires instructional designs that emphasize conceptual coherence, explicit place-value representation, and sustained engagement with contextual problem structures. By highlighting the interplay between conceptual, procedural, and representational dimensions, this study contributes to a more nuanced understanding of learning barriers in social arithmetic and offers pedagogical directions for strengthening mathematical problem-solving competence in middle school classrooms.
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