An analysis of students’ difficulties in multiplication and division of large numbers (thousands and millions) in social arithmetic at junior high school

Bhoke, Wilibaldus
Finu, Maria Dafrosa
Ewol, Novalia Sudiatik

Desimal: Jurnal Matematika
Vol. 8 No. 3 (2025): Desimal: Jurnal Matematika

This study aims to analyze students’ difficulties in solving multiplication and division problems involving large numbers, specifically thousands and millions, within the context of social arithmetic at SMP Negeri 2 Bajawa. The participants consisted of 65 seventh-grade students from classes VIID and VIIF, and a descriptive qualitative approach was employed to obtain an in-depth understanding of the types and underlying factors of these difficulties. Data were collected through participant observation, in which the researcher acted as both teacher and observer, documenting learning activities, students’ responses to instructional strategies, procedural errors, place value difficulties, and problem-solving strategies used during the learning process. Data analysis was conducted descriptively through the stages of data reduction, data organization, interpretation, and conclusion drawing. The findings indicate that students experienced interconnected difficulties related to conceptual understanding, procedural competence, and place value knowledge. Conceptually, students tended to treat multiplication and division as mechanical procedures without understanding their meanings, leading to errors in selecting appropriate operations for word problems. Procedurally, students often applied calculation steps inconsistently, resulting in inaccurate solutions, while difficulties in place value were evident in the incorrect positioning of thousands and millions digits. In addition, limited practice, low learning motivation, and weak connections between mathematical tasks and real-life contexts contributed to students’ difficulties. These results suggest that students’ challenges in large-number operations are influenced by conceptual understanding, procedural skills, place value knowledge, problem-solving strategies, and learning context, highlighting the importance of contextual and problem-based mathematics instruction supported by regular practice to improve students’ ability to solve social arithmetic problems effectively.