Akademik Veri Yönetim Sistemi
New Research and Applications in Mathematics Education and Differential Geometry, YÜCESAN AHMET, Editör, BZT Turan Publishing House, Delaware, ss.1-26, 2025
The aim of the study is to investigate the preferred and actual strategy use in interpreting remainders within division problems of undergraduate preservice mathematics teachers. The qualitative case study, which comprises 23 senior students in primary mathematics education, employed a semi-structured interview protocol to explore strategies that participants applied themselves in problem solving and posing, and those they preferred to employ for instructional purposes. Strategies discussed were Zero Remainder (R0), Ignoring Remainder (R1), Rounding/Adding Remainder (R2), Sharing/Dividing Remainder (R3), and Interpreting Remainder to Find the Initial Amount (R4). Accordingly, the most frequently employed strategy during application was R3 with 43%, indicating a tendency toward contextual sharing and exact solutions by means of fractions or decimals. On the other hand, R3 and R2 were equally preferred at 30% each, wherein R2 was valued regardless of its perceived cognitive demands. A significant discrepancy was found in that 70% of participants employed different strategies in use compared to their preference. Qualitative analysis identified key reasons for this gap, including awareness of strategies, differences between instructional planning and implementation, connection with daily life, and considerations pertaining to mental effort and student habits. The study concludes that this mismatch between preference and use reflects not a deficiency but rather the strategic flexibility of the participants and their contextual awareness. This pinpoints the need of teacher education programs in developing metacognitive awareness and deeper understanding of how, when, and why to apply different remainder interpretation strategies, thus bridging the gap between conceptual knowledge and practical application.