<![CDATA[Elementary school students frequently struggle to master addition and subtraction of whole numbers up to 100,000, because the transition from three-digit to five-digit numbers sharply increases cognitive load and disrupts place-value understanding. This qualitative case study examined how integrating Problem-Based Learning (PBL) with the “Papan Jurang” (Chasm Board) manipulative supported Grade V students’ arithmetic proficiency at SDN 2 Lumansari, Kendal, Indonesia, viewed through the lens of Tarbiyah Islamiyah. Data were collected from July 2024 to mid-2025 through classroom observation, in-depth interviews with eight informants (the principal, the curriculum vice-principal, and six Grade V students), and document analysis, then analyzed thematically following the Miles and Huberman model. Findings show that the PBL–Papan Jurang synergy was associated with a marked improvement in students’ place-value understanding and procedural fluency, eased the enactive–iconic–symbolic transition, and reduced regrouping errors alongside mathematics anxiety. Tarbiyah values were observed operationally: tafakkur manifested as students’ reflective reasoning about numerical patterns, and taisir as the ease the board provided in bridging concrete and symbolic representation. This study contributes a model that converges Cognitive Load Theory with Islamic educational philosophy, offering primary schools—particularly faith-based ones—a locally grounded, low-cost alternative to digital manipulatives for teaching large-number arithmetic.]]>
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