A Local Instructional Theory of Multiplication Rules and Permutation Using Tourism Context - Aan Putra; Zulkardi Zulkardi; Ratu Ilma Indra Putri; Laswadi Laswadi (Mathematics Education Journal, 2026)
Permutation is a core topic in combinatorics but is perceived as difficult because it often relies on memorizing formulas and is detached from meaningful contexts. Tourism activities offer a meaningful context for students and provide enumeration rule problems that can help them reinvent the concept of multiplication rule and permutation. This study aims to design a Local Instructional Theory (LIT) of multiplication rule and permutation using the context of tourism activities. The study used a validation studies within a design research methodology consisting of three phases: preparation and design, design experiment, and retrospective analysis. The participants included one mathematics teacher and 40 twelfth-grade students from Jambi, Indonesia. Data were gathered through students’ written tasks, classroom observations, and interviews, and were analyzed retrospectively. The LIT of multiplication rule and permutation using the context of tourism activities consists of seven activities: identifying and constructing the round-trip routes, listing and counting pairs of transportation modes, constructing tree diagrams, generalizing patterns of the multiplication rule, applying the multiplication rule in solving contextual problems, transforming the multiplication rule into factorial notation, and formulating permutation formulas using factorial notation. These activities help students reinvent the concept of multiplication rule and permutation and apply the concepts flexibly across various problem contexts. Therefore, this study underscores the pedagogical potential of the tourism context to teach the concept of multiplication rule and permutation through reinvention and provides a transferable framework for context-based mathematics teaching.