Culturally responsive modular arithmetic instruction: Development of digital lucky modal cards inspired by the lucky 9 card game

Abstract

Properties of modular arithmetic are usually taught through a conventional instructional approach that continuously poses a low level of mastery to many students. The Lucky Modal Card Game is an innovative substitute for the traditional card game embedded in Filipino culture, Lucky 9. Lucky 9, the cultural concept of swerte (luck), is associated with memory enhancement and strategic thinking. Developing learning material from this culturally familiar game provides engaging gameplay for teaching and learning modular arithmetic. The study was guided by the Developmental Research Design ADDIE model, systematically undertaking analysis, design, development, implementation, and evaluation phases. These phases incorporated learners’ mastery and speed in solving modular arithmetic, learners’ acceptability, and expert validation. Findings revealed that students performed better in modular arithmetic regarding speed of response and accuracy on the operations of addition and multiplication than on operations like inverses (additive and multiplicative inverse), which procedures were not clearly scaffolded, and raising to a power and factorization, which require complex iterative processes. Scheffe tests suggested the following groupings in terms of difficulty: 1) addition and multiplication, 2) inverses (additive and multiplicative inverse), and 3) raising to a power and factorial. The developed learning material demonstrated high usability, instructional quality, and positive learners’ acceptability. Students reported increased motivation, ease of navigation, and clearer conceptual understanding. Expert evaluations confirmed that the material was highly valid in content, aligned with curriculum competencies, and appropriately managed cognitive load.