Making equivalent resistance visible: a Scratch–Arduino digital–physical learning suite for secondary physics

Abstract This paper presents a classroom-ready digital–physical learning suite designed to support secondary students’ understanding of resistor colour codes and equivalent resistance in electric circuits. Students often experience difficulties both in interpreting resistor colour codes and in reasoning step by step about the simplification of resistor networks in electric circuits. While many simulations and circuit tools are available, few explicitly make the underlying reasoning processes visible to learners or combine virtual and physical representations in ways that are practical for everyday classroom use. To address this need, we developed a suite of interconnected tools using Scratch and Arduino that integrates interactive simulations, physical computing, and formative assessment activities within a coherent learning environment. A central feature of the suite is a novel step-by-step visual simplification mechanism that externalises expert reasoning during circuit reduction, allowing students to follow how short circuits, out-of-circuit components, and series and parallel combinations are systematically identified and simplified. The tools are designed for students aged 15–16 and emphasise conceptual transparency, interactivity, and ease of classroom implementation. They are low-cost, adaptable, and intended to be readily modified or extended by teachers without advanced programming expertise. Rather than focusing on large-scale empirical evaluation, this paper aims to share a practical design approach and concrete teaching tools that can support inquiry-based learning and formative assessment in secondary physics classrooms. The learning suite illustrates how digital–physical environments can be used to make abstract circuit reasoning explicit and usable for both students and teachers.