A lightweight interactive platform for stepwise formative assessment in algebra from single variable equations to matrix form linear systems in inclusive classrooms

Abstract

Many digital mathematics tools validate only final answers, whereas teachers often need students to produce specific intermediate forms and to receive immediate guidance on where a transformation went wrong. This need is particularly important in inclusive classrooms, where low-stakes, non-judgmental, step-based interaction can support differentiated teacher intervention. This paper presents a lightweight interactive platform for step-based formative assessment in algebra covering two canonical tasks: solving single-variable equations of the form $$ax+b=c$$ and solving matrix-form linear systems $$AX=B$$ under fixed scaffolds. Across both tasks, the platform separates formula verification from deterministic numeric checking, locks progression step by step, provides explicit error labels, and records process-oriented traces for teacher-facing analytics. Unlike equivalence-oriented or CAS-dependent algebra tools, the proposed platform is designed for teacher-specified canonical intermediate forms, lightweight local deployment, and teacher-facing process analytics across two algebra tasks. The technical core is a CPU-only pipeline based on character n-gram TF–IDF, targeted numeric cues, and a compact multilayer perceptron. For the single-variable equation task, the classifier reaches 99.62% accuracy and 0.9962 macro-F1 on held-out test data. For the $$AX=B$$ task, the corresponding classifier reaches 99.87% accuracy and 0.9987 macro-F1. Beyond synthetic evaluation, the paper analyzes authentic classroom interaction logs, including timing, attempts, step-level error concentration, and cohort-aware usage patterns. These results are interpreted as exploratory classroom evidence rather than as causal proof of learning effectiveness. The contribution is a unified, locally deployable platform that combines reliable step-level diagnosis with teacher-facing analytics in an inclusion-oriented setting.