article · Discover Education
Digital tools for mathematics education often check only final answers rather than intermediate working. To address this, a lightweight platform provides step-by-step formative assessment for single-variable equations and matrix-form linear systems. The system separates formula verification from deterministic numeric checks, enforces step-by-step progression, delivers explicit error labels, and captures process traces for teacher dashboards. Powered by a CPU-only pipeline combining character n-gram TF-IDF, numeric cues, and a compact multilayer perceptron, the underlying classifiers achieve over 99.6 percent accuracy and macro-F1 scores on held-out test data for both equation types. Authentic classroom interaction logs reveal timing, attempt counts, and step-level error concentrations across student cohorts. Designed for local deployment without relying on computer algebra systems, the system supports differentiated instruction and formative feedback within inclusive classroom settings.
Many digital mathematics platforms only verify final solutions, leaving learners unaware of where intermediate calculation errors occur. Providing automated, step-level diagnosis helps teachers pinpoint specific misunderstandings quickly in inclusive classrooms. Because the platform runs locally on standard central processing units without complex computer algebra systems, it offers an accessible, low-resource method to deliver immediate feedback and actionable classroom learning analytics.
The platform is designed for educational technology applications, specifically for classroom teachers seeking automated, step-level assessment tools for secondary or introductory tertiary algebra. Because it relies on a lightweight CPU-only pipeline and local deployment, it suits resource-constrained school environments. Having been evaluated on test data and piloted with authentic classroom interaction logs, the technology represents an applied prototype ready for broader field trials and potential integration into learning management systems.
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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.
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DOI: 10.1007/s44217-026-02085-6
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