Development of NUMA: An Adaptive-Constructivist AI-Assisted Drill-and-Practice Application for Grade 3 Elementary Students

Abstract

Low conceptual understanding remains one of the more persistent problems in elementary mathematics, and it is not helped by instructional approaches that lean on procedural drilling instead of building genuine conceptual grounding. Plenty of mathematics applications exist, yet very few bring diagnostic assessment, adaptive mastery progression, structured scaffolding, and teacher monitoring together on a single free platform. This paper documents the initial Research and Development (R&D) cycle of NUMA (Numeracy Understanding through Multistage Assistance), a cross-platform mobile application for Grade 3 students built through the Design Thinking framework. NUMA pairs generative-AI-assisted item and hint generation with a rule-based adaptive engine, and brings together a diagnostic pretest, three scaffolded learning levels, a four-stage Polya hint system, and a teacher analytics dashboard. The scope here is the design and development process and its expert validation, not yet a full evaluation of instructional effectiveness. Expert validation across four domains indicated highly valid ratings, with scores ranging from 4.41 to 4.73. A small-scale test with ten Grade 3 students produced positive technology acceptance (PU: M = 4.29; PEOU: M = 4.25) and a preliminary descriptive learning gain of 19.33 points. As an initial cycle, these findings are design-stage evidence rather than proof of learning impact; a controlled classroom experiment at a much larger scale is planned for the next cycle.