Publication record
- Original publication period
- January–June 2021
- Digitized / uploaded online
- August 11, 2026
The digitization/upload date records when this file was added to the website; it is not the article's original publication date.
Abstract
Printed modules can preserve mathematics practice when classroom contact is interrupted, but distribution alone does not establish learning. This conceptual review examines achievement as the product of a feedback loop among task interpretation, worked examples, independent practice, error evidence, and instructional response. Evidence through 2021 suggests that modular mathematics becomes fragile when prerequisite gaps are invisible, examples display procedures without reasoning, answer keys replace diagnosis, and delayed feedback allows misconceptions to consolidate. The article proposes a Worked-Example Feedback Loop in which each module identifies prerequisite knowledge, models a complete solution with self-explanation prompts, sequences practice by variation, collects interpretable learner work, and routes errors to a targeted response. The approach protects learner authorship by assigning caregivers a support role rather than asking them to teach unfamiliar procedures. It also recommends separating module completion, procedural accuracy, and conceptual transfer in assessment. This is a design framework, not an empirical estimate of achievement. Its purpose is to make the instructional mechanisms inside modular delivery visible and testable.