Big-Concept-Based Design of High School Mathematics Review Lessons: Function-Based Approaches to Inequalities
Abstract
High school mathematics review lessons often emphasize repeated exercises and isolated techniques, which may limit students' ability to connect previously learned knowledge and transfer problem-solving methods to unfamiliar situations. This study aimed to develop and preliminarily examine a big-concept-based design for a Grade 12 review unit on function-based approaches to inequalities. An exploratory, post-test-only classroom comparison was conducted with 95 students from two classes at K High School in City N. One class received three lessons based on the proposed design, while the other received conventional review instruction. Data were collected through a nine-item post-test and semi-structured student interviews. Descriptive results showed that the experimental class had a lower failure rate than the comparison class (2% vs. 10%) and generally higher performance in knowledge mastery, comprehensive understanding, and transfer and application. The available interview summaries suggested clearer connections among functions, derivatives, monotonicity, equations, and inequalities, as well as improved awareness of auxiliary-function construction and reverse reasoning. Unlike conventional review instruction organized around separate question types, the proposed design integrates fragmented knowledge around the transferable idea of auxiliary-function construction. The findings provide preliminary evidence of feasibility; however, because standardized pre-test data and inferential analyses were unavailable, the results should be interpreted cautiously.
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