Integrating Analogical Reasoning to Improve Erroneous Worked Examples as a Learning Intervention

This research explores the integration of analogical reasoning to enhance the effectiveness of erroneous worked examples (WE) as a learning intervention for linear functions (LF). Mastery of LF is critical for mathematical proficiency, yet students often struggle with conceptual and procedural challenges, particularly when transitioning between tabular, algebraic, and graphical representations. Prior research indicates that WE with error-processing tasks can improve learning outcomes, though their effectiveness varies depending on students’ prior knowledge. To address this gap, this research investigates whether pairing WE with structural analogs of prerequisite knowledge can facilitate conceptual change and improve LF problem-solving. Two experimental studies were conducted, each employing a 3×2 between-subjects design. Participants were assigned to one of six conditions that varied by WE type (error detection, error indicated, or no WE) and the presence or absence of an analog task. Findings suggest that integrating analogs significantly enhances students' ability to process and learn from erroneous WEs, particularly for those with lower prior knowledge. The results demonstrate that analogical reasoning supports conceptual change by promoting error detection, cognitive conflict, and knowledge restructuring. This study contributes to instructional design by offering a novel approach to improving mathematical learning through targeted intervention strategies.