Measuring changes in students' informal statistical reasoning skills through the ethno-flipped classroom model: Stacking and racking analysis

Statistical reasoning is widely recognized as a fundamental skill for preparing students to navigate a data-driven global society. However, research on the development of informal statistical reasoning, particularly when facilitated through an ethno-flipped classroom model, remains limited. Furthermore, few studies employ longitudinal approaches, such as stacking and racking, to assess continuous changes in students' reasoning development over time. Most existing research relies on pre–post comparisons and lacks comprehensive analysis at both the person and item levels. This study investigates changes in students' informal statistical reasoning using the Partial Credit Rasch Model, incorporating stacking and racking analysis. A total of 152 twelfth-grade students participated in a 12-week ethno-flipped classroom intervention. The informal statistical reasoning test, consisting of five open-ended items, demonstrated sufficient validity for use in both the instructional intervention and the Rasch-based analysis. Item validity was assessed as a key parameter within the Rasch measurement framework. The findings revealed significant improvements in student proficiency and a decrease in item difficulty. Notably, 66 students reached Level 5, reflecting integrated process reasoning. These results support the effectiveness of the ethno-flipped classroom model in enhancing informal statistical reasoning. This study contributes to the design of contextual, adaptive instruction and offers a robust Rasch-based framework for monitoring reasoning development longitudinally.