Box plots-based informal inferential reasoning levels in Thai lower secondary students

Abstract

This study investigated students’ informal inferential reasoning (IIR) levels when interpreting and comparing box plots. This case study purposively selected 36 grade 9 students from a public secondary school in Bangkok, and 29 complete worksheets were analyzed. Using content analysis, the responses were iteratively coded using Pfannkuch’s four levels of IIR (levels 0-3). Responses were distributed across all four levels, predominantly at levels 2 and 3. Level 0 responses identified single values without comparing distributions, while level 1 responses relied on everyday visual descriptions with limited statistical evidence. Level 2 responses justified conclusions using a single distributional feature, whereas level 3 responses coordinated multiple distributional features but often reflected area-represents-frequency-schema heuristics. Instructional design should emphasize integrating multiple distributional features to strengthen reasoning. These findings provide guidance for supporting students’ IIR through box plot instruction.