Uncovering student errors in measures of dispersion: An APOS theory analysis in high school statistics education

Despite statistics learning becoming more important during this information explosion era, many students still deem the subject complex and challenging. Measures of dispersion, a critical component of statistical knowledge that students often struggle with, have received little attention in research on statistics education. The goal of this study was to uncover students' errors in solving problems involving measures of dispersion by examining students’ response in the diagnostic test through the lens of APOS theory. The participants consisted of 85 grade 11 high school students and were then divided into three groups according to their performance to better understand the difficulties and errors made by students from different cognitive levels. The findings revealed that majority of low achievers operate at the action level, as indicated by the numerous conceptual errors discovered during the test. These students have limited conceptual understanding on the topic which required proper remedial from the educators. The study's results are discussed, as well as potential implications for education.