Examining Constructs of Statistical Variability Using Mobile Data Points

Statistical variability is considered by researchers and educators as the very foundation of statistics and without variability, there would be no use for statistics. Research studies, however, show that while students are good at calculating the formal measures of variability such as range, interquartile range and standard deviation, many are challenged by what these measures mean. I assumed that post–secondary students’ difficulties with the formal measures of variability are partly imposed by the predominantly static environments in which they learn those concepts. Thus, I designed two dynamic mathematics sketches (DMS) using The Geometer’s Sketchpad and explored how first year university statistics students think about variability, focussing on their constructs of distribution, mean and standard deviation. Five students were clinically interviewed, firstly without using the DMS; secondly, while using the DMS ; and lastly after interacting with the DMS. I used task-based interviews and collected data following foundations of statistical thinking theoretical perspectives. Analysis of video transcripts and screen shots also relied on the foundations of statistical thinking, focusing on students’ considerations of variability including aggregate reasoning with data; and also on semiotic mediation theoretical perspective. Data analysis revealed that before using the DMS, my participants were more likely to think about measures of variability in terms of procedures and calculations. However, during and after their interactions with the DMS, participants showed a difference in that they were more likely to link the changes in data distribution with change in standard deviation and the mean, and to discuss the functional connections in their own words. The findings seem to suggest that applying dynamic computing tools could provide students with deeper understanding of the meaning of statistical variability, and thus could help them build stronger foundation for understanding more challenging concepts in statistics and mathematics. The study also sheds light on the contributions of dynamic, physical and tactile learning tools in mediating meanings of statistical concepts. I also propose a multi-variation reasoning framework based on participants’ interactions with the DMS in the computer-based environment. More contributions to, and implications for, university/college statistics research and curriculum are discussed.