Developing Consideration of Variation: Case Studies from a Tertiary Introductory Service Statistics Course

Abstract

An important issue in statistics education is how to help students develop statistical thinking, reasoning and literacy. Research in this area is extensive (e.g., Chance, 2002; Garfield, 2002; Rumsey, 2002). Wild and Pfannkuch (1999) identified consideration of variation as one of the fundamental types of statistical thinking, while MacGillivray (2004) reinforced the importance of variation by introducing the notion of statistics as the 'science of variation'. Also, as Bakker (2003, p.3) explains, 'If students do not expect any variability in a particular context ... they neither have an intuition of why one would take a sample or look at a distribution.'Other recent research also highlights the importance of understanding of variation to the development of students' statistical thinking (e.g., Meletiou-Mavrotheris & Lee, 2002; Reading & Reid, 2004; Reading & Shaugnessy, 2004; Torok & Watson, 2000).Much of the research to date on the role of variation (or lack of) in statistical reasoning in education has been at the pre-tertiary level. There has been concern that too little emphasis has been placed on the notion of variation by educators at this level (e.g., Torok & Watson, 2000; Meletiou-Mavrotheris & Lee, 2002). Reading and Shaughnessy (2004) asserted that there is an emphasis on measures of location, to the detriment of consideration of variability, and Meletiou-Mavrotheris and Lee (2002) were concerned by the negative impact that a deterministic approach in the mathematics curriculum would have on statistics instruction. This lack of stochastic awareness may leave students embarking on their tertiary statistics education ill-prepared to consider the more advanced notions of the statistical model as a combination of both systematic and random effects. Reading and Reid (2004) suggested that without an appreciation of the complete statistical model, students may view statistics as a list of techniques to be learned in isolation. A sound understanding of variation could help promote a more comprehensive approach to learning statistics.