Teaching Students the Stochastic Nature of Statistical Concepts in an Introductory Statistics Course

Abstract

The article argues that the persistence of student difficulties in reasoning about the stochastic, despite significant reform efforts, might be the result of the continuing impact of the formalist mathematical tradition, affecting instructional approaches and curricula and acting as a barrier to instruction that provides students with the skills necessary to recognize uncertainty and variability in the real world. It describes a study driven by the conjecture that the reform movement would have been more successful in achieving its objectives if it were to put more emphasis on helping students build sound intuitions about variation. It provides an overview of how the conjecture guiding the study was developed and linked to classroom practice, and briefly discusses the experiences and insights gained from a teaching experiment in a college level, introductory statistics classroom, which adopted a nontraditional approach to statistics instruction with variation at its core. By contrasting students’ intuitions about the stochastic prior to instruction to their stochastical reasoning at the completion of the course, it illustrates the potential of the instructional approach as an alternative to more conventional instruction.
 First published December 2002 at Statistics Education Research Journal: Archives

Exploring Students’ Conceptions of the Standard Deviation

“…Reading and Shaughnessy (2004) present evidence of different levels of sophistication in elementary and secondary students' reasoning about sample variation. Meletiou-Mavrotheris and Lee (2002) found that an instructional design that emphasized statistical variation and statistical process produced a better understanding of the standard deviation, among other concepts, in a group of undergraduates. Students in the study saw the standard deviation as a measure of spread that represented a type of average deviation from the mean.…”

Measuring the Development of Students’ Consideration of Variation

“…Much of the research to date on the role of variation in statistical reasoning in education has been at the pre-tertiary level. This research has expressed concern that educators have placed too little emphasis on the notion of variation (e.g., Meletiou-Mavrotheris & Lee, 2002;Torok & Watson, 2000). For example, measures of location have been emphasized to the detriment of consideration of variability (Reading & Shaughnessy, 2004), and there is the potential for the deterministic approach of the mathematics curriculum to have a negative impact on statistics instruction (Meletiou-Mavrotheris & Lee, 2002).…”

“…This research has expressed concern that educators have placed too little emphasis on the notion of variation (e.g., Meletiou-Mavrotheris & Lee, 2002;Torok & Watson, 2000). For example, measures of location have been emphasized to the detriment of consideration of variability (Reading & Shaughnessy, 2004), and there is the potential for the deterministic approach of the mathematics curriculum to have a negative impact on statistics instruction (Meletiou-Mavrotheris & Lee, 2002). 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.…”

“…The importance of variation was flagged when consideration of variation was proposed as one of the fundamental types of statistical thinking (Wild & Pfannkuch, 1999). Also understanding of variation has been reported as contributing to the development of students' statistical thinking (e.g., Meletiou-Mavrotheris & Lee, 2002;Reading & Shaugnessy, 2004;Torok & Watson, 2000). Many researchers have reinforced this view.…”

Untitled

“…This knowledge allows students to think flexibly (e.g., Jones, Jones, & Vermette, 2011), and transfer knowledge to novel problems (e.g., Bude, Imbos, van de Wiel, & Berger, 2011;Bude, van de Wiel, Imbos, & Berger, 2010;Paas, 1992), choose which type of analysis to use (e.g., Bude et al, 2010;Bude et al (e.g., Garfield & Chance, 2000). Regrettably, many statistics classes do not emphasise a high level of conceptual understanding (delMas, Garfield, Ooms, & Chance, 2007;Meletiou-Mavrotheris & Lee, 2002;Pfannkuch, Wild, & Parsonage, 2012). As a result, learning concepts is more difficult than learning methods (Leppink, Broers, Imbos, van der Vleuten, & Berger, 2012).…”