Little statisticians grow up: Exploring the concept of variability in young children

LITTLE STATISTICIANS GROW UP: EXPLORING THE CONCEPT OF VARIA BILITY IN YOUNG CHILDREN Gianmarco Altoè and Franca Agnoli Università degli Studi di Padova, Padova, Italy gianmarco.altoe@unipd.it Variability is a central concept in statistic al reasoning. Indeed, a major goal of most introductory statistics courses is to help student s understand and be aware of the omnipresence of variability and the quantification and explanation of variability (Cobb, 1992). However, in curriculum design and in statistics education r esearch, variability has not been given enough attention (Reading & Shaughnessy, 2004). Despite the widespread belief in the importa nce of this concept, only recently have educational researchers devoted their attention to the study of how reasoning about variability develops (Garfield & Ben-Zvi, 2005). Current resear ch on the concept of statistical variation has mainly focused on high school and college students (e.g., del Mas & Liu, 2005). These studies demonstrate that it is extremely difficult for students with statistical training – and even for their teachers - to reason about variability. However, little is known about the understanding of statistical variability in young children. The main aim of this study is to explore intuitive ideas about variability in 4-6-year old children using a quantity judgment task. Specifi cally, we assessed whether children’s responses were affected by increasing levels of stimulus va riability. In addition, we investigated the role of age and numerical skills in children’s performance. Participants included 110 children (49% boys) aged 4-6 years recruited in two kindergartens and a primary school in Northern It aly. Children were individually assessed using a computerized task in which they were asked to co mpare two sets of chocolate bars. In the first set, the mean and standard deviation of the chocolate bars were held constant; in the second set, both were manipulated. A standardized test of numerical ability was also administered. The key findings were: 1) Children’s perform ance was affected by stimulus variability following a non-monotonic trend. Increasing levels of variability were associated with a decrease in correct responses, but very low levels of variability (i.e., close to 0) were also unexpectedly related to a decrease in response accuracy; 2) Children’ s performance significantly increased with age following a linear trend; in addition, marked inte r-individual differences were found; 3) Statistical and numerical skills were only moderately intercorrelated. Overall, these results suggest that young child ren have an intuitive idea of the concept of variability. The reasoning processes underlying this concept are complex and need to be further investigated. The next steps will be to replicat e this study among children and young adults to analyze the characteristics of st atistical reasoning about variability across different age groups. In our opinion, understanding how children’s concept of variability develops is necessary to implement efficient teaching strategies in multiple educational settings. REFERENCES Cobb, G. W. (1992). Report of the joint AS A/MAA committee on undergraduate statistics. In the American Statistical Association 1992 proceedings of the Section on Statistical Education , (pp. 281–283). Alexandria, VA: American Statistical Association. delMas, R. C., & Liu, Y. (2005). Exploring stude nts’ conceptions of the standard deviation. Statistics Education Research Journal , 4 (1), 55–82. Garfield, J., & Ben-Zvi, D. (2005). A frame work for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1) , 92–99. Reading, C., & Shaughnessy, J. M. (2004). Reas oning about variation. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 201– 226). Dordrecht, The Netherlands: Kluwer Academic Publishers.