Elementary Students’ Abilities to Evaluate Uncertain Data Presented as Contingency Tables: Basic Understanding, the Influence of Context and Numerical Data Integration

• In Event: Public Understanding of Science: The Educational Challenges of Scientific “Uncertainty”

Abstract

The appropriate evaluation of scientific evidence requires a basic understanding of probability and chance, as such evidence is inevitably afflicted with uncertainty. In our research project, primary students’ abilities in scientific thinking and relevant stochastical abilities are investigated from an interdisciplinary perspective. Recent research in Cognitive Development, as well as in Mathematics Education indicates a nascent understanding of the probability of events as well as basic knowledge about the characteristics of sampling and the need for baserate-information in primary school students. However, even adults show inadequate strategies when evaluating data presented in contingency tables (for an overview see e. g. Zimmerman, 2007).
The study reported here focused on the ability to analyse contingency tables in two different contextual settings: In the everyday-life condition (EL) contingency tables were presented as the result of a study that compares the effect of two fertilizers on plants. In the abstract-formal condition (AF), the contingency tables were used to represent the outcome of a game of chance for two different classes of objects where a certain colour wins. Students had to evaluate the tables with respect to an advantage of a fertilizer-treatment over the other in the science experiment (EL), and the chance of winning for the classes of objects in the mathematical context (AF). In addition, they were asked to justify their decision. The numerical representation of the distributions in the problems was selected to be especially suited to elicit early competencies in young students (Zhu & Gigerenzer, 2006).
A cross-sectional study with a total of N = 158 (68 female) students from 2nd, 4th, and 6th grade (n = 52/53/53) was conducted. The students were tested individually with a series of contingency tables in both conditions. The solutions as well as the justifications given for the solutions were recorded.
The results showed that students’ had difficulties in evaluating contingency tables in both conditions up to grade 6. A progress with age can only be seen for the EL condition between grades 4 and 6 (ANOVA for the 4-item scale score AF: F(2,155) = 2.89, p > .05, η2 = .04; EL: F(2,155) = 9.35, p < .01, η2 = .11). There was no general context effect. However, for tables with easy distributions (one of the probabilities 0 or 1), the everyday-life context was a facilitating factor. In addition, the level of students’ justifications was higher for items in the everyday-life than in the abstract-formal condition, since students took into account more of the cells in the everyday-life condition. However, students did not succeed in integrating the information numerically correct.
The potentially facilitating effect of everyday life contexts in combination with simple distributions can be utilised in instructional settings to foster the basic understanding of contingency tables. Typical misleading strategies are identified through the qualitative analyses and can be addressed in instruction. However, in order to develop powerful abilities of students, the correct numerical integration of the information needs also care.

Authors

• Anke Lindmeier, IPN Kiel

• Kristina M. Reiss, TU München

• Petra Barchfield, Ludwig-Maximilians-Universität München

• Beate Sodian, University of Munich