Can Children use Numerical Reasoning to Compare Odds in Games?

• In Event: New Developments in the Science of Numerical Thinking

Abstract

Board games and card games have been a source of entertainment for centuries. Not only are they enjoyable, they also provide excellent means for developing language skills and numerical reasoning. Indeed, from Chess to Go Fish, most games involve elements of numbers, probabilities and odds. Therefore , board games and card games are an excellent means through which children can hone these skills.

Decades of research indicate that children have an intuitive number sense (Feigenson et al., 2004; Xu & Spelke, 2000), as well as basic intuitions about probabilities (Teglas et al., 2007; Xu & Garcia, 2008). In this study, we investigated whether 3- to 6-year-old children apply their numerical reasoning to recognize which of two games offer better chances of winning.

We tested 130 children (Mage=4.52 years; data collection stopped due to COVID-19). In the Finder condition (N=68), participants were asked to help a fictional character find gold coins and in the Hider condition (N=62), they were asked to help a character hide gold coins (Figure 1). They helped the character by choosing which game they should play. In each of three trials, they were presented with two games to choose from with different numbers of cups (2vs4; 3vs6; 5vs10) and a single gold coin to be found/hidden under one cup in the chosen game. Thus, in the Finder condition, children should choose games with fewer cups and in the Hider condition, they should choose games with more cups. We assigned a 1 when children chose the game with more cups on a trial and assigned a 0 when they chose the game with fewer cups.

We conducted a GEE binary logistic regression with condition (Hider, Finder) as a between-subjects factor, trial-type (2vs4; 3vs6; 5vs10) as a within-subjects factor, and age in months mean-centred and entered as a covariate. We found a main effect of condition, Wald X2(1)=7.63, p=.006, where children selected the game with more cups more often in the Hider condition than the Finder condition, and a significant condition-by-age interaction, Wald X2(1)=13.23, p<.001 (Figure 2). To investigate this interaction, we split our sample at the median age (Median=61.41 months) and examined responses in the two conditions for each group. Older children were more likely to select the game with more cups in the Hider than Finder condition, p=.001, but younger children were not (p=.720).

Thus, around age 5, children appear to recognize differences in odds of winning games of chance. The main aim of this research is to extend this paradigm to examine whether children can detect cheating or lying in the context of a game, by presenting children with characters who are winning games more often than should be predicted by chance. While games clearly provide a means for developing children’s number and language skills, they could also contribute to their social cognitive development, as games are often competitive or cooperative in nature. We hope to replicate the current finding online and extend this to cheating detection.

Authors

• Julianna Lu, University of Waterloo
  Presenting Author

• Tiffany Doan, University of Toronto
  Non-Presenting Author

• Stephanie Denison, University of Waterloo
  Non-Presenting Author