关键词: 儿童, 贝叶斯推理, 嵌套集合建模能力, 数字表征

Abstract: Bayesian reasoning plays an important role in children's future development of probabilistic reasoning literacy and better solving practical problems. Despite common in people’s daily life, previous studies have indicated that the adults seem to be unable to solve the Bayesian problem. According to previous studies, preschoolers are able to make qualitative Bayesian reasoning based on prior probability and evidence information before they have been systematically taught literacy and math skills (Girotto & Gonzalez, 2008). Zhu and Gigerenzer (2006) proved that primary school children could quantitatively perform Bayesian inference according to an appropriate number representation format through experiments. Their results showed that, when the natural frequency format was used, half of the sixth-graders answered the Bayesian question correctly. However, Pighin and Girotto’s study (2017) based on an Italian sample failed to replicate the results of Zhu and Gigerenzer (2006), with only 16% answer accuracy in natural frequency representation condition.
Recently, Brase (2021b) combined nested set view and mental model theory (Johnson-Laird, 1983) and proposed the concept of the nested sets modeling ability, which is the ability to conceptually construct mental models of nested sets. The results of their study showed that the nested sets modeling ability can predict the subjects’ Bayesian reasoning performance to some extent, and the reasoning performance of individuals with high nested sets modeling ability is significantly better than that of individuals with low nested sets modeling ability (Brase, 2021b). At the same time, the chance format is also believed to clarify the relationship between the nested subsets in Bayesian problem, thus promoting reasoning performance (Girotto & Gonzalez, 2001). However, Brase (2021a) found that even adopt equivalent natural sampling and integer format, still could not achieve the same promoting effect as the natural frequency. Hence,if using the chance representation can also clarify the set nesting relation, do children with higher nested sets modeling ability perform better in Bayesian reasoning problem than those with low ability?
To sum up, this study proposes the following hypotheses:(1) There are differences in children’s solving Bayesian reasoning problems when problems are represented in different formats; (2) The Bayesian reasoning performance of children with highly nested sets modeling ability is better than that of children with low nested sets modeling ability; (3) Children with highly nested sets modeling ability benefit more from natural frequency representation, followed by chance. In probability format condition, the effect of nested sets modeling ability is not significant.
To test these hypotheses, 285 primary school students were recruited to take part in a 2(highly nested sets modeling ability or low nested sets modeling ability) × 3(probability, chance or natural frequency) between-subjects experiment. The dependent variable was Bayesian reasoning performance, with 2 criteria: the score and the strategy children use on Bayesian problems.
The results were as follows: The main effect of number representation(F(2, 278)=13.890, p < .01, η_p²= .092) and the nested sets modeling ability (F(1, 279)=14.813, p< .01, η_p²= .051) were significant, meanwhile, the interaction effect of those two are also significant (F(2, 278)=4.023, p < .05, η_p²= .028). Based on the results, we draw the following conclusions:(1) Children with highly nested sets modeling ability have better Bayesian reasoning performance. (2) Compared with probability and chance formats, children are more suitable for reasoning in natural frequency format questions. (3)There was no difference in the reasoning performance of the subjects with highly or low nested sets modeling ability under probability format, but under natural frequency and chance format, the reasoning performance of the subjects with highly nested sets modeling ability was better than that of the subjects with low nested sets modeling ability.

Key words: children, Bayesian reasoning, nested sets modeling ability, numerical representation