The Influence Of Graphic Representation On The Problem Of Bayesian Reasoning For Junior Middle School Students: The Role Of Problem Context And Space Ability

Bayesian reasoning that one important field of probabilistic reasoning has been widely used in these fields such as medicine,justice,education and artificial intelligence,etc.Bayesian rule has a vital effect on making correct judgement or decision for people in dealing with uncertain event,such as diagnosing the probability of having cancer by detecting positive information in breast cancer diagnosis to make decision on patient's condition and corrresponding treatment plan.Howener,people has a great difficuty on dealing with such problems based on a large number of experimental results in psychology.Therefore,many scholars have studied how to promote Bayesian reasoning,and representative views at present can be summarized as: 1.to promote Beyasian reasoning by using natural frequency;2.clearing set relationship nested by raphical representation.A lot of research has been done on using natural frequencies to promote Bayesian reasoning.However,the role of graphical representation in Bayesian reasoning is not clear: one view is that adding graphics can promote reasoning;another view is that additional graphics can interfere with understanding information and thus hinder reasoning.The Full-time Compulsory Education Mathematics Curriculum Standards stipulates that probabilistic content is one of the core areas of mathematics curriculum in primary and secondary schools.Graphics and Geometry is also an essential part of mathematics teaching for junior high school students.It is helpful that exploring the influence of graphical representation on probabilistic reasoning for junior high school students to develop space concept.While cultivating their geometric intuition,these concept and intuition can be used in practice to promote their reasoning ability,and also to ascertain the influence factor on making important decision and inference for they in future.Therefore,this study attempts to use junior school students as subjects,and to explore how graphical representation affects the cognitive mechanism of junior school students to solve Bayesian inference problems through two experiments.Experiment 1 investigates whether the effect of graphical representation on Bayesian reasoning is consistent in different problem contexts;Experiment 2 compares that the different graphics are suitable for person with specific space ability.In addition to analyzing whether the reasoning results are correct,this paper combines the inference strategies used in the reasoning process to verify the authenticity of the inference results.Conclusion as follow:1.Junior school students can solve Bayesian inference problems,and reasoning effect is best in familiar lying problems while reasoning is difficult in unfamiliar breast cancer problems.2.Graphical representation can promote junior school students to solve Bayesian reasoning problems in appropriate conditions.Graphical representation can promote the reasoning performance of junior school students for the breast cancer problem,but there is no promotion effect on the lying problem.3.When the junior school students solve the Bayesian reasoning problem,the reasoning performance on the unit square graph is better than the tree graph,and those with high spatial ability have the best perform on the unit square graph.4.Bayesian strategy and conservative strategy are adopted as reasoning strategy of junior school students,and the reasoning is basically consistent with the correct reasoning results and change with problem situation or spatial ability.5.The results of experiment 1 and experiment 2 both support set theory nested.The tree diagram implies a set relationship nested,which belongs to the branch style.The unit squared graph shows the set relationship nested,which belongs to the nested style.Therefore,the unit square graph is one of the more ideal graphs for clarifying set relationships nested,and can be used for risk communication and mathematics education.Finally,the conclusions of this study have the following implications in mathematics education: It is necessary to focus on cultivating middle school students' ability to map and draw,and train them to actively construct graphics when solving complex mathematical problems to transform complex mathematical problems into simple problems.