Research On The Influence Factors To The Primary School Pupil's Bayesian Reasoning Problem Solving

Bayesian inference that conforms to Bayes formula is an important category of probabilistic reasoning.At present,it has been widely used in people's daily life,such as medical diagnosis,market forecasting,signal estimation and product examination.It is an important research subject for the fields of cognition psychology and mathematics education that whether someone can figure out the questions of Bayesian inference without any concept of Bayesian Formula.Research has shown that the answer is negative.However,it has been shown that proper information representation and task context can help pupils to find Bayesian formula.Bayesian inference is closely related to fraction problem.In this study,the author focuses on Bayesian reasoning factors that influence the primary school students to solve Bayesian inference,and tries to explore the cognitive mechanism used by the primary school students to solve the Bayesian reasoning with the aim of providing insight to the fractional teaching.By referencing and revising Zhu Liqi's test scale on the cognitive analysis of pupil's solving Bayesian problem,a three-factor experiment,including 3(the test grade)× 3(representation strategy)× 3(data format)is designed and he following conclusions are drawn with two scoring standard and the 2268 papers :1.In the high-level primary school,the scores of the higher grade students solving the Bayesian reasoning problem significantly are higher than that of lower grade students,and the answer rate of forth /fifth/sixth grade is 13%,18% and 34%.2.The data format plays a significant role in pupil's solving of the Bayesian reasoning problem.The students achieve the best score(42%)in the natural frequency format,followed by the percentage format(19%),and the student have a good performance in the fractional format(4%).3.The way of graphic representation helps primary school students to solve the problem of Bayesian reasoning and the answer rate of the students is 24% in graphic representation,19% without graphical representation.Generally,the students have a poor ability of reading graph.4.Grade factor,data format factors,representation strategies and the interaction effects of second-order and third-order are very significant.5.Higher grade pupils have a certain ability to achieve the positive transfer of content and graph.Last but not least,the conclusion of this research reveals that it is effective to cultivate the mathematical literacy of students in primary schools by developing the ability of multiple representations in math.