Learning Progression Of Content Of "Probability" In Math In High School

Probability and statistics,as one of the main contents of high school mathematics curriculum,play an important role in entire high school mathematics.However,the probability thought is different from the traditional "deterministic" mathematics due to the particularity of research object of probability theory.Therefore,it is of great significance for teaching and learning to study the stages that students may go through in the process of changing from "deterministic" mathematics to "random" mathematics and how to cross these stages until they fully understand random phenomena.The advanced learning in the science education community is a framework that describes students’ continuous and more proficient development in the process of learning knowledge and time activities,as well as the construction of the framework needs to understand how learners understand knowledge and which method they use to,therefore,it is of theoretical and practical significance to introduce it into the field of mathematics education and develop a set of advanced learning with high school mathematics probability as the content.Firstly,the paper systematically collates and analyzes the related literatures on advanced learning in recent years in order to clarify the meaning,characteristics and research methods of the theory.Then,through the research on the subject ontology of high school probability content and the development study of course documents and students’ understanding,the paper constructs an advanced learning element model with high school probability as the content,which is composed of four dimensions: cognitive problem,cognitive object,cognitive mode and cognitive task.The model takes the cognitive object and the cognitive mode as advanced variables,and through the understanding for some problems,such as the high school students’ understanding of random phenomena,the theoretical calculation of probability and utilization of probability information,it forms a hypothesis advancement that describes the high school students’ understanding of probability content(Table 4.3).Next,the article use the Rasch model based on the project response theory to develop test tools and carry out examination for some high school students,test and correct the hypothesis advancement.Finally,it is formed a specific advanced learning that describes how the high school students’ understanding of probabilistic content gradually develop(Table 6.1).In addition,it is found through research that the advanced order of the six cognitive methods of high school students for probabilistic content is expressed from low to high as follows:Method 1: The understanding of a single experiment based on the concreteness-probability list.Method 2: The understanding of the multi-step experiments based on the concreteness-probability list.Method 3: The understanding of the two-step experiment based on the concreteness-probability list.Method 4: The understanding of the random phenomena based on the concreteness-probability distribution.Method 5: The understanding of the multi-step experiments based on the abstraction-probability distribution.Method 6: Accurate understanding of random variables based on abstraction-probability distribution.By analyzing the test results,it is also obtained that the relationship between the students’ understanding level and the school segment are: the first grade students are mainly in the first and second stages;the second grade students are mainly in the first,second and fourth stages,and some students can reach the level five;And most of the seniors are in the second,third and fourth stages,and a few are in the first and fifth stages,which roughly shows the normal distribution trend.Finally,the paper proposes several suggestions for the follow-up researchers to explore the curriculum arrangement and teaching of advanced learning and high school probability content based on the research findings.