An Empirical Study On The Teaching Of Probability Modeling For Children

The teaching and learning of mathematical modeling is an important research field in the world.Probabilistic modeling and mathematical modeling have similarities and similarities in research objectives,research theories,practices and strategies.In the past,the models involved in mathematical modeling are mostly deterministic mathematical models,such as the distance-time-velocity model of primary schools,tree-planting models,various functional models in middle and high schools,and rarely involving non-deterministic mathematical models,such as Probability models,especially in primary schools,have almost no probabilistic models,and there are few studies on the teaching of children’s probability modeling and the methods used by children in solving probabilistic modeling problems,namely,probabilistic modeling cognitive strategies..To explore the cognitive process and cognitive strategies of 11-year-old(5th grade)children’s probabilistic modeling,this study is based on Kaiser’s five modeling steps: Reality Situation(RS),Reality Model(RM),Mathematical Model(MM),Mathematical results(MR),realistic results(RR)design teaching tasks,that is,learning paths,and these five steps are divided into three modeling processes: RS→MM,MM→MR,MR→RR,and carry out empirical research.Research questions in this study.(1)Probabilistic modeling learning path research: What is the optimal probability modeling learning path? How to verify that the probability modeling learning path is optimized?(2)Probabilistic Modeling Cognitive Strategy Research: What is the Probability Modeling Cognitive Strategy List? What is the distribution of cognitive strategies in different modeling processes of two teaching practices? Different modeling of different experimental stages(pre-test,intervention,post-test,migration,delay test 1,delay test 2)What are the development strategies of cognitive strategies in the process? What is the relationship between cognitive level and academic achievement in children’s probability modeling?The research is carried out according to the following process: the research framework is based on the research questions;the teaching plan and the test volume are compiled,and several seminars and revisions are carried out;the optimization process of the probabilistic modeling learning path is explored through the teaching practice;Exploring the strategies used by children in the probabilistic modeling process;based on SPSS 17.0 and Excel software quantitative analysis of the distribution of cognitive strategies and the division of strategy levels,qualitative analysis of probabilistic modeling learning path optimization process based on classroom record data and after-school interview data There are problems in the process;draw conclusions and make recommendations.The main conclusions of this study.(1)The optimized probability modeling learning path is to use the classical probability model to transform the real problem into a mathematical problem.(2)Probabilistic modeling Cognitive strategy list includes: possibility unpredictable;random guess or subjective judgment;error analogy strategy;addition strategy;subtraction strategy;multiplication strategy;division strategy;error sample space strategy;fuzzy sample space strategy;Conversion strategy;precise conversion strategy;precise sample space(painting tree)strategy.(3)The main cognitive strategies used by children in the different modeling processes of teaching practice are:(1)RS→MM process: random guessing or subjective judgment;partial conversion strategy;precise conversion strategy.(2)MM→MR process: fuzzy sample space strategy;accurate sample space(drawing tree diagram)strategy.(3)MR→RR process: error sample space strategy;fuzzy sample space strategy;accurate sample space(drawing tree diagram)strategy.(4)In the different modeling process of children in different experimental stages,the main routes of cognitive strategy development are:(1)RS→MM process: monotonically increasing,from secondary level to maintaining three levels;cyclic fluctuation type,from three Level level to level 2 returns to level 3.(2)MM→MR process: constant type,maintaining three levels.(3)MR→RR process: monotonically increasing,from the first level to the third level.(5)There is a significant positive correlation between children’s probabilistic modeling level and academic achievement,that is,the higher the academic performance,the higher the probability modeling level of students.This study is recommended for course labels,textbooks,and teaching.In the Course Standards,students can experience and experience a simple probabilistic modeling process in the second semester.In the preparation of textbooks,probabilistic modeling can be arranged as an after-school extension.In teaching,first of all,we should pay attention to guiding students to connect with real life to transform real problems into real models.Secondly,when transforming from realistic models to mathematical models,classical probability models should be selected for transformation.Finally,students should pay more attention to the model solving process.To understand the "sample space",choose the appropriate mathematical method for teaching.