Microgenetic Study On The Development Of Cognitive Strategies Of Probability For 11-year-old Children

The study of mathematical cognitive strategies opens a window for exploring the entire cognitive strategy.At present,there are few studies on probabilistic cognition strategies and their development,and there is no research that follows the probabilistic concept cognition order.In order to understand the development of children’s probabilistic cognition strategy,this study selected 35 students from the fifth grade of a primary school in Hangzhou as the research object,according to the five-level probabilistic task cognition order(in order of cognitive randomness,fuzzy cognition,quantification,randomization).Distribution and scores indicate that the last three probabilistic tasks include three models with increasing difficulty.Take the ball as an example: model one: simple probability model(touch 1 ball);model 2: complex probability model(touch 2 balls)Model 3: Independent repeat probability model(with 2 balls touched back)),using micro-generation method to divide each task cognitive strategy teaching into four stages: pre-test,intervention(teaching),post-test and migration.A fine analysis of the cognitive process of developing cognitive strategies after a child acquires a certain strategy.The research questions are as follows: What cognitive strategies are there for different cognitive tasks at different stages? After the probabilistic cognitive strategy is divided into four levels from the zero level to the third level,how do cognitive strategies develop at different stages of the same cognitive task?The main conclusions of this study:1.The main probabilistic cognitive strategies used by childrenThe main strategy for solving the random task of 11-year-old children is to correctly understand the possibility;the main strategies for solving fuzzy cognitive tasks and quantitative tasks are judged correctly based on the quantitative relationship;the main strategies for solving the three model tasks of random distribution are respectively It is based on accurate sample space(labeling method),based on accurate sample space(connection method)and based on accurate sample space(drawing tree diagram);the main strategy for solving scores representing three model tasks is based on quantitative relationship calculation,based on Accurate sample space(wiring method)and based on accurate sample space(painted tree).2.The development of probability cognition strategies at different stages(1)For "awareness of randomness",the main development route of children’s probability cognition strategy is to maintain the first level.Its cognitive strategy develops quickly and slowly.The breadth of its cognitive strategy has not been promoted during the migration phase.(2)For "fuzzy cognition",the main development route of children’s probability cognition strategy is the diminishing process from the second level to the zero level.Its cognitive strategy has developed rapidly.(3)For "quantitative",the main development route of children’s probability cognition strategy is to maintain the secondary level.Its cognitive strategy develops quickly and slowly.The breadth of its cognitive strategy has been promoted during the migration phase.(4)For "random distribution",the main development route of children’s probability cognition strategy is the increasing process from the second level to the third level.As the difficulty level of the model increases,the level of the strategy becomes more stable at the third level.Its cognitive strategy develops quickly and slowly.The breadth of its cognitive strategy has been promoted during the migration phase.(5)For the "score representation",the main development route of the child probability cognition strategy is to maintain the third level and the level from the second level to the third level.Its cognitive strategy develops quickly and slowly.The breadth of its cognitive strategy has been promoted during the migration phase.The study’s recommendations for courses,textbooks,and teaching: In the course,the teaching of probabilistic computing content can be appropriately advanced;in the textbook organization,the combined knowledge can be set before the content of "calculating the probability size";Take an intuitive teaching approach.