Study On The Cognitive Development Of The Concept Of The Sample Space Of Children

With the advent of the information age, the probability plays an important role in people’s daily life, work and study increasingly. People pay more and more attention to the cognitive of the concepts, such as randomness, the size of the possibility, the sample space, and so on. The probability content is an important area of the compulsory education. The sample space is basic areas of learning of the probability. The cognitive development is an important basis for the curriculum reform. The cognitive of the concepts is the fundamental basis of the implemented teaching. Although the concept of the sample space is one of the basic concepts of the probability, but people often ignore it. And people ignore the children to the cognitive of the concept of the sample space especially. Then in previous studies, the domestic and foreign researchers of the concept of the sample space of children are less, and especially the targeted researches are even less. Based on this, this research will be study on the cognitive development of the concept of the sample space of children from a more micro level.The main problems of this research are the following studies.(1) Studying on the cognitive development of the concept of the sample space of children has two main aspects. Firstly, longitudinally, study on the cognitive development stage and the cognitive level of the concept of the sample space of children. Secondly, laterally, study on the cognitive level of the concept of the sample space of children in the different problem situations, such as taking out ball or cards, and allotting books.(2) Studying on the cognitive errors of the concept of the sample space of children have two main aspects. Firstly, what the main cognitive errors of the concept of the sample space of childre are. Secondly, in the cognitive errors of the concept of the sample space of children, which by subjective or objective factors can be eliminated, and which will be gradually eliminated with age, and which are not gradually eliminated with age(refractory cognitive errors).The main processes of this research have the following steps.(1) Through literature, questionnaires, interviews and other methods to collect research data.(2) Through qualitative analysis, quantitative analysis and other statistical analysis to analyse the data, draw conclusions, and give advices.This research obtains the following main conclusions.(1) The general level and law about the cognitive development of the concept of the sample space of children: the cognitive level of the concept of the sample space of children has obvious age characteristics, namely gradually increase with age.(2) The cognitive development stage and the critical period of the concept of the sample space of children: the cognitive development of the concept of the sample space of children appears the features of the more distinct phases. Generally, there is a significant difference for children aged 8-10 and 11-13. But there is no significant difference for children aged 7-8, 10-11 and 13-14. The critical period of the cognitive development of the concept of the sample space of children is about 8 years old and 11 years old.(3) The cognitive level of the concept of the sample space of children has significant difference in the different problem situations, such as taking out ball or cards, and allotting books.(4) The main cognitive errors of the concept of the sample space of children are abandoning judgments, subjective or intuitive judgments, analyzing the question unclearly or creating the deviation of understanding question, and using improper problem-solving strategies.(5) The cognitive errors of the concept of the sample space of children have obvious characteristics about age: the various cognitive errors will produce some changes with age. Some cognitive errors gradually eliminate with age, such as subjective or intuitive judgments. Some are not gradually eliminated with age(refractory cognitive errors), such as abandoning judgments. And the other can be eliminated by subjective or objective factors, such as analyzing the question unclearly or creating the deviation of understanding question, and using improper problem-solving strategies, and so on.In short, the cognitive development of the concept of the sample space of children tends to improve with age. And it is the process of maturing and eliminating errors gradually.In view of the above findings, givie the following recommendations.(1) For the curriculum standards, propose consideration of curriculum standards and curriculum reform. In order to rich knowledge base of children, whether the knowledge of the probability is introduced early, through classroom teaching and other channels directly into course content, or through the practice of education and other means indirectly.(2) For the classroom teaching, implementation of teaching should pay attention to the acceptable range of children’s knowledge, and do not blindly teach, but also have targeted to remove the cognitive errors of children.(3) For the preparation of teaching materials, arrange teaching material should focus on the way of showing knowledge and the media of presenting knowledge.