Figures Of 0.6 To 7-year-old Children Estimated The Capacity Development Of The Follow-up Study

As an important part of the mathematical cognition, estimation reflects people's general understanding of mathematical concepts, mathematical relationships and mathematical strategies and the information of children's mathematical cognition development. It's the basis of advanced mathematical cognition, and also the achievement and the symbol of early childhood's development of mathematical cognition.The previous studies has shown that estimation was related to mathematical cognition and other mathematical activities, such as arithmetic, sorting numbers and comparing numbers, but 5 to 10 years old children were not good at arithmetic, location of numbers or estimating distance, amount of money or number of objects. So developing the ability of children's estimation draws more and more attention. Numerical estimation is a significant type of estimations, and number-line is the most popular research paradigm because of the outstanding ecological validity. Researches in other domains has calculated that 6 to 7 years old is the key development period of Chinese children's estimation, but most focused on adult and pupil, and few on kindergarten children. Most of the previous studies couldn't investigate the whole process and key change points of estimation generally. For that reason, the present study designed 2 sub-studies, analyzing the estimation accuracy, pattern and variability of 6 to 7 years old Chinese children, and the relation between them, and the relation between the numerical estimation and mathematical cognition. This survey was conducive to highlight the cognitive psychology and educational psychology theories, and to further enrich the theory and research on numerical estimation development of early childhood. At the same time this study also provided evidence on the mathematical abilities development of children for education authorities, nurseries and parents, and theoretical guidance and scientific basis for educators to develop intervention programs.59 kindergarten children participated in study I. By three different number ranges number-line(0 to 10,0 to 100 and 0 to 1000) and three different circumstances number-line (numbers, dots and candies), study I examined the numerical estimation and the relation with math achievement. Study II traced the 32 children who had been primary pupil on the numerical estimation, the relation with mathematical cognition and the predictive value of kindergarten children's numerical estimation on primary pupil's mathematical cognition, using 0 to 100 and 0 to 1000 number-line. The conclusions are as follow:1. Estimation accuracy existed significant difference. The accuracy on 0 to 1000 number-line was higher than 0 to 100 number-line, which was higher than 0 to 10 number-line. For the 0 to 10 number-line, numerical type's accuracy was higher than the dots type and candies type, but there was no significant difference between dots type and candies type.2. Children in kindergarten and primary school showed the linear estimation on 0 to 10,0 to 100 and 0 to 1000 number-line, and there was no significant gender difference but on 0 to 1000 number-line.3. There was no "Scale Variability" on all kinds of number-line, in other words, the variability did not rise with the increase of estimation magnitude. The estimation variability existed significant age difference, and the primary's estimation variability was lower than the kindergarteners. At last, the estimation variability rose with the increase of the range of number-line.4. The degree of linearity was proved to be a good predictor of estimation accuracy, and the degree of linearity could account for more variance of the estimation accuracy than the estimation variability.5. Both for kindergarten children and primary pupil, the estimation on 0 to 100 and 0 to 1000 number-line was found to have a significantly positive correlation with mathematical cognition.And the estimation on 0 to 100 and 0 to 1000 number-line in kindergarten period also showed a significantly positive correlation with mathematical cognition in primary school.