The Development Of Psychological Numbers For Children Aged 3 To 5 Years

Mental number line is an important part of mathematical concept which is related with many other mathematical abilities. In this research,487 children aged 3 to 5 (with 259 boys and 228 girls, average age was 56.82-month-old) were picked from Nanjing and Lianyungang randomly to take part in the number line estimation test. The test was meant to explore the children's estimation pattern, estimation accuracy as well as the estimation strategy of mental number line in two different estimation circumstances with three different number line range. Based on the latent class analysis of the date from the test, three conclusions are drawn as follows:1. Children's estimation pattern of mental number line(1)Apart from standard linear and logarithmic pattern, children aged 3 to 5 had many other kinds of estimation patterns such as nonstandard linear pattern, stretching pattern and centered pattern.(2)The estimation pattern of mental number line was constantly changing which was affected by the age, estimation circumstances and number line range.(3)There were many pathways for children's estimation pattern of mental number line developing from other pattern to standard linear pattern. On the whole, the estimation pattern developed from other pattern to logarithmic and centered pattern, than towards to stretching and nonstandard linear pattern, and the last was standard linear pattern.2. The percent absolute error (PAE) of children's number line estimation(l)Except in the first circumstances with number line range from 1 to 5, the number line estiation PAE of children aged 4 to 5 was lower than that of children aged 3 to 4 in all circumstances and number line range.(2)The PAE of children's number line estimation in the second circumstance was lower than that of the first ciecumstance.(3)There was significant difference in the estimation pattern of children's number line estimation PAE. The standard linear pattern had the lowest PAE.(4) There was significant difference in the number line range of children's number line estimation PAE.The lowest PAE of the number line range was 1-10.3. Characteristics of children's number estimation strategy of mental number line(1) Children aged 3 to 5 showed abundant estimation strategies which include "visual cues", "counting", "referring to the endpoint", "number relations" and so on.(2)There was significant difference in age, circumstances and number line range of children's number line estimation strategy.(3)The chidren who had a high level estimation strategy were apt to show more advanced estiation pattern and higher estimation accuracy.