The Study On The Development Of Understanding And Use Of Addition-subtraction Inverse Principle In Young Children Aged 4-6

The purpose of this study was to investigate the developmental levels and characteristics in young children's understanding and use of the addition-subtraction inverse principle, and the relationship between the understanding of this principle and their arithmetic skills .A sample of 122 children aged 4～6 was randomly selected from 6 classes in three ordinary preschools in Shanghai. The test "simple two-term arithmetic problems" to assess young children's arithmetic skills in this study was developed by the investigator , and the other tests to examinate young children's understanding and use of the addition-subtraction inverse principle was adapted from Baroody and Meng-lung Lai's study(Baroody & Meng-lung Lai , 2007). Individual interview was the main method used in this study, and meanwhile observation of young children's response in the whole test process was also used to investigate young children's understanding and use of the addition-subtraction inverse principle. The cluster analyses in this study revealed four subgroups with different profiles of conceptual understanding and arithmetical skill, namely " high ability group"," low ability group","high conceptual understanding and low arithmetic skills group" and " low conceptual understanding and high arithmetic skills group " .The results indicated: 1) there are no gender differences in young children aged 4～6's understanding and use of the addition-subtraction inverse principle. Young children has already developed an unreliable or a localized understanding of the addition-subtraction inverse principle, and has begun to use this understanding in solving problems at least at the age of 4, but not until 5 years old or later did they can achieve a relatively consistent and reliable level. Compared with the understanding of inversion in 4 year olds, the children aged 5 performed much better; 2) the relations in young children's understanding of addition-subtraction inverse principle and their arithmetic skills were complicated, the level of principle understanding may be in accordance with one's arithmetic skills and yet may present the opposite trend; 3) different problem situations——the control problems (adding and subtracting different amounts of objects on the original collection) and inverse problems (adding and subtracting the same amount of objects on the original collection)——had certain influence on young children's understanding and use of addition-subtraction inverse principle; 4) the factor of simultaneously presenting the written numerical symbols when show children the concrete objects of adding and subtracting operations generally did not affect the performance of the young children aged 4～6, but individual differences also existed.