Traditional mathematics education is confronted with the challenge from the development of modern society. Computational estimation adapts to the change about desire for computation in new times. Introducing computational estimation into mathematics education relaxes such a dilemma, that is, mathematics is reluctant for student to learn and difficult for teacher to teach. At the same time, it also offers a new perspective for us to reveal the regularity of individual's cognitive development. Thus a research about primary school children's computational estimation is very important in theory and in practice.Seeing that those problems in earlier researches, this dissertation systematically investigated many aspecls of primary school children's computational estimation competence in China, such as the status quo, developmental regularity, external and internal factors, et al. Furthermore, the process of individual's computational estimation was inquired and some theoretical considerations and practical suggestions for instruction in arithmetic were provided.In this research, it was found that primary school children had the same laws as other groups in computational estimation, and also had the special ones. Under the conditions of this investigation, some conclusions were drawn as follows.There were significant differences of problem types in primary school children's computational estimation competence. As the problem difficulty went up, the rate by which estimates differed from the exact answer gradually increased. Subjects used thirteen kinds of strategies during the course of computational estimation. They might be divided into four categories, that is general strategy, whole number strategy, decimal strategy and fraction strategy. The differences in frequency were very great. As a whole, some strategies were used more frequently than others, that is rounding, truncating, ignoring the decimal part, trying to find a common denominator, regarding digit as arithmetic unit "1", and changing fraction to another fraction easier to work with, et al. Different strategies showed great differences in efficacy.Some features about the development of primary school children's computational estimation competence and strategy were also found. The third grade might be a crucial period to the development of whole number and decimal computational estimation ability, and the fifth grade might be a better period to the development of fraction. In addition, children gave emphasis to different strategies at different periods. Those inferior and moderate strategies in efficacy were developed at preliminary grades, but other superior ones emerged at middle grades and become the emphasis in place of those inferior strategies at last. Although children were inclined to using moderate strategies in computational estimation of whole number as their ages increased, they preferred some better strategies in efficacy in computational estimation of decimal and fraction. This made clear that there was a limited adapability in the strategy use of primary school children's computational estimation, and different typical errors lay at different grades. Most of them were brought about by inappropriate use to computational estimation strategy.As a result of different problem characteristics, the computational estimation performance rapidly declined as the problem difficulty rose. Many problem characteristics, such as digit size, adjusting degree and problem type, had significant influence on the speed of children's computational estimation. The appearance of redundant condition in word problem could obviously postpone their speeds of computational estimation. Children could adopt different strategies to deal with computational estimation problems with different features and also might make different errors. Rough mental computation was shown more frequently in small-digit-size problems than in big-digit-size ones. Truncating was used more often in big-adjusted problems than in small-adjusted ones, and rounding was just on the contrary.