Abstract: In this study, a microgenetic method was used to obtain the detailed data on the qualitative and quantitative aspects of change, such as the path, rate, breadth, source and variability of cognitive change. In each of the five testing sessions the data of solution time and accuracy and verbal report on strategies for solving mathematical equivalence problems were collected from 30 3rd-grade children. The results showed that because of having no knowledge base and special strategies for solving new problems participants had to use many general strategies (such as add-subtract or equalize), moreover they also had to use many incorrect strategies (such as add all or add to equal sign). Then when they constructed correct representation of problems, they mainly used correct strategies, and they could discover domain-special shortcut strategies. At this stage, the variability of strategy decreased. Once they confronted hard transfer task, the proportion of using shortcut strategy cut down significantly, and they had to use general or incorrect strategies. That is to say, at this stage the variability of strategy increased. So it could be concluded that the acquisition of strategies is an evolution process from using incorrect strategies to the correct, from tentatively using many strategies to using only one, from using domain-general strategies to using domain-special shortcut strategy. The process is a constructive one, but it might be affected by knowledge presented by formal or informal instruction. It was worth paying attention to that the patterns of exercise have effect on the acquisition of shortcut strategy. The blocked problems led to higher levels of activation and discovery of the shortcut strategy than the mixed problems. But the latter is more facilitated to the transfer of shortcut strategy than the former

Key words: problem solving, strategy, the microgenetic method