Abstract: Abstract The aim of the present study was to conduct a microgenetic analysis of the change of representation and its correlates in children’s solving a specific form of an addition task. Karmiloff-Smith’s theory of Representation Redescription was adopted as the theoretical framework of this study. Karmiloff-Smith (1992) suggested that representation redescription is an important way to gain knowledge, and that the change of representation includes three phases, which are procedural, meta-procedural and conceptual phase. During the procedural phase, children’s problem solving behavior is considered to be “success-oriented”. Separate units of behavior are not brought into contact with one another. At the end of this phase, consistently successful performance is achieved, but the change of representation does not stop. In the meta-procedural phase, an overall organization of the internal representation occurs and children can generate “organization-oriented” behavior. They move beyond procedural success to a phase of internal representational organization and the generation of a unified, single approach for all the parts of the problem. Finally, in the conceptual phase, the interaction between external data and internal representation is regulated and balanced as a result of the combination of internal and external control. Representation sustaining children’s behavior in this phase is considered to be richer and more coherent, even though children’s behavior in this phase may appear similar to the procedural phase.
In our opinion, the change of representation as described by Karmiloff-Smith takes place not only at the macro-developmental level, such as changing from one year to another, but also at the micro-developmental level, such as in the context of short-term repeated problem solving. However, a new question is whether Karmiloff-Smith’s theory can be directly applied to describe the micro-development of representation. Thus, in the present study the microgenetic method was used to explore changes of representation that occur within the context of a specific form of digital division and combination task and within the boundaries of a sequence of limited-in number-sessions. There were eight sessions that included the three stages of pretest, practice and transfer. Based on a sample of 120 first and second graders, we explored representational change in the process of problem solving as well as the related age and practice effects.
The results showed that, in the pretest, the number of 2nd-grade children who achieved the conceptual phase was significantly higher than that of the 1st graders. There were no significant age differences among those children who achieved the procedural phase with both practice and the near transfer problem during the pre-test, although, in the far transfer problems, the performance of 2nd-graders was better than that of the 1st-graders. Practice patterns affected representational change in three ways: (1) A complex practice pattern facilitated children’s representational change much more than a simple practice pattern. That is, more children achieved representational change in the complex practice pattern than in the simple practice pattern. (2) In the complex practice pattern, children’s representational change accelerated in the two practice sessions in which difficult problems were inserted, whereas, in the simple practice pattern, children’s representational change accelerated between the 2nd and 3rd sessions and the rate of representational change remained constant afterwards. (3) There were no significant differences in transfer performance between participants under two practice patterns, although performance became different in near and far transfer tasks.
As described in Karmiloff-Smith’s model, results of this study demonstrated that changes of representation were beyond children’s successful problem solving behavior. However, the present study found various pathways and different rates of change that were predicted by Karmiloff-Smith. Furthermore, the practice patterns had an effect on the change of representation. For example, solving hard problems or overcoming cognitive obstacles could facilitate the representational change. It is concluded that development at the macro and micro level may be different in many aspects

Key words: representation, knowledge construction, the microgenetic method