We thought that the framework of the two groups correspond s with that of Skemp's instrumental understanding and relational understanding. This shows that there are more phases of understanding besides Skemp's instrumental understanding and relational undrestanding which we discussed before. And there neeed tobae another set phases to explain our result. We thought that the set of phases, with which we cannot explain our result, correponds with Brown's external understanding or Saeki's practicing socially and developmental enlargement. Pupils cannot solve the problem by using the formura.
Pupils can use the formura and cn exlain.
The consideration of phase D pupils can develop the creative activities themselves after entering a wider societly, such as play-ground and parks, out from the classroom situation. Phase D puppils can also distingush themselves at changing perspectives. Also, they are the children who can name their own unit because of the attachment of the unit based upon their own classroom activities. Using the unit, they further can create the new units one after another according to the new situations. As a result, they will have grown into the children who can undrestand the background of the birth of universal unit.