抄録
In Japanese primary school geometry, one of the subject matters whose position in curriculum are unstable is "inclusion relations between geometrical figures". The unstableness seems to be due to unclearness about causes of difficulties, ways of teaching, or students' processes of understanding about the subject matter. So, the purpose of this paper is to clarify the causes of difficulties and the growing processes in understanding it, by way of interpreting the data from interviews through "the model of understanding". The findings and implications from the investigation are follows. 1. Students seem to conceive geometrical figures as being static and fixed. 2. There is a tendency that tacit irrelevant properties are added in the students' conception of geometrical figures. For example, in parallelogram there are two irrelevant properties - the lengths of neighboring sides are not equal, and the sizes of neighboring angles are not equal. 3. In order to understand inclusion relations between geometrical figures, it is very useful to use "operational material" that can move a geometrical figure and transform from one figure to the other. 4. Students can recognize the statement like "rhombus is a kind of parallelogram", if they interiorize the common properties of parallelogram and rhombus. 5. But if students take conscious of properties proper to the figure that is inside in inclusion relation, for example, neighboring sides are equal in rhombus, then they also take conscious of tacit property at the same time, for example, the lengths of neighboring sides are not equal in parallelogram, and soon return to their exclusive conception because of their conflict. 6. If students have ever constructed flexible images of the figure that is outside in inclusion relation, i.e. the image that deny the tacit (irrelevant) property, then their images are reflected, coordinated, and they can grow their understanding about inclusion relations between geometrical figures.
