| Research Abstract |
In this research, I investigated fraction, area, and problematic problems based on the inquiry to reveal how students understood them and on experimental lessons to conquest confusion generated by each subject matter.
1. The diachronic inquiry on the third and fourth graders' understanding about the representation of quantities by fractions (RQF) revealed that their confusion on RQF was observed just after finishing their learning of the unit of Fraction treated in the third grade. Moreover, their responses to the task of RQF changed according to the representation of problems and diagrams adopted in the task. Based on these results, I implemented experimental lessons of which subjects were the fourth graders. As a result, a class in which the location of fractions on the number line was treated in the first lesson showed little confusion on their understanding of RQF treated in the second lesson. It suggested the effectiveness of the number line model to enhance students' RQF.
2. Experimental lessons on the separation of area from perimeter were implemented for the fourth graders. The results of pre- and posttest showed insufficient accomplishment of the aim of the lessons. However, inquiry administered at the end of each lesson indicated that students' mathematical activities to draw various figures on a grid and to construct them on a geoboard promoted students' interest in the tasks employed in the lessons.
3. Preliminary inquiry on problematic problems suggested that problem situations and instruction described on a test sheet influenced students' responses to the problematic problems.
These results suggest that, at the introductory part of a concept in particular, how to set a problem situation and how students act in the situation affect their subsequent learning to a considerable degree.
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