Difference in Parallel Concept among Grade 4, Grade 5 and Grade 6 Pupils － A Viewpoint of the Concept image and Concept Definition
Date Issued
2008
Date
2008
Author(s)
Chen, Chi - Ju
Abstract
This is a study on 4 tasks of parallel concept on a group of elementary school pupils; 249 in grade 4, 246 in grade 5, and 237 in grade 6. The results indicated that grade 4 pupils, who have not yet formally learned the concept, show significant difference from grade 5 and 6. There are marginal difference between grade 5 who have just learned the concept and grade 6 who have learnt the concept for a while. Their performance in verbal task is not as good as in their figural task. Restrained by the techniques of drawing, the effect of coordinates and the relation with points and lines is significant but the variation is insignificant. The accuracy rate for grade 4 pupils in identifying parallelograms varied significantly. Direction, relative position, and length significantly affected performance. Performance of grade 5 and grade 6 pupils only the capacity in identifying oblique and unequal length was low, indicating typical image affected the performance of grade 4 pupils at significant level and not as significant for grade 5 and grade 6 pupils. Pupils in grade 4 could write, determine, and describe the equidistance of parallel lines. Equidistance may be a spontaneous concept definition. After learning the definition of non-intersection, pupils in grade 5 and grade 6 can correctly apply the concept in different situations. It is more difficult to learn the 3rd vertical line and pupils can remember only the definition in mathematics and can not apply the concept in real life situations. This study started from the theories of Vinner and Tall. Grade 4 pupils who have not yet received formal learning of the concept demonstrated their spontaneous deviation from the attributes of parallelogram and the scope of their concept image is limited. Grade 5 and grade 6 pupils demonstrated their diversities in their concept image and learn certain formal definitions. Their performance in figural task is good after abundant concept image have been aroused. Their performance in verbal task varied with proper retrieval of concept definition. This study indicated that it is necessary to provide a diversity of parallelograms in mathematics courses. Additional examples are also necessary for breaking the misconception of lines with the same length. The highly intuition notion of equidistance can be properly applied as well.
Subjects
parallel concept
concept image
concept definition.
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