The longitudinal analyses of change processis in understanding fraction concepts

1988 Fiscal Year Final Research Report Summary

• Project/Area Number: 62510061
• Research Category: Grant-in-Aid for General Scientific Research (C)
• Allocation Type: Single-year Grants
• Research Field: Psychology
• Research Institution: Miyazaki University
• Principal Investigator: YOSHIDA Hajime Miyazaki University Associate Prof., 教育学部, 助教授 (80094085)
• Co-Investigator(Kenkyū-buntansha): KARIYAMA Kazuhiro Miyazaki Women's College Associate Prof., 助教授 (10170094) ; UDA Hirofumi Miyazaki University Associate Prof., 教育学部, 助教授 (50040994)
• Project Period (FY): 1987 – 1988
• Keywords: fraction concepts / incorrect strategies / cognitive task analysis / spefic domenin of know ledge / 知識の領域固有性 / 全体としての1の概念

Research Abstract

This research found some intetresting results on understanding processes of fraction concepts.
1. Changing processes of magnitude for the fraction concepts. A framework to advance our research was (1)per-test two or three months before begining the fraction unit, (2)individual interviews to children with some incorrect strategies, (3)three or four weeks teaching of the fraction in public elemenatary schools, and (4)pre-test immediately after finishing the unit. Children possessed correct informal knowledge on the fraction concepts before receiving formal instruction in their school. However, after learning the fraction concepts, children who understood the concepts correctly dropped from 92 % in the pre-test of the third grade to 76 % in the post-test. This wea very interesting results. Children interrupted their informal correct knowledge vy taking formal instruction.
2. Cocept of 1 as a whole in fraction. Children had great difficulty for understanding the concept of one as a whole in fractin. Across the six tests, about 40 % of children showed always incorrect strategies on this concepts. However, we do not yet analyze relation between incorrect strategies on magnitude of the fraction and on concept as a whole.
3. Drawing pictures. To make children draw the magnitude of the fractions reflected fairly well situation of knowledge for fraction concepts in children. Almost all children with Rule B drew the figrues whose magnitude per unit was always same. However, such figures seemed to be correct for the fraction problems with same denominators.