Understanding fraction in children and intervention to them

Research Project

Project/Area Number	01510070
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 Univ. / Faculty of Education Associate Professor, 助教授 (80094085)
Co-Investigator(Kenkyū-buntansha)	ETO Shunsi Miyazaki Univ. / Faculty of Education Teacher, 教育学部, 教諭 KURIYAMA Kazuhiro Miyazaki Women's College Associate Professor, 助教授 (10170094) UDA Hirofumi Miyazaki Univ. / Faculty of Education Professor, 教育学部, 教授 (50040994)
Project Period (FY)	1989 – 1991
Project Status	Completed (Fiscal Year 1991)
Budget Amount *help	¥2,100,000 (Direct Cost: ¥2,100,000) Fiscal Year 1991: ¥400,000 (Direct Cost: ¥400,000) Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000) Fiscal Year 1989: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords	incorrect strategy / knowledge / fraction / 既有知識 / 知識の統合 / 誤り方略 / 知識構造 / 分数概念 / 知識の表象
Research Abstract	The present study pursued the following questions ; (1) How do children acquire concepts like fraction or decimal frictions, (2) What kind of knowledge do they represent? (3) What kind of intervention is it possible to conduct? To examine these questions, we have conducted longitudinal study over the three years using children in public elementary school. Framework of the research was(1)collective pre-test before learning fraction unit, (2)individual interview based on analyses of the pre-test, (3)intervention of fraction unit by formal teacher, and(4)post-test after finishing the unit. We found very interesting results. However, we summed up some of the results. (1)Before learning fraction, almost all children had understood basic meaning of fraction although their knowledge was based on pre-existing knoweledge. After learning the fraction unit in three grade, percentage of those who understood fraction concept correctly dropped 63 %. This result was very surprising because children's understanding got worse by learning formal knowledge on fraction. The tendency was accelerated for ten months when children had no formal lesson on fraction. (2)Children's strategies on judging magnitude of fractions were divided into one of main three patterns, (1)formal strategy, in which children applied formal knowledge of fraction, (2)Rule S strategy, in which children ordered fractions whose number(denominator or numerator)is big as small magnitude, (3)Rule L strategy, in which children ordered fractions whose number(denominator or numerator)is big as big magnitude. (3)By interview, those who had Rule S changed to formal knowledge of fraction easily to some exten. However, those who Rule L resisted to change such knowledge and they possessed the original strategy.