This paper reports on a longitudinal study of teaching and learning the subject of fractions in two matched groups of ten 9-10-year-old students. In the experimental group fractions are introduced using the bar and the number line as (mental) models, in the control group the subject is introduced by fair sharing and the circle-model. In the experimental group students are invited to discuss, in the control group students work individually. The groups are compared on several occasions during one year. After one year, the experimental students show more proficiency in fractions than those in the control group. © 2003 Elsevier Science Ltd. All rights reserved.
Utafiti huu ulionyesha jinsi wanafunzi wa miaka 9 na 10 walivyojifunza na kujifunza kuhusu sehemu ndogo za hesabu katika makundi mawili ya wanafunzi wa miaka 10 na 10. Katika kundi la majaribio, vipande vya vipande vimeanzishwa kwa kutumia bar na mstari wa nambari kama mifano ya akili, katika kikundi cha kudhibiti, mada hiyo inaanzishwa kwa kushiriki haki na mfano wa mduara. Katika kikundi cha majaribio wanafunzi wanaalikwa kujadili, katika kikundi cha kudhibiti wanafunzi hufanya kazi kwa kibinafsi. Vikundi hivyo vinalinganishwa mara kadhaa katika mwaka mmoja. Baada ya mwaka mmoja, wanafunzi wa majaribio walionyesha ustadi zaidi katika sehemu ndogo kuliko wale wa kikundi cha kudhibiti. Elsevier Science Ltd. Haki zote zimehifadhiwa.