Identifying Fractions on Number Lines

Bright, George W.; Behr, Merlyn J.; Post, Thomas R.; Wachsmuth, Ipke

doi:10.2307/749066

Cited by 70 publications

(51 citation statements)

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“…In Pesen's (2008) study, similar to the findings of this study, it was seen that while the students divide into equal parts the units, they place points as the number of the denominator of the fraction. Again, in the study of Bright et al (1988), as similar to the results of this research, it seemed that the students have difficulty in separating the whole to pieces. Another misconception in this question was to show the fraction on number line without dividing to the units.…”

Section: Conclusion Discussion and Recommendationssupporting

confidence: 77%

“…The number line is a useful model to better understand which fraction is smaller or bigger and to reinforce that there is always another fraction between two fractions (Van De Walle, Karp, & Bay-Williams, 2012). Related to the representation of fractions on number line; it is seen that there are misconceptions about how to divide the whole into pieces, how many of them will be taken, and how to determine the unit in simple and compound fractions (Bright, Behr, Post and Wachsmuth, 1988;Okur & Çakmak Gürel, 2016;Önal & Yorulmaz, 2017;Pesen, 2008;Yanik et al, 2008;Yetim & Alkan, 2010). …”

Section: Introductionmentioning

confidence: 99%

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The Misconceptions of Sixth Grade Secondary School Students on Fractions

Aliustaoğlu¹,

Tuna²,

Biber³

2018

iejee

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The purpose of this study is to determine the misconceptions of 6th-grade secondary school students in terms of part-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions. The sample of this study is composed of 104 students who are being educated in 6th-grade of five secondary schools in 2017-2018 teaching year in a province which takes place in the north part of Turkey. Fractional information test, which consists of 5 open-ended questions developed by researchers, was used as data collection tool. The data of the study were analyzed using the content analysis method and in this method frequency/percentage tables were used. By examining the explanations that the students have made, the incorrect answers are divided into categories, and the misconceptions in each question are presented separately. As a result of the study, it has been seen that students have misconceptions in terms of parts-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions.

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Section: Conclusion Discussion and Recommendationssupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

The Misconceptions of Sixth Grade Secondary School Students on Fractions

Aliustaoğlu¹,

Tuna²,

Biber³

2018

iejee

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“…Contrairement aux nombres rationnels pour lesquels de nombreuses études ont permis de mettre en lumière les difficultés que représente leur enseignement (Ni, 1998(Ni, , 2000Harrison, Brindley et Bye, 1989;Bright, Behr, Post et Wachsmuth, 1988;Lesh, Bei-Iii et Post, 1987;Bednarz et Dufour-Janvier, 1984), peu de recherches nous guident quant à l'enseignement des nombres irrationnels (Voskoglou et Kosyvas, 2011, 2012Zazkis et Sirotic, 2004, 2007b, 2010. Au Québec, les programmes d'études d'hier comme ceux d'aujourd'hui les abordent peu dans leur spécificité (Gouvernement du Québec, 1993, 1996, 1997, 2004 et les manuels scolaires n'en donnent que des définitions qui les opposent aux nombres rationnels sans pour autant mettre en valeur leur nature et leurs caractéristiques (Vinner, 1991).…”

Section: Le Problème De L'enseignement Des Irrationnelsunclassified

Des pistes pour enseigner le scandale des nombres irrationnels

Petit

2014

ncre

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Contrairement aux nombres rationnels pour lesquels de nombreuses études ont permis de mettre en lumière les difficultés que représente leur enseignement, peu de recherches nous guident quant à l’enseignement des nombres irrationnels. Afin de mieux en saisir les enjeux, nous nous sommes intéressés à l’évolution du concept pour ensuite établir un cadre grâce à ses dimensions historiques et culturelles. Selon une approche cognitiviste et avec l’expérimentation didactique comme méthode de recherche, nous avons dressé un portrait de la compréhension d’élèves de secondaire 3 (14-15 ans) à l’égard des différents ensembles de nombres, et plus particulièrement des nombres irrationnels, afin d’en arriver à identifier des caractéristiques d’un enseignement stratégique de cette notion. Les résultats permettent un avancement quant à la façon de concevoir l’enseignement du nombre irrationnel au secondaire et offrent différentes voies afin de poursuivre l’étude de ce concept d’un point de vue didactique.In contrast with rational numbers, whose difficulties have been addressed by numerous studies from a pedagogical standpoint, little research offers guidance on the teaching of irrational numbers. To better grasp the issues involved, we examined the evolution of this concept and then established a framework drawing upon its historical and cultural dimensions. Based on a cognitivist approach and using didactic experimentation as our method of research, we sketched a portrait of secondary three (14-15 year old) students’ understanding of different sets of numbers, and more specifically irrational numbers, to be able to identify the characteristics of a strategic approach to teaching this concept. The results contribute to the knowledge on how to conceive the teaching of irrational numbers at the secondary level, and offer various avenues by which to pursue the study of this concept from a didactic standpoint.Contrariamente a los números racionales por los cuales varios estudios han permitido poner de relieve las dificultades que representa enseñarlos, pocas investigaciones existen para orientarnos en cuanto a la enseñanza de los números irracionales. Con el objetivo de entender mejor los desafíos que esto representa, nos hemos interesados a la evolución del concepto para después establecer un marco gracias a sus dimensiones históricas y culturales. Según un enfoque cognitivista y con la experimentación didáctica como método de investigación, esbozamos el retrato de la comprensión de alumnos de tercer año de la secundaria (14-15 años) respecto a los diferentes conjuntos de números, en particular a los números irracionales, para lograr identificar características de una enseñanza estratégica de esta noción. Los resultados permiten un avance en cuanto a la manera de concebir la enseñanza del número irracional en la secundaria y proporcionan varias pistas para seguir con el estudio de este concepto de un punto de vista didáctico

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“…We call this kind of simple but fundamental knowledge an equal-whole schema. Although this schema is crucial in learning fractions, it has not been included in the formal curriculum (Ministry of Education, 1985) or even in experimental programs (Behr et al, 1984;Bright, Behr, Post, & Wachsmuth, 1988).…”

mentioning

confidence: 99%

The influence of instructional intervention on children's understanding of fractions

Yoshida

Shinmachi

1999

Jpn Psychol Res

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An experimental instructional program based mainly on an equal‐whole schema in fractions was given to two fourth‐grade classes of a Japanese elementary school. As a control, conventional teaching based on a traditional Japanese textbook was given to another fourth‐grade class. The study tested the hypothesis that students given the experimental program would understand order and magnitude as central characteristics of fractions better than those who were instructed using the traditional textbook. Students in the experimental group showed better understanding of both the order of fractions and the representation of the sizes of fractions than did the textbook group. However, there were no differences between the experimental and textbook groups in the performance of assessment tasks which were less related to the equal‐whole schema. These results are discussed in view of the important instructional aim of having students understand fractions.

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Identifying Fractions on Number Lines

Cited by 70 publications

References 0 publications

The Misconceptions of Sixth Grade Secondary School Students on Fractions

The Misconceptions of Sixth Grade Secondary School Students on Fractions

Des pistes pour enseigner le scandale des nombres irrationnels

The influence of instructional intervention on children's understanding of fractions

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