Why do Pre-Service Teachers Pose Multiplication Problems Instead of Division Problems in Fractions?

Ünlü, Melihan; Ertekin, Erhan

doi:10.1016/j.sbspro.2012.05.148

Cited by 19 publications

(10 citation statements)

References 12 publications

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“…Therefore, fractions are one of the primary mathematics subjects which are difficult for teachers and students. Moreover, studies show that students have learning difficulties related to the concept of fraction at every class level (Chan, Leu & Chen, 2007;Isik & Kar, 2012;Moss & Case, 1999;Ni & Zhou, 2005;Olkun & Toluk, 2003;Olkun & Toluk-Ucar, 2012;Soylu & Soylu, 2005;Soylu, 2008;Stafylidou & Vosniadou, 2004;Unlu & Ertekin, 2012). The structure of fractions and the teaching method of it can be shown as the basic reason for these difficulties (Birgin & Gurbuz, 2009;Soylu & Soylu, 2005;Streefland, 1991;Yilmaz & Yenilmez, 2008).…”

Section: Introductionmentioning

confidence: 99%

Student Errors in Fractions and Possible Causes of These Errors

Aksoy¹,

Yazlık

2017

JETS

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In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method, was used. For this reason, this study was conducted in a state and a private secondary school on a voluntary basis with 105 5th graders and 84 6th graders, with a total of 189 secondary school students from different levels of achievement. In order to determine students' errors and misconceptions about fractions, two tests were prepared by researchers, ten open-ended questions for 5th graders and twelve open-ended questions for 6th graders. Before these tests were formed, the related field was scanned and the existing misunderstandings were determined. Content analysis method was used on the analyzing of the data. The answer papers of the students were coded and students' solving were examined in three categories as correct, wrong and blank. In addition to this the solving belongs to wrong category was examined in detail and mistakes of the students were coded and the reason of these mistakes were dwelled on. It is seen from the result of the study that students have misunderstanding and mistakes about fractions. It is seen that students are not using the modellings on the operations with fractions because of that most of the mistake and misunderstandings are about operations with fractions.

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Section: Introductionmentioning

confidence: 99%

Student Errors in Fractions and Possible Causes of These Errors

Aksoy¹,

Yazlık

2017

JETS

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“…They also report that students usually manifest difficulty operating between numbers written in the form of fraction, because "do not realize the meaning of the elements in the fraction" (T2), have difficulty to "identify the dividend and the divisor" (T1). To suit the results obtained by Unlu and Ertekin (2012) who investigated the knowledge of a group of mathematics teachers on the division between numbers written in the form of fraction, they realized that the knowledge about the division operation with fractions does not go beyond functional knowledge. These teachers were able to apply the rules and the process inherent in the division, but were unable to explain its meaning.…”

Section: Discussionmentioning

confidence: 99%

“…For Greer (2012) inverting is a relational fundamental building block in mathematics and within the purely formal arithmetic, the inverse relationship between addition and subtraction, and multiplication and division, have important implications for the assessment of conceptual understanding of students. Unlu and Ertekin (2012) conducted a study to investigate knowledge of a group of mathematics teachers on the division in the form of fraction. Their results showed that the understanding of the problems raised by fractions, some students applied the multiplication of fractions instead of the fractional division, using reverse algorithm.…”

Section: The Tricky Topic "Division"mentioning

confidence: 99%

Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool

Cruz

Lencastre

Coutinho

et al. 2016

Proceedings of the 8th International Conference on Computer Supported Education

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Abstract:This paper presents a study developed within the international project JuxtaLearn. This project aims to improve student understanding of threshold concepts by promoting student curiosity and creativity through video creation. The math concept of 'Division', widely referred in the literature as problematic for students, was recognised as a 'Tricky Topic' by teachers with the support of the Tricky Topic Tool and the Problem Distiller tool, two apps developed under the JuxtaLearn project. The methodology was based on qualitative data collected through Think Aloud protocol from a group of teachers of a public Elementary school as they used these tools. Results show that the Problem Distiller tool fostered the teachers to reflect more deeply on the causes of the students' misunderstandings of that complex math concept. This process enabled them to develop appropriate strategies to help the students overcome these misunderstandings. The results also suggest that the stumbling blocks associated to the Tricky Topic 'Division' are similar to the difficulties reported in the literature describing Threshold Concepts. This conclusion is the key issue discussed in this paper and a contribution to the state of the art.

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“…PSTs tend to overly rely on the algorithm for division with fractions, solving by rote in a way that is disconnected from meanings of division (Ball 1990;Unlu and Ertekin 2012;Zembat 2004). PSTs have also found it difficult to provide a conceptual justification for the division with fractions algorithm (Borko et al 1992;Simon 1993;Tirosh 2000).…”

Section: Prospective Teachers and Division With Fractionsmentioning

confidence: 99%

“…This primitive model may lead to a commonly reported error among PSTs and practicing teachers: writing incorrect story problems to represent division number sentences (Ball 1988;Ma 1999), usually as multiplication instead of division (Armstrong and Bezuk 1995;Unlu and Ertekin 2012;Zembat 2004Zembat , 2007. This prevalent error has been found in tasks with a unit fraction as a divisor.…”

Section: Prospective Teachers and Division With Fractionsmentioning

confidence: 99%

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

Jansen

Hohensee

2015

J Math Teacher Educ

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The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs' performance on tasks to elaborate upon PSTs' conceptions of the operation of partitive division. This study contributes new insights into PSTs' conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.

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Why do Pre-Service Teachers Pose Multiplication Problems Instead of Division Problems in Fractions?

Cited by 19 publications

References 12 publications

Student Errors in Fractions and Possible Causes of These Errors

Student Errors in Fractions and Possible Causes of These Errors

Threshold Concepts Vs. Tricky Topics - Exploring the Causes of Student´s Misunderstandings with the Problem Distiller Tool

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

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