Identification of Error Types in Preservice Teachers' Attempts to Create Fraction Story Problems for Specified Operations

McAllister, Cheryl; Beaver, Cheryl

doi:10.1111/j.1949-8594.2011.00122.x

Cited by 26 publications

(46 citation statements)

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“…Bu hata türleri içerisinde sadece H 10 hata türü kesirlerle çıkarma işlemine özgüdür. Benzer şekilde araştırmacılar (Işık & Kar, 2012d;McAllister & Beaver, 2012), birim kargaşası, parça-bütün ilişkisini kuramama, işlemi soru köküne yansıtamama ve işlem sonucuna doğal sayı anlamı yükleme hata türlerinin kesir işlemlerine yönelik kurulan problemlerde oransal olarak daha fazla görüldüğünü belirtmişlerdir. Bu sonuçlar, öğrencilerin bu hata türlerinde daha fazla güçlük yaşadıklarını göstermesi yanında, kavramsal olarak görülen eksikliklerin işlemlerin yapısından bağımsız olduğunu ve köklerinin kesir kavramına yönelik eksikliklere dayandığını ortaya koymaktadır.…”

Section: Tartişma Sonuç Ve öNeri̇lerunclassified

“…Problem kurma, öğrencilerin verilen bir duruma yönelik beceri, tutum ve kavramsal öğrenmeleri hakkında öğretmenlere fikir vermektedir Lavy & Shriki, 2007;McAllister & Beaver, 2012). Bu bağlamda problem kurmanın değerlendirme aracı olduğu (Barlow & Cates, 2006;English, 1998) dikkate alındığında, bu araştırmanın sonuçları öğrencilerin kesirlerle çıkarma işlemine yönelik problem kurma sürecinde de birçok eksikliklerinin olduğunu ortaya koymuştur.…”

Section: Tartişma Sonuç Ve öNeri̇lerunclassified

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Ortaokul Yedinci Sınıf Öğrencilerinin Kesirlerle Çıkarma İşlemine Kurdukları Problemlerin Analizi

Kar¹,

Işik²

2014

İlköğretim Online

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ABSTRACT:The purpose of the study was to determine potential errors, which might be experienced by seventh grade middle school students related to the problems posed by them about the subtraction operation with fractions. The study was conducted with 143 students studying at six middle schools existing in Erzurum. Problem posing test composed of four items about the subtraction operation with fractions was used as a data collection tool. The answers given by the students were classified in accordance with the categories of problem, not a problem and empty. Then, the errors in the answers within the category of problem were analyzed. Twelve errors were determined in the problems posed by the students. Moreover, students made more errors in posing problems about the subtraction operations with fractions which the minuend and subtrahend fractions are mixed fractions.

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Section: Tartişma Sonuç Ve öNeri̇lerunclassified

Ortaokul Yedinci Sınıf Öğrencilerinin Kesirlerle Çıkarma İşlemine Kurdukları Problemlerin Analizi

Kar¹,

Işik²

2014

İlköğretim Online

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“…A number of researchers employed similar questions when investigating operations with fractions (McAllister and Beaver, 2012;Toluk-Uçar, 2009). Firstly, the test prepared by the researcher was examined by an expert in doctoral dissertation in elementary mathematics education.…”

Section: Data Collection Tools and The Collection Of Datamentioning

confidence: 99%

“…On the other hand, the studies performed on problem posing show that the level of competence in problem posing skills leaves much to be desired (Işık et al, 2011;Işık and Kar, 2012b). McAllister and Beaver (2012) have analyzed the errors pre-service primary school teachers had with the İskenderoğlu 241 problems they posed with respect to operations with fractions. Işık and Kar (2012c) on the other hand, analyzed the errors committed in the problems posed with respect to additions with fractions, in a study involving seventh year students in primary education.…”

Section: Purpose Of the Studymentioning

confidence: 99%

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The problems posed and models employed by primary school teachers in subtraction with fractions

Ä°skenderoglu¹

2017

Educ. Res. Rev.

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Students have difficulties in solving problems of fractions in almost all levels, and in problem posing. Problem posing skills influence the process of development of the behaviors observed at the level of comprehension. That is why it is very crucial for teachers to develop activities for student to have conceptual comprehension of fractions and operations involving fractions. The achievement of such conceptual comprehension can be accelerated through the use of mathematical models. For this, the aim of the study is to identify the errors in the problems posed by primary school teachers with respect to subtractions with fractions, and the models they employ to solve these problems. The present study employs both quantitative and qualitative methods together. This study was carried out with 31 primary school teachers. The teachers involved in the study were selected through random sampling. The study employs the "Problem Posing Test" comprising four items of subtractions with fractions. The test drawn up with reference to the operation of subtraction with fractions includes one item for each: subtracting a proper fraction from another proper fraction, and subtracting a mixed fraction from another mixed fraction. First of all, the answers provided by the teachers were categorized as problem, not-a-problem, or blank. Following such a classification is an analysis of the errors observed in the responses provided in the problem category. At the end, the study reveals that the rate of correct responses offered in the problem category falls as one progresses from item, one where both the minuend and the subtrahend are proper fractions, towards item four where a mixed fraction is subtracted from another mixed fraction. The fact that nine distinct types of errors were observed in the study reveals that the teachers have significant shortcomings when posing problems regarding subtraction with fractions.

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University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

Powell

Nelson

2020

Psychology in the Schools

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To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's response and identified error patterns for items answered incorrectly. Students attempted foundational understanding and calculations problems more often than word problems, and students made fewer errors with foundational understanding and calculation items. Students demonstrated the most unique errors with calculations and word problems items. Given all items on the rational numbers assessment required elementary or middle school knowledge of rational numbers, the number and diversity of errors with a sample of university students demonstrates the persistent difficulties with rational numbers that students carry into adulthood. Elementary, secondary, and developmental mathematics educators should be aware of such errors and provide specific instruction on avoiding such errors.

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Identification of Error Types in Preservice Teachers' Attempts to Create Fraction Story Problems for Specified Operations

Cited by 26 publications

References 10 publications

Ortaokul Yedinci Sınıf Öğrencilerinin Kesirlerle Çıkarma İşlemine Kurdukları Problemlerin Analizi

Ortaokul Yedinci Sınıf Öğrencilerinin Kesirlerle Çıkarma İşlemine Kurdukları Problemlerin Analizi

The problems posed and models employed by primary school teachers in subtraction with fractions

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

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