Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8

Reys, Robert E.; Reys, Bárbara J.; Nohda, Nobuhiko; Emori, Hideyo

doi:10.2307/749477

Cited by 45 publications

(45 citation statements)

References 3 publications

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“…Many authors see N10 and 1010 as the two basic strategies for addition and subtraction up to 100 (Cobb, 1995;Fuson, 1992;Jones, Thornton, & Putt, 1994;Reys et al, 1995;Thompson, 1994). For Dutch children N10 is the more effective computation procedure (Wolters, Beishuizen, Broers, & Knoppert, 1990), whereas 1010 causes more errors, especially in subtraction problems requiring regrouping (Beishuizen, 1993; see also Table 1 for a typical error).…”

Section: Empty Number Line In Dutch Second Gradesmentioning

confidence: 99%

“…Many researchers in the field of mathematics education hold similar viewpoints (cf. Cobb, 1995;Freudenthal, 1991;Gravemeijer, 1994;Hiebert et al, 1996;Müller & Wittmann, 1995;Resnick, Bill, & Lesgold, 1992;Reys, Reys, Nohda, & Emori, 1995). In the Netherlands these ideas have been incorporated in the theoretical framework of Realistic Mathematics Education (RME) (Freudenthal, 1973(Freudenthal, , 1991Gravemeijer, 1994;Treffers, 1987Treffers, , 1991.…”

Section: In the International Handbook On Mathematics Educationmentioning

confidence: 99%

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The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

Klein¹,

Beishuizen²,

Treffers³

1998

Journal for Research in Mathematics Education

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In this study we compare 2 experimental programs for teaching mental addition and subtraction in the Dutch 2nd grade (N = 275). The goal of both programs is greater flexibility in mental arithmetic through use of the empty number line as a new mental model. The programs differ in instructional design to enable comparison of 2 contrasting instructional concepts. The Realistic Program Design (RPD) stimulates flexible use of solution procedures from the beginning by using realistic context problems. The Gradual Program Design (GPD) has as its purpose a gradual increase of knowledge through initial emphasis on procedural computation followed by flexible problem solving. We found that whereas RPD pupils showed a more varied use of solution procedures than the GPD pupils, this variation did not influence the procedural competence of the pupils. The empty number line appears to be a very powerful model for the learning of addition and subtraction up to 100.Key Words: Addition, subtraction; Children's strategies; Early childhood, K-4; Early number learning; Mental arithmetic; Representations, modeling; Whole numbers Becker and Selter (1996) gave an overview of recent developments in mathematics education in elementary schools. Their central thesis was that "teaching is no longer seen as a treatment and learning as the effect. Learners are people who actively construct mathematics" (p. 511). Mental arithmetic plays a central role in this respect, stimulating not only conceptual understanding and procedural proficiency but also number sense and the understanding of number relations (McIntosh, Reys, & Reys, 1992). Many researchers in the field of mathematics education hold similar viewpoints (cf. Cobb, 1995;Freudenthal, 1991;Gravemeijer, 1994;Hiebert et al., 1996;Müller & Wittmann, 1995;Resnick, Bill, & Lesgold, 1992;Reys, Reys, Nohda, & Emori, 1995). In the Netherlands these ideas have been incorporated in the theoretical framework of Realistic Mathematics Education (RME) (Freudenthal, 1973(Freudenthal, , 1991Gravemeijer, 1994;Treffers, 1987Treffers, , 1991. RME came into prominence after a national evaluation study of mathematics education in the Netherlands in primary schools (Wijnstra, 1988) 1998, Vol. 29, No. 4, 443-464 Research reported in this article was supported by the Dutch National Science Foundation Grant 575-90-607. In the International Handbook on Mathematics Education, which Journal for Research in Mathematics EducationThis material may not be copied or distributed electronically or in any other format without written permission from NCTM.Copyright © 1998 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. pointed to an unacceptably low level of procedural competency in certain domains; for example, only 55% of the Dutch third graders were capable of solving the subtraction problem 64 -28 correctly. This study also revealed a generally low level of flexibility in using arithmetic strategies. As a result of this evaluation study, Treffers and De Moor (1990) published a...

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Section: Empty Number Line In Dutch Second Gradesmentioning

confidence: 99%

Section: In the International Handbook On Mathematics Educationmentioning

confidence: 99%

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

Klein¹,

Beishuizen²,

Treffers³

1998

Journal for Research in Mathematics Education

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“…İlkokul düzeyindeki öğrencilerle yapılan nicel ve nitel araştırmalarda bu öğrencilerin toplama ve çıkarmaya yönelik problem çözerken kullandıkları zihinden hesaplama stratejileri, yanlış kullanılan stratejilerdeki hatalara yönelik düşünceleri, zihinden hesaplama yetenekleri ve bu yeteneklerin sayı hissi kavramıyla olan ilişkileri incelenmiştir (Beishuizen, 1993;Carraher, et al, 1987;Cooper, Heirdsfield & Irons, 1995;Heirdsfield, 2002;Heirdsfield & Cooper, 2004a, 2004bMcIntosh & Dole, 2000;Morais & Serrazina, 2013;Reys et al, 1995). Bu çalışmalardan elde edilen sonuçlarda ilkokul öğrencilerinin zihinden hesaplama konusunda yetersiz oldukları ve farklı stratejiler yardımıyla çözüme ulaşmada başarısız oldukları görülmüştür.…”

Section: Tablo 1 Toplama Ve çıKarma İşlemlerine Yönelik Zihinden Hesunclassified

“…Sayı duygusunun gelişmesinde (Wyatt, 1985), öğrenmenin kolaylaştırılmasında (Rubenstein, 2001) ve temel bilgilerin çağrılmasında (Sowder, 1988) önemli olan zihinden hesaplama stratejileri bu özelliklerinden dolayı uluslararası öğretim programlarında odak noktası haline gelmiştir (Reys & Barger, 1994;Reys, Reys, Nohda & Emori, 1995;Treffers & de Moor, 1990;Willis, 1990). Matematik Öğretmenleri Ulusal Konseyi (NCTM) belirlediği standartlarda öğrencilerin zihinden hesaplama stratejilerine yönelik kavrayışlarını ve kullanımlarını değerlendirerek iyi problem çözücü olma noktasında öğretmenlerin öğrencilere yardımcı olması gerektiğini açıklamıştır (NCTM, 2000).…”

Section: Introductionunclassified

Ortaokul Öğrencilerinin Zihinden Hesaplama Yaparken Kullandıkları Stratejiler

Duran¹,

Doruk²,

Kaplan³

2016

İlköğretim Online

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ÖZ. Bu araştırmanın amacı ortaokul beşinci sınıf öğrencilerinin toplama-çıkarma işlemi yaparken kullandıkları ve tercih ettikleri ideal zihinden hesaplama stratejilerini belirlemektir. Nitel araştırma modellerinden özel durum çalışmasına göre desenlenen bu araştırma, 2014-2015 öğretim yılının güz döneminde gerçekleştirilmiştir. Araştırma, bir devlet ortaokulunda öğrenim gören 16'sı erkek 17'si kız olmak üzere toplam 33 beşinci sınıf öğrencisiyle gerçekleştirilmiştir. Araştırmanın verileri araştırmacılar tarafından geliştirilmiş etkinlik temelli yarı yapılandırılmış görüşme formu ile toplanmıştır. Görüşme formundan elde edilen veriler mevcut zihinden toplama ve çıkarma yapma stratejilerine göre betimsel olarak çözümlenmiştir. Araştırmadan elde edilen sonuçlara göre toplama işleminde öğrencilerin en fazla "onluklara ve birliklere ayırarak ekleme" stratejisini, en az ise "sayıları onu referans alarak parçalama" stratejisini kullandıkları belirlenmiştir. Çıkarma işleminde ise öğrencilerin en fazla "onar onar eksiltme" stratejisini, en az ise "onlukları ve birlikleri ayırarak çıkarma" stratejisini kullandıkları tespit edilmiştir. Buna rağmen çoğu öğrencinin zihinden toplama ve çıkarma işlemlerine yönelik herhangi bir stratejiyi doğru şekilde kullanmadığı ya da bu sorulara cevap vermediği belirlenmiştir. Öğrencilerin tercih edilen zihinden hesaplamaları değerlendirmeleri incelendiğinde, büyük oranda kullandıkları stratejiler yönünde tercihte bulundukları tespit edilmiştir. Anahtar Kelimeler. Zihinden Hesaplama, Strateji, Ortaokul Öğrencileri, Matematik Eğitimi ABSTRACT. The purpose of this research is to determine mental computation strategies used to make additionsubtraction by fifth grade students. Also, the students' choices for the ideal mental computation strategies are examined in this research. The research designed according to case study of qualitative research models was carried out in the fall semester of 2014-2015 academic terms. The research was conducted with 33 fifth grade students, including 16 boys and 17 girls, studying in a state middle school. The research data were collected with a task based semi-structured interview protocol developed by researchers. Qualitative data obtained from the interview protocol were examined by descriptive analysis according to existing mental computation strategies of addition-subtraction. According to the results of the research students used at most "Adding by dividing into decimal and unity" and at least "Dividing based ten" in addition. Also, students used at most "Subtracting ten by ten" and at least "Subtracting by dividing into decimal and unity" in subtraction. Nevertheless, most students did not use any strategy for addition-subtraction and answer the questions correctly. When the students' assessments for the favoured mental computation strategies examined, the students preferred the strategies that they use substantially. Keywords. Mental Computation, Strategy, Middle School Students, Mathematics Education SUMMARY Purpose and Significance: Mental computation...

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“…Hence, this research would help in instilling and strengthening mental calculation skill within the students as this skill is also considered as higher-level mathematic thinking skill (Reys et al 1995).…”

Section: Mental Computationmentioning

confidence: 99%

Enhancing Mathematics Students’ Mental Computation in Calculating Percentage by Using the Bubble Method

Lubis¹,

Tengah²,

Shahrill³

et al. 2017

International Conference on Education

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Abstract:As students progressed from primary to secondary school, they are exposed to the constant use of calculators in Mathematics. Due to this reason, some of them are becoming too comfortable and too dependent on calculator even for simple arithmetic. Hence, this study was conducted to promote mental computational skills amongst secondary students by using the Bubble Method. A total of 44 mathematics students from two different schools were selected to be the participants of this study and were involved in intervention lessons using the Bubble Method. Based on the analysis result of pre-test and post-test, administered before and after the intervention respectively, 11 students were selected for further interview. Based on the findings, the effect of the students" performance in calculating percentage has been found to be not statistically significant using the Bubble method, however, all the students who were interviewed agreed that the Bubble Method improved their mental computational skill.

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Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8

Cited by 45 publications

References 3 publications

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

Ortaokul Öğrencilerinin Zihinden Hesaplama Yaparken Kullandıkları Stratejiler

Enhancing Mathematics Students’ Mental Computation in Calculating Percentage by Using the Bubble Method

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