Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers

Heirdsfield, Ann M.; Cooper, Thomas J.

doi:10.1016/j.jmathb.2004.09.005

Cited by 51 publications

(60 citation statements)

References 21 publications

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“…Star and Newton (2009) define it as knowing multiple solution pathways as well as having the capacity to choose the most appropriate for a given problem. Other authors see the flexibility as the use of efficient strategies (Heirdsfield & Cooper, 2004). Baroody and Rosu (2006) reject the strategy-choice model proposed by Thorndike (1992), relating it to a passive storage view in which fluency is best achieved through repeated practice and each basic combination is stored discretely in a factual memory network.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

'Day Number': A Promoter Routine of Flexibility and Conceptual Understanding

2017

JME

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This article reports part of the research developed by a project focused on flexible calculation developed by teachers of the Higher Education Schools of Lisbon, Setúbal and Portalegre in Portugal. The objective of the Project is to build knowledge about the development of quantitative reasoning and calculation flexibility of students from 6 to 12 years. The Project focuses on the following critical aspects: (i) the relationship between the development of quantitative reasoning and the development of calculation flexibility; and (ii) teachers' practices oriented towards the implementation of hypothetical learning trajectories in this domain. The research questions for this article are: (1) How do students develop flexible calculation?; (2) How does the calculation flexibility and the process of concept formation relate to one another?We present a classroom routine called "Day number" developed in a class of students in their first year of schooling (6 years old), and analyze how

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Section: Theoretical Frameworkmentioning

confidence: 99%

'Day Number': A Promoter Routine of Flexibility and Conceptual Understanding

2017

JME

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“…For example, after learning the standard computing algorithms, students tend to prefer them and do not utilize previously learned strategies, even when the latter continue to be more advantageous and appropriate (Selter, 2000(Selter, , 2001. Moreover, when students learn through examples, they tend to learn specific procedures rather than general rules or relationships, which in turn leads to a negative impact on the development of mental flexibility (Heirdsfield & Cooper 2004;Klein, Beishuizen, & Treffers, 1998;Schütte 2004). Others have reported that student strategies are related to the context of usage, as occurs with different target operations , specific problem characteristics (Blöte et al, 2000;Torbeyns et al, 2009), and student-initiated recognition of problem characteristics (Rathgeb-Schnierer, 2006, 2010.…”

Section: Research Findingsmentioning

confidence: 99%

“…In this context, students' ability to solve multi-digit arithmetic problems, without using paper and pencil computing algorithms, has come under increasing scrutiny among researchers (see e.g., Blőte, Klein, & Beishuizen, 2000;Heirdsfield & Cooper, 2004;Rathgeb-Schnierer, 2006;Threlfall, 2009).…”

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confidence: 99%

Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

2017

JME

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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

“…Çoğu öğrencinin zihinden toplama-çıkarma işlemlerine yönelik herhangi bir stratejiyi doğru kullanmamış ya da cevap vermemiş olmasının nedeni öğrencilerin stratejileri uygularken sayı duygusunu kaybetmelerinden (Beishuizen, 2001;Heirdsfield & Cooper, 2004a) kaynaklanıyor olabilir. Öğrencilerin sahip oldukları güçlükler öğrencilere bu konuda verilen eğitimin yeterli olup olmadığı sorusunu da akla getirmiştir.…”

Section: Tartişma Ve Sonuçunclassified

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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Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers

Cited by 51 publications

References 21 publications

'Day Number': A Promoter Routine of Flexibility and Conceptual Understanding

'Day Number': A Promoter Routine of Flexibility and Conceptual Understanding

Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

Ortaokul Öğrencilerinin Zihinden Hesaplama Yaparken Kullandıkları Stratejiler

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