Prospective Elementary Teachers' Conceptual Understanding of Integers

Reeder, Stacy; Bateiha, Summer

doi:10.1080/24727466.2016.11790352

Cited by 5 publications

(11 citation statements)

References 13 publications

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“…The present research is important as it meets the need for developing meaningful alternative model for the concept and operations of integers [24,32]. It is also important as it provides solutions to the encountered problems reported in some previous studies [8,12,16,17,18,19].…”

Section: Conclusion and Discussionmentioning

confidence: 95%

“…Although students don't have any difficulty in placing negative numbers on number line, they have problems in comparing the value of them. The greatest problem encountered with operations in negative numbers is the use of "+" and "-" symbols, which also represent addition and subtraction operations [8,16]. Similarly, [17] suggested that making operations with two positive numbers weren't difficult for learners, while defining negative numbers and operations with two negative numbers or one positive ne negative number were hard to understand for them.…”

Section: Introductionmentioning

confidence: 99%

“…When they learn something new, they try to understand in relation with their previous mindscapes [20]. However, when learners encounter negative numbers, they cannot relate to their previous learning of cardinal numbers [16].…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, teachers reported that counters made the learning process difficult, but they had to prefer modeling with counters since they didn't have enough content knowledge on the different modeling methods [32]. Besides, studies on how pre-service teachers present the subject of integers to their students [16,32] showed that pre-service teachers' instructional explanations were generally at operational level. Teachers require meaning models that help students form schemas on their minds so that they can present the subject, which forms the basis of algebra, at a conceptual levels, because learners cannot realize a deep meaningful learning as long as they are just provided with rules [16].…”

Section: Introductionmentioning

confidence: 99%

“…Besides, studies on how pre-service teachers present the subject of integers to their students [16,32] showed that pre-service teachers' instructional explanations were generally at operational level. Teachers require meaning models that help students form schemas on their minds so that they can present the subject, which forms the basis of algebra, at a conceptual levels, because learners cannot realize a deep meaningful learning as long as they are just provided with rules [16]. On this issue, a study includes suggestions for enriching alternative models and activities that teachers can use in their classes [32].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching: Opposite Model Sample

Çetin¹

2019

ujer

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Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model, unlike thermometer, elevator, sea level, or number line, which are directional models. Additionally, it presents solutions to the problem of learning the concept of and operations in integers through models used in teaching integers for primary school 6 th grade students. Opposite model is an integer model, which is based on theory and enables the easy learning of the concept of integers and addition and subtraction operations tested with experimental study by [9]. The present research is believed to contribute students' meaningful learning of the concept and operations of integers and alternative thinking through opposite model. The present research discusses the necessity of opposite model, which is to be offered as an alternative mathematical model for teaching the concept of integers and addition-subtraction operations, in light of the findings obtained through literature review.

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Section: Conclusion and Discussionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching: Opposite Model Sample

Çetin¹

2019

ujer

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Prospective Teachers’ Attention to Realism and Consistency with Negative Integers, Addition, and Temperature

Wessman-Enzinger

Tobias

Olanoff

2020

Investigations in Mathematics Learning

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Matematik Öğretmeni Adaylarının Tamsayılarda Çıkarma İşlemini Sayı Doğrusu ve Sayma Pulları İle Yapabilme Durumlarının İncelenmesi

Özdemir

2022

Kastamonu Eğitim Dergisi

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Purpose: In the present study, the ability of middle school prospective mathematics teachers to subtract integers with counters and a number line was investigated.Design/Methodology/Approach: A case study method was used for the investigation. The research was conducted with 37 prospective teachers who were training in a state university's undergraduate program on primary mathematics in northern Turkey. Four questions developed by the researcher for subtraction in integers were used as a data collection tool. The data of the study were analyzed in two stages. In the first stage, the answers of the prospective teachers were determined as right or wrong; subsequently, in the second stage, the mistakes that led to the wrong answers were determined. Findings:The prospective teachers were relatively successful with respect to both modeling types. The prospective teachers had the highest rates of success in modeling with counters, with a rate of approximately 97% in subtracting a negative integer from a positive integer ((+3) − (−5)), and the lowest rates of success in subtracting a negative integer from a negative integer, with a rate of around 89% for the operation ((−4) − (−7)). In modeling with the number line, the highest success rate was approximately 91% for subtracting a positive integer ((+2) − (+5)) from another positive integer, whereas the lowest success rate was around 86% for subtracting a negative integer from a negative integer in the operation of ((−4) − (−7)).Highlights: According to the results of the research, the prospective teachers were relatively successful in modeling the subtraction of integers using counters and a number line. ÖzÇalışmanın amacı: Bu çalışmada ortaokul matematik öğretmeni adaylarının tam sayılarda çıkarma işlemini sayma pulları ve sayı doğrusu ile yapabilme durumları araştırılmıştır.Materyal ve Yöntem: Durum çalışması yöntemi kullanılmıştır. Araştırma Türkiye'nin kuzeyinde yer alan bir devlet üniversitesinin ilköğretim matematik öğretmenliği lisans programında eğitim gören 37 öğretmen adayı ile yürütülmüştür. Veri toplama aracı olarak araştırmacı tarafından geliştirilen ve tam sayılarda çıkarma işlemine yönelik 4 soru kullanılmıştır. Çalışmanın verileri iki aşamada analiz edilmiştir. Birinci aşamada öğretmen adaylarının doğru veya yanlış cevaplara ulaşma durumları belirlenmiş, ikinci aşamada ise yanlış cevaplara sebep olan hatalar tespit edilmiştir.Bulgular: Çalışmada öğretmen adayları tam sayılarda çıkarma işlemlerini her iki modelleme türünde de oldukça başarılı olmuşlardır. Öğretmen adayları sayma pulları ile modellemede en yüksek başarıyı yaklaşık %97'lik oranla pozitif bir tam sayıdan negatif bir tam sayının çıkarılması ((+3)-(-5)), en düşük başarıyı ise yaklaşık %89'luk oranla negatif bir tam sayıdan negatif bir tam sayının çıkarılması ((-4)-(-7)) işleminde göstermişlerdir. Sayı doğrusu ile modellemede en yüksek başarıyı yaklaşık %91'lik oranla pozitif bir tam sayıdan pozitif bir tam sayının çıkarılması ((+2)-(+5)), en düşük başarıyı ise yaklaşık %86'lık oranla negatif b...

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Prospective Elementary Teachers' Conceptual Understanding of Integers

Cited by 5 publications

References 13 publications

Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching: Opposite Model Sample

Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching: Opposite Model Sample

Prospective Teachers’ Attention to Realism and Consistency with Negative Integers, Addition, and Temperature

Matematik Öğretmeni Adaylarının Tamsayılarda Çıkarma İşlemini Sayı Doğrusu ve Sayma Pulları İle Yapabilme Durumlarının İncelenmesi

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