Development of Middle School Pre-Service Mathematics Teachers' Problem Posing and Solving Skills for Division by Fractions

Ebru Mutlu

Makale detayları

Development of Middle School Pre-Service Mathematics Teachers' Problem Posing and Solving Skills for Division by Fractions

Yazarlar:

Ebru Mutlu

Yayıncı:

Kyrgyz-Turkish Manas University

Dergi:

MANAS Sosyal Araştırmalar Dergisi Vol.12 Issue 3, pp.927-943

Belge Tipi:

Makale

Yayın Tarihi:

7/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001295814

pISSN:

1694-7215

Anahtar kelimeler:

Özet:

 This study examines the development of middle school mathematics pre-service teachers ability to create and solve problems involving the meanings of division by fractions. Ten senior pre-service teachers studying at a state university during the spring semester of the 2021-2022 academic year involved in the study. In the first phase of the study, pre-service teachers were asked to construct and answer problems involving division of a natural number into a fraction, a fraction into a natural number, a large fraction into a small fraction, and a small fraction into a big fraction. The pre-service teachers then participated in a professional development process in which they discussed the problems that may be used to explain the meanings of division by fractions and different representations that can be employed in the solutions of these problems. Following the professional development process, in the second phase of this study, pre-service teachers were asked to create and solve the similar problems in the first phase. The problem statements of the pre-service teachers gathered in both the first and second phases, and written responses to the solutions to these problems was used as a data collection tools. The research is based on the case study model, which is one of the qualitative research methods, and the data were analyzed by content analysis. Our finding shows that, in the first phase, the pre-service teachers had trouble or were unable to construct problems, particularly when dividing small fractions into large fractions, and they preferred to employ algorithms when solving the problems. In the second phase, the candidate teacher extended the problem diversity and demonstrated significant improvements in their problem-solving abilities by using various representation types and algorithms.

 This study examines the development of middle school mathematics pre-service teachers ability to create and solve problems involving the meanings of division by fractions. Ten senior pre-service teachers studying at a state university during the spring semester of the 2021-2022 academic year involved in the study. In the first phase of the study, pre-service teachers were asked to construct and answer problems involving division of a natural number into a fraction, a fraction into a natural number, a large fraction into a small fraction, and a small fraction into a big fraction. The pre-service teachers then participated in a professional development process in which they discussed the problems that may be used to explain the meanings of division by fractions and different representations that can be employed in the solutions of these problems. Following the professional development process, in the second phase of this study, pre-service teachers were asked to create and solve the similar problems in the first phase. The problem statements of the pre-service teachers gathered in both the first and second phases, and written responses to the solutions to these problems was used as a data collection tools. The research is based on the case study model, which is one of the qualitative research methods, and the data were analyzed by content analysis. Our finding shows that, in the first phase, the pre-service teachers had trouble or were unable to construct problems, particularly when dividing small fractions into large fractions, and they preferred to employ algorithms when solving the problems. In the second phase, the candidate teacher extended the problem diversity and demonstrated significant improvements in their problem-solving abilities by using various representation types and algorithms.

 This study examines the development of middle school mathematics pre-service teachers ability to create and solve problems involving the meanings of division by fractions. Ten senior pre-service teachers studying at a state university during the spring semester of the 2021-2022 academic year involved in the study. In the first phase of the study, pre-service teachers were asked to construct and answer problems involving division of a natural number into a fraction, a fraction into a natural number, a large fraction into a small fraction, and a small fraction into a big fraction. The pre-service teachers then participated in a professional development process in which they discussed the problems that may be used to explain the meanings of division by fractions and different representations that can be employed in the solutions of these problems. Following the professional development process, in the second phase of this study, pre-service teachers were asked to create and solve the similar problems in the first phase. The problem statements of the pre-service teachers gathered in both the first and second phases, and written responses to the solutions to these problems was used as a data collection tools. The research is based on the case study model, which is one of the qualitative research methods, and the data were analyzed by content analysis. Our finding shows that, in the first phase, the pre-service teachers had trouble or were unable to construct problems, particularly when dividing small fractions into large fractions, and they preferred to employ algorithms when solving the problems. In the second phase, the candidate teacher extended the problem diversity and demonstrated significant improvements in their problem-solving abilities by using various representation types and algorithms.

 Bu çalışmada ortaokul matematik öğretmeni adaylarının kesirlerle bölmenin anlamını içeren problem oluşturma ve çözme becerilerindeki gelişim incelenmiştir. Çalışmaya bir devlet üniversitesinde 2021-2022 eğitim öğretim yılının bahar döneminde öğrenim gören son sınıf on matematik öğretmen adayı katılmıştır. Çalışmanın başlangıcı olan ilk uygulamada, öğretmen adaylarından bir doğal sayıyı bir kesre, bir kesri bir doğal sayıya, büyük kesri küçük kesre ve küçük kesri büyük kesre bölme anlamını içeren farklı problemler oluşturmaları ve çözmeleri istenmiştir. Öğretmen adayları daha sonra kesirlerle bölmenin anlamlarını içeren farklı problem türlerini ve farklı temsillerle çözümlerini kapsayan bir mesleki gelişim sürecine katılmışlardır. Ardından yapılan son uygulamada öğretmen adaylarından tekrar belirtilen durumları içeren problemler oluşturmaları ve çözmeleri istenmiştir. Veri toplama araçları olarak öğretmen adaylarının ilk ve son uygulamada oluşturdukları problemleri ve çözümlerini içeren yazılı yanıtları kullanılmıştır. Araştırma nitel araştırma yöntemlerinden bir olan durum çalışması modeline dayalı olup veriler içerik analizi ile analiz edilmiştir. Çalışmanın bulgularında ilk uygulamada öğretmen adaylarının özellikle küçük kesri büyük kesre bölerken problem oluşturmakta zorlandıkları ya da problem oluşturamadıkları, problemleri çözerken genel olarak algoritmaları kullanma eğiliminde oldukları belirlenmiştir. Son uygulamada ise öğretmen adaylarının oluşturdukları problem türlerinin genişlediği tespit edilmiştir. Ayrıca öğretmen adayları oluşturdukları problemleri çözerken algoritmaların yanında farklı temsil türlerini de kullanarak problem çözme stratejilerinde olumlu yönde değişimler göstermişlerdir.

Makale detayları

Development of Middle School Pre-Service Mathematics Teachers' Problem Posing and Solving Skills for Division by Fractions

Yazarlar:

Ebru Mutlu

Yayıncı:

Kyrgyz-Turkish Manas University

Dergi:

MANAS Sosyal Araştırmalar Dergisi Vol.12 Issue 3, pp.927-943

Belge Tipi:

Makale

Yayın Tarihi:

7/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001295814

pISSN:

1694-7215

Division by Fractions

Problem Posing

Problem Solution

The Professional Development ProcessKesirlerle Bölme

Problem Oluşturma

Problem Çözme

Mesleki Gelişim Süreci

Sayı

Makale detayları

Yazarlar: Ebru Mutlu

Yayıncı: Kyrgyz-Turkish Manas University

Dergi: MANAS Sosyal Araştırmalar Dergisi Vol.12 Issue 3, pp.927-943

Belge Tipi: Makale

Yayın Tarihi: 7/2023

Belge Dili: Türkçe

Document ID (Org No.): 2001295814

pISSN: 1694-7215

Sayı

Yazarlar:

Ebru Mutlu

Yayıncı:

Kyrgyz-Turkish Manas University

Dergi:

MANAS Sosyal Araştırmalar Dergisi Vol.12 Issue 3, pp.927-943

Belge Tipi:

Makale

Yayın Tarihi:

7/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001295814

pISSN:

1694-7215