Examination of Proof Schemes of Elementary Mathematics Teachers

Funda Kurttekin; Mustafa Akıncı

Makale detayları

Examination of Proof Schemes of Elementary Mathematics Teachers

Yazarlar:

Funda Kurttekin | Mustafa Akıncı

Yayıncı:

Zonguldak Bulent Ecevit University

Ana Başlıklar:

Alan Eğitimleri

Dergi:

Yükseköğretim ve Bilim Dergisi Vol.13 Issue 2, pp.245-262

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001296915

pISSN:

2146-5959

Anahtar kelimeler:

Özet:

 The purpose of this study is to identify the proof schemes employed by elementary mathematics teachers. This is a case study which employs the qualitative research methodology. The convenience sampling method, one of the types of purposive sampling method, was used to select the participants of the study. The data were collected by using task-based interviews which consist of worksheets and a test including proof processes related items A pilot study was made to ensure the validity and reliability of the data collection tools. The data collection tools were prepared by taking into account the results of the pilot study, expert opinions and studies carried out. Elementary mathematics teachers proof schemes were investigated based on Harel and Sowderss proof schemes. In the analysis of the findings, the descriptive analysis method which was one of the types of qualitative analyses was used to analyze the data. Results showed the characteristics of external, experimental and analytical proof schemes in three basic categories in teachers verifications were observed while the characteristics of external authoritarian and symbolic proof schemes in the sub-categories were not encountered. It was seen that teachers performed characteristics based on more than one schema in some of the items. In addition, the most frequently used scheme was the analytical transformational proof scheme. It is concluded that teachers lack confidence in their ability to articulate themselves and have deficiencies in their knowledge of proof despite the analytical proof schemes were employed frequently which were at the highest level in proof. Some recommendations are given based on the results of the study.

 The purpose of this study is to identify the proof schemes employed by elementary mathematics teachers. This is a case study which employs the qualitative research methodology. The convenience sampling method, one of the types of purposive sampling method, was used to select the participants of the study. The data were collected by using task-based interviews which consist of worksheets and a test including proof processes related items A pilot study was made to ensure the validity and reliability of the data collection tools. The data collection tools were prepared by taking into account the results of the pilot study, expert opinions and studies carried out. Elementary mathematics teachers proof schemes were investigated based on Harel and Sowderss proof schemes. In the analysis of the findings, the descriptive analysis method which was one of the types of qualitative analyses was used to analyze the data. Results showed the characteristics of external, experimental and analytical proof schemes in three basic categories in teachers verifications were observed while the characteristics of external authoritarian and symbolic proof schemes in the sub-categories were not encountered. It was seen that teachers performed characteristics based on more than one schema in some of the items. In addition, the most frequently used scheme was the analytical transformational proof scheme. It is concluded that teachers lack confidence in their ability to articulate themselves and have deficiencies in their knowledge of proof despite the analytical proof schemes were employed frequently which were at the highest level in proof. Some recommendations are given based on the results of the study.

 The purpose of this study is to identify the proof schemes employed by elementary mathematics teachers. This is a case study which employs the qualitative research methodology. The convenience sampling method, one of the types of purposive sampling method, was used to select the participants of the study. The data were collected by using task-based interviews which consist of worksheets and a test including proof processes related items A pilot study was made to ensure the validity and reliability of the data collection tools. The data collection tools were prepared by taking into account the results of the pilot study, expert opinions and studies carried out. Elementary mathematics teachers proof schemes were investigated based on Harel and Sowderss proof schemes. In the analysis of the findings, the descriptive analysis method which was one of the types of qualitative analyses was used to analyze the data. Results showed the characteristics of external, experimental and analytical proof schemes in three basic categories in teachers verifications were observed while the characteristics of external authoritarian and symbolic proof schemes in the sub-categories were not encountered. It was seen that teachers performed characteristics based on more than one schema in some of the items. In addition, the most frequently used scheme was the analytical transformational proof scheme. It is concluded that teachers lack confidence in their ability to articulate themselves and have deficiencies in their knowledge of proof despite the analytical proof schemes were employed frequently which were at the highest level in proof. Some recommendations are given based on the results of the study.

 Çalışmanın amacı, ilköğretim matematik öğretmenlerinin kullandıkları kanıt şemalarını ve bu şemaların nasıl ortaya çıktığını belirlemektir. Nitel araştırma yönteminin benimsendiği bu çalışma, durum çalışmasıdır. Çalışmanın araştırma grubunu oluşturan, dört ilköğretim matematik öğretmeninin seçiminde; amaçlı örnekleme yöntemi olan kolay ulaşılabilir örnekleme yönteminden yararlanılmıştır. Çalışmanın verileri, görev temelli görüşmeler yardımıyla toplanmıştır. Görev temelli görüşmeler, çalışma kâğıdı ve kanıt süreçlerine ait soru formundan oluşmaktadır. Veri toplama araçlarının geçerlilik ve güvenirliğini sağlamak amacıyla pilot uygulama yapılmış, veri toplama araçları; pilot uygulama sonuçları, uzman görüşleri ve yapılan araştırmalar dikkate alınarak son halini almıştır. Öğretmenlerin sahip oldukları kanıt şemaları, Sowder ve Harelin 1998 kanıt şemaları kavramsal çerçevesine göre belirlenmiştir. Elde edilen olguların analizinde, nitel veri analizi olan betimsel analiz yöntemi kullanılmıştır. Öğretmenlerin görev temelli görüşmelerden elde edilen bulguları göz önüne alındığında dışsal, deneysel ve analitik kanıt şemaları şeklinde üç temel kategorideki kanıt şemalarına ait özelliklere sahip oldukları görülmüştür. Bununla beraber öğretmenlerin doğrulamalarında dışsal otoriter ve sembolik kanıt şeması özelliklerine rastlanmamıştır. Öğretmenlerin bir soruya ait doğrulamalarında farklı şemalara ait özelliklere sahip olduğu belirlenmiştir. Görev temelli görüşmelerde en fazla kullanılan şema analitik dönüşümsel kanıt şeması olmuştur. Analitik kanıt şemalarının ağırlıklı kullanılmış olmasına rağmen öğretmenlerin kendilerini ifade etme konusunda çekimser bir tavır sergiledikleri ve kanıta ait bilgilerinde eksikler olduğu görülmüştür. Çalışmanın sonuçlarına bağlı olarak bazı önerilerde bulunulmuştur.

Makale detayları

Examination of Proof Schemes of Elementary Mathematics Teachers

Yazarlar:

Funda Kurttekin | Mustafa Akıncı

Yayıncı:

Zonguldak Bulent Ecevit University

Ana Başlıklar:

Alan Eğitimleri

Dergi:

Yükseköğretim ve Bilim Dergisi Vol.13 Issue 2, pp.245-262

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001296915

pISSN:

2146-5959

Proof

Proof schemes

Elementary mathematics teacherKanıt

Kanıt şemaları

İlköğretim matematik öğretmenleri

Sayı

Makale detayları

Examination of Proof Schemes of Elementary Mathematics Teachers

Yazarlar: Funda Kurttekin | Mustafa Akıncı

Yayıncı: Zonguldak Bulent Ecevit University

Ana Başlıklar: Alan Eğitimleri

Dergi: Yükseköğretim ve Bilim Dergisi Vol.13 Issue 2, pp.245-262

Belge Tipi: Makale

Yayın Tarihi: 8/2023

Belge Dili: Türkçe

Document ID (Org No.): 2001296915

pISSN: 2146-5959

Proof

Proof schemes

Elementary mathematics teacherKanıt

Kanıt şemaları

İlköğretim matematik öğretmenleri

Sayı

Yazarlar:

Funda Kurttekin | Mustafa Akıncı

Yayıncı:

Zonguldak Bulent Ecevit University

Ana Başlıklar:

Alan Eğitimleri

Dergi:

Yükseköğretim ve Bilim Dergisi Vol.13 Issue 2, pp.245-262

Belge Tipi:

Makale

Yayın Tarihi:

8/2023

Belge Dili:

Türkçe

Document ID (Org No.):

2001296915

pISSN:

2146-5959