Examining the learning process of simple mathematical structures

Özlem Çeziktürk; Şevval Gökcen; Yasin Çetin; Özkan Gören; Merve Yıldız; Betül Gebeş; Beyzanur Özbek; Hatice Kübra Öztürk; Ahmet İnci

Article Details

Examining the learning process of simple mathematical structures

Authors:

Özlem Çeziktürk | Şevval Gökcen | Yasin Çetin | Özkan Gören | Merve Yıldız | Betül Gebeş | Beyzanur Özbek | Hatice Kübra Öztürk | Ahmet İnci

Publisher:

Yildiz Technical University

Main Topics:

Matematik Eğitimi | Fen ve Matematik Alanları Eğitimi (Diğer)

Journal:

Yıldız Eğitim Araştırmaları Dergisi Vol.8 Issue 2, pp.110-121

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001309533

pISSN:

2564-7431

Keywords:

Abstract:

 A structure is a construction block that is formed under some specific rule, theory, axiom, etc. Mathematical structures, on the other hand, consist of elements and with these elements acting together, the structure gains integrity. Especially in teacher education, since advanced mathematical structures require high cognitive power and can quickly cause anxiety and result in giving up mathematics, it is necessary to focus on how simple mathematical structures are learned by pre-service teachers. In this study conducted with pre-service teachers taking the Analytic Geometry course, sample structures and related structures under the concepts in the course content were tried to be analysed. 3-dimensional mathematical objects, some formulae, dynamic geometry with GeoGebra, advanced geometry theorems were the areas where these simple mathematical structures could be decomposed. In addition, in this study, we tried to draw attention to transfer and analysed in which properties of the structures transfer occurs. Sample mathematical structures were shared with the students and the nature of learning was tried to be decomposed with these structures. In this context, since it was aimed to examine the experiences of pre-service teachers, case study, one of the qualitative research designs, was preferred. Data were collected through a questionnaire containing open-ended questions created by the researchers. As a result of the research, one of the prominent results of the study was that pre-service teachers could not recognise the structures well in the learning of simple mathematical structures and had difficulty in establishing relationships between structures because they could not recognise them well.

 A structure is a construction block that is formed under some specific rule, theory, axiom, etc. Mathematical structures, on the other hand, consist of elements and with these elements acting together, the structure gains integrity. Especially in teacher education, since advanced mathematical structures require high cognitive power and can quickly cause anxiety and result in giving up mathematics, it is necessary to focus on how simple mathematical structures are learned by pre-service teachers. In this study conducted with pre-service teachers taking the Analytic Geometry course, sample structures and related structures under the concepts in the course content were tried to be analysed. 3-dimensional mathematical objects, some formulae, dynamic geometry with GeoGebra, advanced geometry theorems were the areas where these simple mathematical structures could be decomposed. In addition, in this study, we tried to draw attention to transfer and analysed in which properties of the structures transfer occurs. Sample mathematical structures were shared with the students and the nature of learning was tried to be decomposed with these structures. In this context, since it was aimed to examine the experiences of pre-service teachers, case study, one of the qualitative research designs, was preferred. Data were collected through a questionnaire containing open-ended questions created by the researchers. As a result of the research, one of the prominent results of the study was that pre-service teachers could not recognise the structures well in the learning of simple mathematical structures and had difficulty in establishing relationships between structures because they could not recognise them well.

 A structure is a construction block that is formed under some specific rule, theory, axiom, etc. Mathematical structures, on the other hand, consist of elements and with these elements acting together, the structure gains integrity. Especially in teacher education, since advanced mathematical structures require high cognitive power and can quickly cause anxiety and result in giving up mathematics, it is necessary to focus on how simple mathematical structures are learned by pre-service teachers. In this study conducted with pre-service teachers taking the Analytic Geometry course, sample structures and related structures under the concepts in the course content were tried to be analysed. 3-dimensional mathematical objects, some formulae, dynamic geometry with GeoGebra, advanced geometry theorems were the areas where these simple mathematical structures could be decomposed. In addition, in this study, we tried to draw attention to transfer and analysed in which properties of the structures transfer occurs. Sample mathematical structures were shared with the students and the nature of learning was tried to be decomposed with these structures. In this context, since it was aimed to examine the experiences of pre-service teachers, case study, one of the qualitative research designs, was preferred. Data were collected through a questionnaire containing open-ended questions created by the researchers. As a result of the research, one of the prominent results of the study was that pre-service teachers could not recognise the structures well in the learning of simple mathematical structures and had difficulty in establishing relationships between structures because they could not recognise them well.

 Belirli bir kural, teori, kuram, aksiyom, problem, vs. bazında bir araya getirilmiş inşa blokları, yapı olarak adlandırılır. Matematiksel yapılar ise elemanlardan oluşur ve bu elemanların birlikte hareket etmesiyle yapı bütünlük kazanır. Özellikle öğretmen eğitiminde ileri matematiksel yapılar yüksek biliş gücü istediğinden ve çabuk kaygı oluşturup matematikten vazgeçme ile sonuçlanabileceğinden, basit matematiksel yapıların da öğretmen adayları tarafından nasıl öğrenildiği üzerine eğilmek gereklidir. Analitik Geometri dersini alan öğretmen adayları ile yürütülen bu çalışmada, ders içeriğindeli kavramlar altındaki örnek yapılar ve ilişkili yapılar çözümlenmeye çalışılmıştır. 3 boyutlu matematiksel cisimler, bazı formüller, GeoGebra ile dinamik geometri, ileri Geometri teoremleri gibi alanlar bu basit matematiksel yapıların ayrıştırılacağı alanlar olmuştur. Ayrıca bu araştırmada transfere dikkat çekilmeye çalışılmış ve transferin yapıların hangi özelliklerinde oluştuğu konusunda incelemeler yapılmıştır. Örnek matematiksel yapılar öğrencilerle paylaşılmış ve bu yapılarla öğrenmenin doğası ayrıştırılmaya çalışılmıştır. Bu bağlamda öğretmen adaylarının deneyimlerini incelemek amaçlandığından, nitel araştırma desenlerinden durum çalışması tercih edilmiştir. Veriler araştırmacılar tarafından oluşturulan açık uçlu sorular içeren anket yoluyla toplanmıştır. Araştırma sonucunda basit matematiksel yapıların öğreniminde öğretmen adaylarının yapıları iyi tanıyamadığı, iyi tanıyamadıkları için yapılar arasında ilişki kurmakta zorlandıkları öne çıkan sonuçlardandır.

Article Details

Examining the learning process of simple mathematical structures

Authors:

Özlem Çeziktürk | Şevval Gökcen | Yasin Çetin | Özkan Gören | Merve Yıldız | Betül Gebeş | Beyzanur Özbek | Hatice Kübra Öztürk | Ahmet İnci

Publisher:

Yildiz Technical University

Main Topics:

Matematik Eğitimi | Fen ve Matematik Alanları Eğitimi (Diğer)

Journal:

Yıldız Eğitim Araştırmaları Dergisi Vol.8 Issue 2, pp.110-121

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001309533

pISSN:

2564-7431

Mathematical structure

learning

mathematics education.Matematiksel yapı

öğrenme

matematik eğitimi.

Issues

Article Details

Examining the learning process of simple mathematical structures

Authors: Özlem Çeziktürk | Şevval Gökcen | Yasin Çetin | Özkan Gören | Merve Yıldız | Betül Gebeş | Beyzanur Özbek | Hatice Kübra Öztürk | Ahmet İnci

Publisher: Yildiz Technical University

Main Topics: Matematik Eğitimi | Fen ve Matematik Alanları Eğitimi (Diğer)

Journal: Yıldız Eğitim Araştırmaları Dergisi Vol.8 Issue 2, pp.110-121

Document Type: Article

Publication Date: 12/2023

Document Language: English

Document ID (Org No.): 2001309533

pISSN: 2564-7431

Mathematical structure

learning

mathematics education.Matematiksel yapı

öğrenme

matematik eğitimi.

Issues

Authors:

Özlem Çeziktürk | Şevval Gökcen | Yasin Çetin | Özkan Gören | Merve Yıldız | Betül Gebeş | Beyzanur Özbek | Hatice Kübra Öztürk | Ahmet İnci

Publisher:

Yildiz Technical University

Main Topics:

Matematik Eğitimi | Fen ve Matematik Alanları Eğitimi (Diğer)

Journal:

Yıldız Eğitim Araştırmaları Dergisi Vol.8 Issue 2, pp.110-121

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001309533

pISSN:

2564-7431