Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study

ŞEFİK, Özgün; UZUN, Özge ERDEM; Dost, Şenol

doi:10.17522/balikesirnef.1020526

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

2021

DOI: 10.17522/balikesirnef.1020526

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Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study

Özgün ŞEFİK

Özge ERDEM UZUN

Şenol Dost

Abstract: This study aimed to review the APOS Theory, which was developed within the context of conceptual understanding as one of the main aims of mathematics education, studies in the field of mathematics education.The studies with Turkey and international samples related to the APOS Theory were subjected to descriptive content analysis, and a systematic summary was presented. As a result of the analysis, three themes, namely the purpose of using the theory, the use of genetic decomposition, and the aim of the study w… Show more

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2024

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Cited by 4 publications

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APOS Theory in Learning Mathematics (Using Trigonometry as an Example)

Tuktamyshov,

Gorskaya

2024

IntegrEdu

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Introduction. One of the most well-known theories that allows us to study the process of structuring a concept in the mind of a student is the APOS theory, specially created for the study of mental processes in mathematical education and worthy of application in other disciplines. Despite numerous studies on methods of teaching mathematics, in recent years there have been few publications on the problem of students’ understanding of mathematical concepts; there are practically no works devoted to the study of the formation of mental structures in the course of students’ assimilation of mathematical concepts. The aim of the article is to analyze the process of mastering mathematical concepts using the example of trigonometric functions and present the results of the study in accordance with the stages of the APOS theory. Materials and Methods. The study sample included 102 first-year students of the Institute of Construction Engineering under Kazan State University of Architecture and Civil Engineering. The APOS theory was used to study students' perception of mathematical concepts, which allowed us to see the details of mathematical concepts formation at each stage of the APOS theory, as well as to identify characteristic errors and classify them. The empirical basis of the study includes the results of a written survey conducted among students. The quantitative characteristics of each stage of APOS were compared. Results. The effectiveness of the application of the APOS theory was shown, a questionnaire was developed which allowed studying the process of mathematical concept structurization in the student's mind. Within the APOS theory framework, differences in levels of understanding of trigonometry were identified, which allowed for the classification of errors made by students. It was found that most of the students who participated in the experiment made conceptual errors in learning the concept of function. The results demonstrated the importance of investigating the mental structures that emerge during the cognitive process to determine the intellectual reserves of learners. Discussion and Conclusion. The results of the study contribute to the development of scientific understanding of the process of structuring mathematical concepts in the minds of learners and methods for studying the mental structures of abstract concepts. The materials will be useful for university teachers, school teachers in the development of mathematics, as well as in the study of other disciplines.

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APOS Theory in Learning Mathematics (Using Trigonometry as an Example)

Tuktamyshov,

Gorskaya

2024

IntegrEdu

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Development of Mathematics Learning Tools Based on the M-Apos Approach to Improve the Reasoning Ability of Class VII Students

Yerizon,

Sukestiyarn,

Arnellis

2024

RGSA

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Purpose: The purpose of this study was to produce a valid, practical and effective learning tool which is students’ worksheet (LKPD) based on the M-APOS approach to improve the mathematical reasoning abilities of seventh grade junior high school students. Methodology/design/approach: This study uses the Plomp model, which consists of three stages, namely preliminary research, development stage, and assessment stage. The research subjects were seventh grade Junior High School students. The instruments used are LKPD validation sheets, teacher and student response questionnaires, learning implementation observation sheets, and tests. Data was processed using percentages and t-test. Results and conclusion: Based on the results of the research, several conclusions were obtained, namely (1) The learning tools based on the M-APOS approach have met the valid product quality criteria both in terms of content and constructs, (2) The learning tools based on the M-APOS approach were practical to use in the learning process because they are attractive, easy to use, and time efficient, and (3) The learning tools based on the M-APOS approach have also met the criteria for effectiveness because they have a positive impact on students' mathematical reasoning ability. Recommendations: It is recommended that teachers are able to use this LKPD for the learning process. Students should be involved in the process of understanding the learning concepts.

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Matematik Eğitimi Alanında 2017-2021 Yılları Arasında Türkiye’de Yapılan Lisansüstü Tezlerin Araştırma Eğilimleri

Çelik,

Eroğlu,

Sarı Uzun

2024

Milli Eğitim Dergisi

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Bu çalışmada, Türkiye’ de 2017-2021 yılları arasında matematik eğitimi alanında yayınlanmış olan yüksek lisans ve doktora tezlerinin araştırma eğilimleri incelenmiştir. Bu kapsamda matematik eğitimi alanında hazırlanmış ve 1 Ocak 2022 tarihi itibariyle YÖK Ulusal Tez Merkezi’nde tam metin olarak ulaşılabilen toplam 710 tez; yıl, tür, yöntem, matematik konuları ve araştırma konuları gibi kategorilere göre incelenmiştir. Tezlerin incelenmesinde araştırmacılar tarafından hazırlanmış olan tez inceleme formu kullanılmıştır. Nitel yaklaşımla yürütülen çalışmada, doküman incelemesi yapılmış ve verilerin analizi için içerik analizi yapılmıştır. Çalışma sonucunda, 710 tezden 588’inin yüksek lisans, 122’sinin ise doktora tezi olduğu görülmüştür. Tezlerin yıllara göre dağılımında, tez sayısının en çok 2019 yılında olduğu ve tezlerde hedef kitle olarak en çok 7. sınıf öğrencileriyle çalışıldığı belirlenmiştir. Tezlerde çoğunlukla nitel araştırma yaklaşımı tercih edilmiş ve örnek olay araştırma deseni kullanılmıştır. En çok kullanılan veri toplama tekniği doküman incelemesi olmuştur. Tezlere bakıldığında çalışmaların ortaokul matematik konularında yoğunlaştığı ve en çok çalışmanın sayılar ve işlemler konusunda yapıldığı görülmüştür. Beceri ve yetenek kategorisinde ise en çok akademik başarı, düşünme becerileri ve problem çözme üzerine çalışılmıştır. Tezlerde kullanılan öğretim yöntemleri arasında teknoloji-bilgisayar destekli çalışmalar öne çıkmıştır. Tezlerden 124’ünde teorik çerçeve olarak belli bir kuram-yaklaşıma yer verildiği ve ilk üç sırada teorik çerçeve olarak pedagojik alan bilgisi, yapılandırmacılık ve Van Hiele geometrik düşünme düzeylerinin yer aldığı görülmüştür. Çalışmalar ağırlıklı olarak bilişsel boyuta yönelik olsa da duyuşsal boyutun yer aldığı 176 çalışmada en çok tutum üzerine çalışıldığı ortaya çıkmıştır. Bu çalışmanın matematik eğitimi alanında son beş yılda yapılan lisansüstü tezlerin eğilimini ortaya koyarak, bundan sonra yapılacak çalışmalara yön göstermesi beklenmektedir.

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Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study

Cited by 4 publications

References 37 publications

APOS Theory in Learning Mathematics (Using Trigonometry as an Example)

APOS Theory in Learning Mathematics (Using Trigonometry as an Example)

Development of Mathematics Learning Tools Based on the M-Apos Approach to Improve the Reasoning Ability of Class VII Students

Matematik Eğitimi Alanında 2017-2021 Yılları Arasında Türkiye’de Yapılan Lisansüstü Tezlerin Araştırma Eğilimleri

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