Turkish Journal of Computer and Mathematics Education Vol.12 No.1 (2021), 22-70 Corresponding Author: Aytaç KurtuluĢ email: agunaydi@ogu.edu.tr * This study is a part of the first author‟s master‟s thesis which has been developed as a part of the project 2201721A128 and published, and the thesis advisor is the second author. Citation Information: Ünlüer, Ġ. & KurtuluĢ, A. (2021). The Examination of Conceptual and Procedural Understanding Processes of Eighth Grade Students in the Subjects of Identities and Factoring. Turkish Journal of Computer and Mathematics Education, 13(1), 22-70. http://doi.org/10.16949/turkbilmat.698535 Research Article The Examination of Conceptual and Procedural Understanding Processes of Eighth Grade Students in the Subjects of Identities and Factoring * İnci Ünlüer a and Aytaç Kurtuluş b a Ministry of National Education, Beykoz Koç Middle School, Ġstanbul/Turkey (ORCID: 0000-0002-6775-9383) b EskiĢehir Osmangazi University, Education Faculty, EskiĢehir/Turkey (ORCID: 0000-0003-2397-3510) Article History: Received: 4 March 2020; Accepted: 31 October 2020; Published online: 9 January 2021 Abstract: The aim of this study is to examine the conceptual and procedural understanding processes of eighth grade students through syllabi based on 5E Learning Cycle for the subjects of identities and factoring. In this qualitative research, the teaching experiment model was used. The research was carried out with 20 students studying in a public secondary school in Istanbul. The levels of mathematical success of these students were, high, medium and low, and thus were heterogeneous. A readiness test was applied to determine the prior knowledge and skills of students about identities and factoring. According to the data obtained from this test, three different syllabi were designed and implemented to examine students' conceptual and procedural understanding processes for identities and factoring. During the 12-hour teaching experiment, data were collected via researcher's observation notes, readiness test, activity handouts and worksheets. The data were analyzed using descriptive analysis technique. According to the results of the readiness test, students could adequately express their procedural knowledge about algebraic expressions in 6th and 7th grades; however, it was inferred that their conceptual knowledge wasn‟t complete. Furthermore, evaluations were made during the syllabi which were prepared within the scope of the 5E Learning Cycle. According to the data obtained from these evaluations, students were able to express the concept of identity, which is one of the learning outcomes of identities and factoring, in terms of both conceptual and procedural knowledge. However, it was observed that they were not able to completely achieve procedural and conceptual understanding of the identity (a - b) ², and procedural understanding of the identity a² - b². Keywords: Conceptual understanding, procedural understanding, algebra, identity, 5E learning cycle DOI:10.16949/turkbilmat.698535 Öz: Bu araĢtırmada amaç, özdeĢlikler ve çarpanlara ayırma konusuna yönelik, 5E öğretim modeline dayalı hazırlanan ders planları ile sekizinci sınıf öğrencilerinin kavramsal ve iĢlemsel anlama süreçlerini incelemektir. Nitel araĢtırma des enine sahip olan bu çalıĢmada, öğretim deneyi modeli kullanılmıĢtır. AraĢtırma, Ġstanbul ilinde bulunan bir devlet ortaokulunda öğrenim gören 20 öğrenci ile gerçekleĢtirilmiĢtir. Bu öğrencilerin matematik baĢarı düzeyleri yüksek, orta ve düĢük olmak üzere heterojen bir yapıdadır. Öğrencilerin özdeĢlikler ve çarpanlara ayırma konusuna yönelik ön bilgi ve becerilerini belirlemek için hazırbulunuĢluk testi uygulanmıĢtır. Bu testten elde edilen verilere göre özdeĢlikler ve çarpanlara ayırma konusuna yönelik öğrencilerin kavramsal ve iĢlemsel anlama süreçlerini incelenmek amacıyla üç farklı ders planı tasarlanmıĢ ve uygulanmıĢtır. 12 ders saati süren öğretim deneyi sürecinde araĢtırmacının gözlem notları, hazırbulunuĢluk testi, etkinlik kağıtları ve çalıĢma yaprakları ile veriler toplanmıĢtır. Veriler betimsel analiz tekniği kullanılarak analiz edilmiĢtir. HazırbulunuĢluk testinden, öğrencilerin 6. ve 7. sınıfta gördükleri cebirsel ifadeler konusuna yönelik iĢlemsel bilgilerini yeterli Ģekilde ifade edebildikleri; ancak kavramsal bilgilerinde eksiklikler olduğu belirlenmiĢtir. 5E öğretim modeli kapsamında hazırlanan ders planları süresince yapılan değerlendirmelerden elde edilen verilere göre, öğrencilerin özdeĢlikler ve çarpanlara ayırma konusunun alt kazanımlarından özdeĢlik kavramını hem kavramsal hem de iĢlemsel bilgi anlamında ifade edebildikleri, (a-b)² özdeĢliğini iĢlemsel ve kavramsal anlamalarında, a²-b² özdeĢliğini ise iĢlemsel anlamalarında eksiklikleri olduğu görülmüĢtür. Anahtar Kelimeler: Kavramsal anlama, iĢlemsel anlama, cebir, özdeĢlik, 5E öğrenme modeli Türkçe sürüm için tıklayınız 1. Introduction The role of education in our age is more based on the extent to which knowledge is meaningful and practical in real life for a student rather than measuring how much a student learned. In innovative educational environments, the more favored ones are those in which students‟ role is not only to learn but also to interpret, question and analyze processes, and in which they can learn by themselves. Through the change in the revised curriculum (Republic of Turkey Ministry of National Education, 2009), the focus was shifted on a structure that favors not only the student-centered and procedural knowledge but also conceptual knowledge. With this perspective, students should not learn by memorizing and they should be given the chance to thoroughly understand a subject. Conceptual knowledge and procedural knowledge, which are needed to obtain this skill and