Fonksiyonların Cebirsel ve Grafiksel Temsillerinin Anlamlandırılması Sürecinde Öğretmen Adaylarının Enstrümanlı Eylem Şemalarının İncelenmesi

Öz

Bu çalışma, öğretmen adaylarının fonksiyonları teknolojik bir ortamda nasıl temsil ettiklerini ve bu süreçlerde ortaya çıkan enstrümantal oluşum süreçlerini incelemeyi amaçlamaktadır. Araştırma, öğretmen adaylarının fonksiyonları cebirsel ve grafiksel olarak temsil etme ve fonksiyon grafiklerini çizmesüreçlerinde geliştirdikleri enstrümanlı eylem şemalarına odaklanmakta ve teknolojik araçların matematik öğretimine katkısını değerlendirmektedir. Çalışmaya, Türkiye’de bir devlet üniversitesinde ilköğretim matematik öğretmenliği programının ikinci sınıfında öğrenim gören altı öğretmen adayı katılmıştır. Veriler, çalışma yaprakları, görüşmeler ile ekran ve ses kayıtları aracılığıyla toplanmış ve içerik analizi yöntemiyle incelenmiştir. Elde edilen ses kayıtları yazılı yanıtlarla karşılaştırılarak çözümlenmiştir. Veriler kodlanmış, kategorilere ayrılmış ve enstrümantal yaklaşım çerçevesinde temalar hâline getirilerek araştırma amacı doğrultusunda yorumlanmıştır. Sonuçlar, öğretmen adaylarının geliştirdiği enstrümanlı eylem şemalarının, yalnızca kullandıkları dijital veya geleneksel araçlardan değil, bu araçlarla kurdukları etkileşimden beslendiğini; bu etkileşimin ardında yatan dinamikleri kavramada ise enstrümantal oluşum teorisinin, öğrenme süreçlerini anlamak için güçlü bir kuramsal çerçeve olduğunu açıkça ortaya koymaktadır.

Anahtar Kelimeler

• Enstrümantal oluşum
• Enstrümanlı eylem şemalar
• Öğretmen adayları
• Fonksiyon
• Fonksiyonların cebirsel ve grafiksel temsilleri

Etik Beyan

Çıkar Çatışması: Yazarlar herhangi bir çıkar çatışmasının bulunmadığını beyan etmektedir. Finansman Bilgisi: Bu araştırma, kamu, ticari veya kâr amacı gütmeyen herhangi bir fon sağlayıcıdan özel bir destek almamıştır. Etik ve Katılımcı Onamı: Araştırmada tüm etik standartlara uyulmuş olup, çalışmaya katılan tüm katılımcılardan bilgilendirilmiş onam alınmıştır. Veri Erişilebilirliği: Bu çalışma kapsamında üretilen veya analiz edilen tüm veriler hem kâğıt-kalem hem de dijital formatlarda güvenli bir şekilde saklanmaktadır ve erişime açıktır. Yazar Katkıları: Her iki yazar da çalışmanın kavramsallaştırılması, tasarımı, analizi ve yazım süreçlerine eşit düzeyde katkı sağlamıştır.

Investigating Pre-Service Teachers’ Instrumented Action Schemes in the Conceptualization of Algebraic and Graphical Representations of Functions

Öz

This study investigates how preservice teachers represent functions in a technological environment and examines the instrumental genesis processes involved. It focuses on instrumented action schemes for representing functions algebraically and graphicallyand drawing the graphs of functions in paper-and-pencil and dynamic geometry environments, evaluating the contribution of technological tools to mathematics teaching. Six second-year preservice teachers in an elementary mathematics teacher education program at a public university in Türkiye participated. Data were collected through worksheets, interviews, screen and audio recordings and analyzed using content analysis. Recordings were transcribed and checked with written responses. Data were coded, categorized, and organized into themes within the instrumental approach and interpreted according to the research objectives. Findings indicate that instrumented action schemes remained procedural in the paper-and-pencil environment, whereas in the dynamic geometry environment they developed conceptual and interactive schemes. The dynamic environment’s visual and interactive features facilitated preservice teachers’ understanding of functions and their algebraic and graphical representations. This study clearly demonstrates that preservice teachers’ instrumented action schemes are shaped not only by the digital or traditional tools they use but also by their interactions with these tools; understanding the dynamics underlying these interactions highlights that the instrumental approach provides an essential theoretical framework for comprehending the learning process.

Anahtar Kelimeler

• Instrumental approach
• Instrumented action schemes
• Preservice teachers
• Functions
• Algebraic and graphical representations

Etik Beyan

Conflict of Interest: The authors declare that they have no conflict of interest. Funding information: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Ethics and Consent to Participate: All ethical standards were followed, and informed consent was obtained from all participants involved in the study. Data availability: All data generated or analyzed during this study are available and securely stored in both paper-pencil and digital formats. Authors' contributions: Both authors contributed equally to the conception, design, analysis, and writing of the manuscript.

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