21. yüzyıl matematik öğretmen adaylarının kullandıkları temsiller ve eleştirel düşünme becerileri
Küçük Resim Yok
Tarih
2026
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Matematik öğretiminde önemli bir rolü olan problemlerin çözüm süreçlerinde bireylerde bulunması beklenen önemli özelliklerden birisi temsil kullanma becerisi iken bir diğeri ise eleştirel düşünme becerisidir. Bu noktadan hareketle araştırmanın amacı 21. Yüzyıl matematik öğretmen adaylarının kullandıkları temsiller ve eleştirel düşünme becerilerini tespit etmektir. Bu amaç doğrultusunda matematik öğretmen adaylarının Janvier (1987) ve Lesh, Behr ve Post (1987) tarafından geliştirilen temsil sınıflamalarına ait temsilleri (Konuşma dili temsili; problem çözme sürecinde, problemin ve problemin çözümünün ifade edilmesi ve problemle ilgili akıl yürütülmesi. Cebirsel temsil; problem çözme sürecinde matematiksel sembol ya da değişkenler kullanılması. Grafiksel temsil; problem çözme sürecinde, sayı doğrusu, resim, şema veya diyagram kullanılması. Sayısal temsil; problem çözme sürecinde tablo ya da matris kullanılması) ve içinde bulunduğumuz çağın gereksinimleri neticesinde dijital temsilleriyle beraber eleştirel düşünme becerilerine ait görüşleri belirlenmiştir. Araştırma nitel desenli betimsel tarama türündedir. Araştırmanın verileri araştırmacılar tarafından geliştirilmiş görüşme formları (GF) yardımıyla toplanmış, veriler içerik analizi yöntemiyle değerlendirilmiştir. Araştırmada İnönü ve Marmara Üniversitesi Eğitim Fakültesinde 2025-2026 Güz Döneminde öğrenim gören matematik öğretmen adaylarından uygun örnekleme yöntemine göre seçilen öğretmen adaylarına görüşme formları uygulanmıştır. Araştırma verileri MAXQDA nitel veri analiz programında değerlendirilmiş, kod haritaları yardımıyla görselleştirilmiştir. Bulgular analiz edilirken kodlar yardımıyla kategoriler, kategoriler yardımıyla da temalar şekillendirilmiştir. Sonuçlar matematik öğretmen adaylarını sembolik temsillerinin işlemsel ve ölçümsel anlamda, görsel temsillerinin iki ve üç boyutlu alanlarda, sayısal temsillerinin istatistiksel ve niceliksel anlamda ve sözel temsillerinin dışa ve içe dönük alanlarda yoğunlaştığını göstermektedir. Dijital alan temsilleri dinamik yazılımlar ve sanal uygulamalar üzerinde yoğunlaşırken, yapay zekâ temsilleri araçlar ve platformlar üzerine ve sanal manipülatiflere ilişkin temsilleri ise görsel ve sayısal alanlar üzerinde yoğunlaşmıştır. Günlük yaşam temsilleri karar ve durum koşullarına göre yoğunlaşırken ve çoklu temsilleri ikili, üçlü ve dörtlü temsiller şeklinde belirlenmiştir. Ayrıca araştırmada temsillerin problem çözme sürecine ilişkin avantajları ve dezavantajları tespit edilen bir diğer koşuldur. Temsiller anlamlandırma/kolaylaştırma, somutlaştırma, farklı çözüm yolları/stratejiler, kalıcılık, zihinde canlandırma, dikkat, hızlandırma ve ilişkilendirme koşulları için avantaj sağlarken kafa karışıklığı, zaman kaybı, bağımlılık, kavram yanılgısı, yanlış anlama ve dikkat dağınıklığı noktalarında dezavantajlıdır. Araştırmada eleştirel düşünme becerilerinin zihinsel bileşenleri problem çözme süreci açısından, sorunu tanıma ve teşhis etme noktasında, verileri toplama ve seçmede, yapılandırılmış ve yapılandırılmamış varsayımları tanımada, Sonuca Götürücü Varsayımlarını Seçme ve Formüle Etmede, Geçerli Sonuçları Çıkarma ve Çıkarsamaların Geçerliğini Tartışmada üstbilişsel ve bilişsel açıdan değerlendirilmiştir. Ayrıca çalışmada eleştirel düşünme becerilerinin dijital bileşenleri uygulamalar açısından dijital platformlar ve yapay zekâ için belirlenmiştir. Araştırmada ek olarak eleştirel düşünme becerilerinin gelişimini sağlayan dijital kaynaklar; GeoGebra, Desmos, YouTube, PhET, TinkerPlots, EBA ve Wordwall gibi dijital platformlar ile ChatGPT, Khan Academy, Google Gemini ve Matific gibi yapay zekâ araçları olarak ön plana çıkmıştır.
One of the important characteristics expected in individuals during the problem-solving processes that play a significant role in mathematics education is the ability to use representations, while another is critical thinking skills. Based on this, the aim of the research is to identify the representations and critical thinking skills used by 21st-century mathematics teacher candidates. In line with this objective, the study examines the representations used by prospective mathematics teachers according to the representation classifications developed by Janvier (1987) and Lesh, Behr, and Post (1987) (Verbal representation: expressing the problem and its solution and reasoning about the problem during the problem-solving process. Algebraic representation: the use of mathematical symbols or variables in the problem-solving process. Graphical representation: the use of number lines, pictures, diagrams, or charts in the problem-solving process. Numerical representation: the use of tables or matrices in the problem-solving process) and, as a result of the requirements of the current era, their views on critical thinking skills, including digital representations, were determined. The research is a qualitative descriptive survey. The data for the study were collected using interview forms (IF) developed by the researchers and evaluated using content analysis methods. In the study, interview forms were administered to teacher candidates selected according to an appropriate sampling method from among mathematics teacher candidates enrolled at the Faculty of Education at İnönü and Marmara Universities in the Fall Semester of 2025-2026. The research data were evaluated using the MAXQDA qualitative data analysis program and visualized with the help of code maps. While analyzing the findings, categories were shaped with the help of codes, and themes were shaped with the help of categories. The results show that prospective mathematics teachers focus on symbolic representations in operational and measurement terms, visual representations in two- and three-dimensional spaces, numerical representations in statistical and quantitative terms, and verbal representations in external and internal domains. Digital domain representations are concentrated on dynamic software and virtual applications, while artificial intelligence representations are concentrated on tools and platforms, and representations related to virtual manipulatives are concentrated on visual and numerical domains. Representations of daily life are concentrated according to decision and situation conditions, and multiple representations are determined as binary, ternary, and quaternary representations. Another condition identified in the study is the advantages and disadvantages of representations in relation to the problem-solving process. Representations provide advantages in terms of meaning/facilitation, concretization, different solution paths/strategies, permanence, mental visualization, attention, acceleration, and association, while they are disadvantageous in terms of confusion, loss of time, dependency, misconception, misunderstanding, and distraction. In the study, the mental components of critical thinking skills were evaluated in terms of the problem-solving process, specifically in identifying and diagnosing the problem, collecting and selecting data, identifying structured and unstructured assumptions, selecting and formulating assumptions that lead to conclusions, drawing valid conclusions, and discussing the validity of inferences. Furthermore, the digital components of critical thinking skills were identified in terms of applications for digital platforms and artificial intelligence. Furthermore, digital resources that facilitate the development of critical thinking skills, such as digital platforms like GeoGebra, Desmos, YouTube, PhET, TinkerPlots, EBA, and Wordwall, and artificial intelligence tools like ChatGPT, Khan Academy, Google Gemini, and Matific, have come to the fore.
One of the important characteristics expected in individuals during the problem-solving processes that play a significant role in mathematics education is the ability to use representations, while another is critical thinking skills. Based on this, the aim of the research is to identify the representations and critical thinking skills used by 21st-century mathematics teacher candidates. In line with this objective, the study examines the representations used by prospective mathematics teachers according to the representation classifications developed by Janvier (1987) and Lesh, Behr, and Post (1987) (Verbal representation: expressing the problem and its solution and reasoning about the problem during the problem-solving process. Algebraic representation: the use of mathematical symbols or variables in the problem-solving process. Graphical representation: the use of number lines, pictures, diagrams, or charts in the problem-solving process. Numerical representation: the use of tables or matrices in the problem-solving process) and, as a result of the requirements of the current era, their views on critical thinking skills, including digital representations, were determined. The research is a qualitative descriptive survey. The data for the study were collected using interview forms (IF) developed by the researchers and evaluated using content analysis methods. In the study, interview forms were administered to teacher candidates selected according to an appropriate sampling method from among mathematics teacher candidates enrolled at the Faculty of Education at İnönü and Marmara Universities in the Fall Semester of 2025-2026. The research data were evaluated using the MAXQDA qualitative data analysis program and visualized with the help of code maps. While analyzing the findings, categories were shaped with the help of codes, and themes were shaped with the help of categories. The results show that prospective mathematics teachers focus on symbolic representations in operational and measurement terms, visual representations in two- and three-dimensional spaces, numerical representations in statistical and quantitative terms, and verbal representations in external and internal domains. Digital domain representations are concentrated on dynamic software and virtual applications, while artificial intelligence representations are concentrated on tools and platforms, and representations related to virtual manipulatives are concentrated on visual and numerical domains. Representations of daily life are concentrated according to decision and situation conditions, and multiple representations are determined as binary, ternary, and quaternary representations. Another condition identified in the study is the advantages and disadvantages of representations in relation to the problem-solving process. Representations provide advantages in terms of meaning/facilitation, concretization, different solution paths/strategies, permanence, mental visualization, attention, acceleration, and association, while they are disadvantageous in terms of confusion, loss of time, dependency, misconception, misunderstanding, and distraction. In the study, the mental components of critical thinking skills were evaluated in terms of the problem-solving process, specifically in identifying and diagnosing the problem, collecting and selecting data, identifying structured and unstructured assumptions, selecting and formulating assumptions that lead to conclusions, drawing valid conclusions, and discussing the validity of inferences. Furthermore, the digital components of critical thinking skills were identified in terms of applications for digital platforms and artificial intelligence. Furthermore, digital resources that facilitate the development of critical thinking skills, such as digital platforms like GeoGebra, Desmos, YouTube, PhET, TinkerPlots, EBA, and Wordwall, and artificial intelligence tools like ChatGPT, Khan Academy, Google Gemini, and Matific, have come to the fore.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
