Publication: Matematik öğretmen adaylarının üst bilişsel becerilerinin matematiksel modelleme sürecindeki rolü
Abstract
Öğretmenler kendi deneyim ve bakış açılarını öğrencilere yansıtmaktadır. Bu nedenle matematik derslerinde matematik öğretmenlerinin matematiksel modelleme ve üst bilişsel becerilerini geliştirmesi gerekmektedir. Bu çalışmanın amacı matematik öğretmen adaylarının üst bilişsel becerinin matematiksel modelleme sürecindeki rolünü açıklamaktır. Bu amaç doğrultusunda, modelleme sürecinde öne çıkan üst bilişsel becerileri (planlama, izleme, değerlendirme ve tahmin) belirlemek ve bu becerilerin matematiksel modelleme döngüsünün her bir aşamasındaki rolünü açıklamak hedeflenmektedir. Belirtilen bu dört temel üst bilişsel becerinin modelleme sürecindeki rollerini detaylı bir şekilde açıklamak amacıyla bu araştırmanın yöntemi nitel araştırma yöntemlerinden durum çalışması olarak belirlenmiştir. Araştırmanın verileri üç adet matematik modelleme etkinlik kâğıtları, görev temelli mülakat formu, yarı yapılandırılmış görüşme formu ve araştırmacı gözlem formu yardımıyla toplanmıştır. Araştırmanın verileri 2022-2023 eğitim öğretim yılının bahar döneminde İstanbul’da bir devlet üniversitesinde matematik öğretmenliği bölümünde dördüncü sınıfta öğrenim gören üç öğretmen adayı ile birlikte toplam dokuz oturumda gerçekleştirilmiştir. Veriler içerik analizi ile analiz edilmiştir. Verileri analiz edildiğinde öğretmen adaylarının matematiksel modelleme sürecinde üst bilişsel becerilerinin süreçteki rollerinin benzer olduğu; ancak basamaklara göre farklı sıklıklarda dağılım gösterdiği görülmüştür. Öğretmen adayları matematiksel modelleme problemlerine alışık olmadıklarını problem çözme süreçlerini tamamen kendilerinin organize etmeleri konusunda zorluk yaşadıklarını belirtmişlerdir. Sonuç olarak dört temel üst bilişsel becerinin matematiksel modellemenin her basamağında farklı rollere sahip olduğu, genel olarak kolaylaştırıcı, hız kazandırıcı, verim arttırıcı ve daha az hata payı ile gerçek sonuçlara yaklaşma anlamında olumlu bir etki yarattığı belirlenmiştir. Ek olarak üst bilişsel becerilerin farklı becerilerle ilişkili biçimde çalışarak matematiksel modellemenin basamakları arasında geçişlerde önemli role sahip olduğu ve modellemenin döngüsel yapısını koruduğu söylenebilir.
Teachers reflect their experiences and perspectives on their students. Therefore, mathematical strategies in mathematics lessons need to develop comprehensive and high-level techniques. The purpose of this study is to examine the roles of pre-service mathematics teachers' metacognitive skills in their mathematical modelling processes (understanding the task, simplifying/ structuring, mathematization, working mathematically, interpreting, validating). For this purpose, it is aimed to determine the metacognitive strategies (planning, monitoring, evaluation and prediction) during the mathematical modeling process and the roles they play in each phase of this process. To explain the roles of the four basic metacognitive skills during the modeling process in detail, this research was conducted as a case study, one of the qualitative research methods. The data of the research was collected using three mathematical modeling tasks, a task-based interview protocol, a structured interview protocol and the researcher observation form. The data of the research was collected in a total of nine sessions in the spring semester of the 2022-2023 academic year with three pre-service teachers studying in the fourth grade in the mathematics teaching department at a state university in Istanbul. The data were analyzed with content analysis. Analysis of data showed that the roles of pre-service teachers' metacognitive skills in the mathematical modeling process were similar. However, it was observed that they were distributed at different frequencies according to the steps. Pre-service teachers stated that they were not accustomed to mathematical modeling problems and had difficulties in organizing their problem-solving processes entirely on their own. Another important issue that pre-service teachers had difficulty with is the verification step of the modeling cycle. It has been observed that the concept of verification is not sufficiently understood by them. As a result, it has been determined that the four basic metacognitive skills have different roles in each step of mathematical modeling and that they generally have a positive effect in terms of facilitating, accelerating, increasing efficiency and approaching real results with less margin of error. In addition, it can be said that metacognitive skills play an important role in the transitions between the stages of mathematical modeling by working in relation to different skills and preserve the cyclical structure of modeling.
Teachers reflect their experiences and perspectives on their students. Therefore, mathematical strategies in mathematics lessons need to develop comprehensive and high-level techniques. The purpose of this study is to examine the roles of pre-service mathematics teachers' metacognitive skills in their mathematical modelling processes (understanding the task, simplifying/ structuring, mathematization, working mathematically, interpreting, validating). For this purpose, it is aimed to determine the metacognitive strategies (planning, monitoring, evaluation and prediction) during the mathematical modeling process and the roles they play in each phase of this process. To explain the roles of the four basic metacognitive skills during the modeling process in detail, this research was conducted as a case study, one of the qualitative research methods. The data of the research was collected using three mathematical modeling tasks, a task-based interview protocol, a structured interview protocol and the researcher observation form. The data of the research was collected in a total of nine sessions in the spring semester of the 2022-2023 academic year with three pre-service teachers studying in the fourth grade in the mathematics teaching department at a state university in Istanbul. The data were analyzed with content analysis. Analysis of data showed that the roles of pre-service teachers' metacognitive skills in the mathematical modeling process were similar. However, it was observed that they were distributed at different frequencies according to the steps. Pre-service teachers stated that they were not accustomed to mathematical modeling problems and had difficulties in organizing their problem-solving processes entirely on their own. Another important issue that pre-service teachers had difficulty with is the verification step of the modeling cycle. It has been observed that the concept of verification is not sufficiently understood by them. As a result, it has been determined that the four basic metacognitive skills have different roles in each step of mathematical modeling and that they generally have a positive effect in terms of facilitating, accelerating, increasing efficiency and approaching real results with less margin of error. In addition, it can be said that metacognitive skills play an important role in the transitions between the stages of mathematical modeling by working in relation to different skills and preserve the cyclical structure of modeling.