Eğilimler ve Üstbilişsel Deneyimlerin Matematik Problemi Çözme Sürecindeki Rolü *

Abstract

Bu araştırmada, 10. sınıf öğrencilerinin senaryo temelli matematik problemi çözerken ortaya çıkan eğilimlerinin ve sahip oldukları üstbilişsel deneyimlerin neler olduğu ve bunların öğrenim gördükleri okulların akademik düzeylerine göre farklılaşıp farklılaşmadığı araştırılmıştır. Nitel araştırma desenlerinden fenomenoloji kullanılarak gerçekleştirilen bu çalışmada katılımcılar, amaçlı örnekleme yöntemlerinden maksimum çeşitlilik örneklemesi tekniği kullanılarak belirlenmiştir. 2022-2023 eğitim öğretim yılında İstanbul ilinde bulunan 10 farklı akademik düzeydeki ortaöğretim kurumundan seçilen birer 10. sınıf öğrencisiyle nitel görüşmeler geçekleştirilmiştir. Veri toplama aracı olarak araştırmacı tarafından oluşturulan yarı yapılandırılmış görüşme formu, gözlem formu ve iki adet senaryo temelli matematik problemi kullanılmış, elde edilen veriler içerik analizi yöntemiyle çözümlenmiştir. Araştırmadan elde edilen bulgulara göre belirli eğilimleri birlikte sergileyen katılımcıların, bu eğilimleri ayrı ayrı sergileyen katılımcılara göre problem çözme becerilerinin daha yüksek olduğu sonucuna varılmıştır. Ayrıca sergilenen eğilimlerin dikkatli olma eğilimiyle desteklenmediği takdirde problem çözme becerisi karşısında etkisiz kalabildiği ve öz güven eğiliminin bazı durumlarda problem çözme becerisini olumsuz etkilediği ulaşılan sonuçlar arasındadır. Aynı zamanda bulgular, üstbilişsel deneyimlerde yer alan matematik ön yargısının problem çözme becerisini olumsuz etkileyebildiğini, problemi sevmenin problem çözme becerisini sergilemede bir motivasyon kaynağı oluşturduğunu, problemi sevmemenin ise problem çözme becerisini olumsuz etkilediğini göstermektedir.

Keywords

• Eğilimler
• Üstbilişsel Deneyimler
• Problem Çözme Becerisi
• Senaryo Temelli Matematik Problemleri

The Role of Dispositions and Metacognitive Experiences in the Process of Solving Mathematical Problems

Abstract

This study investigated the dispositions exhibited by 10th grade students while solving scenario-based mathematics problems, the metacognitive experiences they possess, and whether these differed according to the academic level of the schools they attended. Conducted using the phenomenology design, one of the qualitative research approaches, the participants were determined using the maximum diversity sampling technique, one of the purposive sampling methods. Qualitative interviews were conducted with one 10th-grade student selected from each of ten different secondary education institutions with varying academic levels in Istanbul during the 2022-2023 academic years. The data collection tools included a semi-structured interview form, an observation form, and two scenario-based mathematics problems developed by the researcher. The obtained data was analyzed using content analysis. The findings of the study revealed that the participants who exhibited certain dispositions simultaneously had higher problem-solving skills compared to those who displayed these dispositions individually. Additionally, it was found that if the exhibited dispositions were not supported by the disposition of being careful, they could be ineffective in problem-solving skills, and the self-confidence disposition negatively impacted problem-solving abilities in some cases. Furthermore, the findings demonstrated that mathematical prejudice as part of metacognitive experience could hinder problem-solving ability, while enjoying mathematics functioned as a motivational factor in displaying problem-solving skills, whereas disliking mathematics negatively influenced these skills.

Keywords

• Dispositions
• Metacognitive Experiences
• Problem-Solving Skills
• Scenario Based Mathematic Problems

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