Investigating Seventh Grade Students' Metacognitive Failures in the Mathematical Modeling Process

Year 2025, Issue: 64, 2230 - 2254, 30.06.2025

Muhammed Özsoy , Handan Demircioğlu

https://doi.org/10.53444/deubefd.1620514

Abstract

The aim of this study is to reveal the metacognitive failures of seventh grade students in the mathematical modeling process. For this purpose, red flag situations and three types of metacognitive failures defined by Goos (1998) were examined. An explanatory/descriptive case study was used in the study. The participants of the study consisted of two students studying in the seventh grade of a public school in the Black Sea Region and selected by criterion sampling, one of the purposeful sampling methods. The Football Field Problem was used to reveal the red flag situations and types of metacognitive failures. Data were collected using the think aloud technique. Data analysis was carried out in the stages of transcribing the data obtained from the think aloud and interviews, coding the thoughts that the students could express, and defining the red flags and metacognitive failures in the mathematical modeling process. The results of the study showed that the students experienced some metacognitive failures related to concepts such as measurement, measurement unit conversions, circle, diameter and radius, ratio and proportion. At the end of the study, it was determined that the students experienced metacognitive blindness 11 times, metacognitive mirage four times, and metacognitive vandalism five times. The types of metacognitive failure such as ‘blindness’, ‘mirage’, ‘vandalism’ that emerged in the study are reinforced especially in cases where monitoring and evaluation cannot be done together.

Keywords

Metacognition , mathematical modeling , metacognitive failure , metacognitive blindness , metacognitive mirage , metacognitive vandalism

Yedinci Sınıf Öğrencilerinin Matematiksel Modelleme Sürecindeki Üstbilişsel Başarısızlıklarının İncelenmesi

Abstract

Bu çalışmanın amacı yedinci sınıf öğrencilerinin matematiksel modelleme sürecindeki üstbilişsel başarısızlıklarının ortaya çıkarılmasıdır. Bu amaç doğrultusunda Goos (1998) tarafından tanımlanan kırmızı bayrak durumları ve üç tür üstbilişsel başarısızlık türleri incelenmiştir. Çalışmada açıklayıcı/tanımlayıcı durum çalışması kullanılmıştır. Araştırmanın katılımcılarını Karadeniz Bölgesi’ndeki bir devlet okulunun yedinci sınıfında öğrenim gören ve amaçlı örnekleme yöntemlerinden ölçüt örnekleme ile seçilen iki öğrenci oluşturmaktadır. Kırmızı bayrak durumları ve üstbilişsel başarısızlık türlerinin ortaya çıkarılması amacıyla Futbol Sahası Problemi kullanılmıştır. Veriler, sesli düşünme (think aloud) tekniği kullanılarak toplanmıştır. Verilerin analizi sesli düşünme ve görüşmelerden elde edilen verilerin yazıya dökülmesi, öğrencilerin ifade edebildikleri düşüncelerinin kodlanması, matematiksel modelleme sürecindeki kırmızı bayraklar ve üstbilişsel başarısızlıkların tanımlanması aşamalarında gerçekleştirilmiştir. Çalışmanın sonuçları öğrencilerin ölçme, ölçü birimi dönüşümleri, çember, çap ve yarıçap, oran ve orantı gibi kavramlarla ilişkili olarak birtakım üstbilişsel başarısızlık yaşadıklarını göstermiştir. Çalışma sonunda öğrencilerin 11 defa üstbilişsel körlük, dört defa üstbilişsel serap ve beş defa üstbilişsel vandalizm yaşadıkları belirlenmiştir. Çalışmada ortaya çıkan “körlük”, “serap”, “vandalizm” gibi üstbilişsel başarısızlık türleri özellikle izleme ve değerlendirmenin birlikte yapılamadığı durumlarda daha da pekişmektedir.

Keywords

Üstbiliş , matematiksel modelleme , üstbilişsel başarısızlık , üstbilişsel körlük , üstbilişsel serap , üstbilişsel vandalizm

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