An Examination of High School and Middle School Students' Solutions to the Mount Everest Journey Modeling Activity in Terms of Their Mathematical Modeling Competencies

Merve Gençer; Özkan Ergene

Makale detayları

An Examination of High School and Middle School Students' Solutions to the Mount Everest Journey Modeling Activity in Terms of Their Mathematical Modeling Competencies

Yazarlar:

Merve Gençer | Özkan Ergene

Yayıncı:

Erciyes University

Ana Başlıklar:

Fen ve Matematik Alanları Eğitimi (Diğer)

Dergi:

Erciyes Journal of Education Vol.9 Issue 1, pp.47-77

Belge Tipi:

Makale

Yayın Tarihi:

5/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001349534

pISSN:

2602-3830

Anahtar kelimeler:

Özet:

 This study aims to examine the mathematical modeling competencies of high school and middle school students within the context of the mathematical modeling elicitng activity Journey to Mount Everest. The study adopts a case study approach, one of the qualitative research methods. The study group comprises 310 students from an Anatolian high school, a science high school, and an Imam Hatip middle school. Data were collected through students written solutions to the Journey to Mount Everest modeling eliciting activity, developed by the researchers based on the principles of model-building activities, with validity and reliability studies conducted beforehand. The data were analyzed using a grading rubric. Analysis of the modeling competencies of students who reported no prior experience with mathematical modeling revealed that they performed well in the problem understanding step. However, students who either failed to apply an appropriate approach or only partially succeeded in the simplification step faced difficulties in subsequent steps. During the mathematization step, students predominantly relied on verbal expressions rather than mathematical representations. In the model validation step, students were found to be insufficient, with none of the middle school students successfully validating the model. Furthermore, high school students demonstrated higher levels of modeling competence compared to middle school students. Based on the findings, it is recommended that students at all educational levels be introduced to mathematical modeling activities. Additionally, these activities should be incorporated into a learning environment where they can be gamified using simulation programs or artificial intelligence tools to enhance engagement and effectiveness.

 This study aims to examine the mathematical modeling competencies of high school and middle school students within the context of the mathematical modeling elicitng activity Journey to Mount Everest. The study adopts a case study approach, one of the qualitative research methods. The study group comprises 310 students from an Anatolian high school, a science high school, and an Imam Hatip middle school. Data were collected through students written solutions to the Journey to Mount Everest modeling eliciting activity, developed by the researchers based on the principles of model-building activities, with validity and reliability studies conducted beforehand. The data were analyzed using a grading rubric. Analysis of the modeling competencies of students who reported no prior experience with mathematical modeling revealed that they performed well in the problem understanding step. However, students who either failed to apply an appropriate approach or only partially succeeded in the simplification step faced difficulties in subsequent steps. During the mathematization step, students predominantly relied on verbal expressions rather than mathematical representations. In the model validation step, students were found to be insufficient, with none of the middle school students successfully validating the model. Furthermore, high school students demonstrated higher levels of modeling competence compared to middle school students. Based on the findings, it is recommended that students at all educational levels be introduced to mathematical modeling activities. Additionally, these activities should be incorporated into a learning environment where they can be gamified using simulation programs or artificial intelligence tools to enhance engagement and effectiveness.

 This study aims to examine the mathematical modeling competencies of high school and middle school students within the context of the mathematical modeling elicitng activity Journey to Mount Everest. The study adopts a case study approach, one of the qualitative research methods. The study group comprises 310 students from an Anatolian high school, a science high school, and an Imam Hatip middle school. Data were collected through students written solutions to the Journey to Mount Everest modeling eliciting activity, developed by the researchers based on the principles of model-building activities, with validity and reliability studies conducted beforehand. The data were analyzed using a grading rubric. Analysis of the modeling competencies of students who reported no prior experience with mathematical modeling revealed that they performed well in the problem understanding step. However, students who either failed to apply an appropriate approach or only partially succeeded in the simplification step faced difficulties in subsequent steps. During the mathematization step, students predominantly relied on verbal expressions rather than mathematical representations. In the model validation step, students were found to be insufficient, with none of the middle school students successfully validating the model. Furthermore, high school students demonstrated higher levels of modeling competence compared to middle school students. Based on the findings, it is recommended that students at all educational levels be introduced to mathematical modeling activities. Additionally, these activities should be incorporated into a learning environment where they can be gamified using simulation programs or artificial intelligence tools to enhance engagement and effectiveness.

 Bu çalışmanın amacı lise ve ortaokul öğrencilerinin matematiksel modelleme yeterliliklerinin Everest Dağına Yolculuk adlı matematiksel modelleme etkinliği bağlamında incelenmesidir. Çalışmada nitel araştırma yöntemi olan durum çalışması araştırma deseni olarak belirlenmiştir. Araştırmaya katılan çalışma grubu Anadolu Lisesi, Fen Lisesi ve İmam Hatip Ortaokulunda öğrenim gören 310 öğrenciden oluşmaktadır. Araştırmanın verileri, araştırmacılar tarafından model oluşturma etkinliği prensipleri doğrultusunda geliştirilen geçerlik ve güvenirlik çalışmaları yapılmış Everest Dağına Yolculuk adlı modelleme etkinliğine yazılı olarak verdikleri çözümler ile toplanmış ve dereceli puanlama rubriği ile analiz edilmiştir. Araştırmada matematiksel modelleme ile daha önce karşılaşmadıklarını belirten öğrencilerin modelleme yeterlilikleri analiz edildiğinde problemi anlama basamağında başarılı oldukları görülmüştür. Problemi sadeleştirme basamağında uygun yaklaşım sergileyemeyen ya da kısmen yaklaşım sergileyen öğrencilerin diğer basamaklarda zorlandıkları anlaşılmıştır. Öğrencilerin matematikselleştirme basamağında matematiksel ifadeler kullanmak yerine daha çok sözel ifadeler ile açıklama yapmaya çalıştıkları görülmüştür. Modeli doğrulama basamağında öğrencilerin yetersiz kaldığı hatta ortaokul öğrencilerinin tamamının modeli doğrulayamadığı saptanmıştır. Ayrıca modelleme yeterlilik düzeylerinde lise öğrencileri ortaokul öğrencilerine göre daha yüksek performans sergilemişlerdir. Araştırma sonuçlarına göre tüm eğitim kademelerindeki öğrencilerin matematiksel modelleme etkinlikleri ile tanıştırılıp etkinliklerin simülasyon programları ya da yapay zekâ ile birlikte oyun şekline dönüştürüldüğü bir öğrenme ortamında gerçekleştirilmesi önerilebilir.

Makale detayları

An Examination of High School and Middle School Students' Solutions to the Mount Everest Journey Modeling Activity in Terms of Their Mathematical Modeling Competencies

Yazarlar:

Merve Gençer | Özkan Ergene

Yayıncı:

Erciyes University

Ana Başlıklar:

Fen ve Matematik Alanları Eğitimi (Diğer)

Dergi:

Erciyes Journal of Education Vol.9 Issue 1, pp.47-77

Belge Tipi:

Makale

Yayın Tarihi:

5/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001349534

pISSN:

2602-3830

Mathematical Modeling

Mathematical Modeling Competencies

High School and Middle School Students

Everest Mountain Journey Modeling ActivityMatematiksel modelleme

Matematiksel Modelleme Yeterlilikleri

Lise ve Ortaokul Öğrencileri

Everest Dağı’na Yolculuk Modelleme Etkinliği

Sayı

Makale detayları

Yazarlar: Merve Gençer | Özkan Ergene

Yayıncı: Erciyes University

Ana Başlıklar: Fen ve Matematik Alanları Eğitimi (Diğer)

Dergi: Erciyes Journal of Education Vol.9 Issue 1, pp.47-77

Belge Tipi: Makale

Yayın Tarihi: 5/2025

Belge Dili: Türkçe

Document ID (Org No.): 2001349534

pISSN: 2602-3830

Sayı

Yazarlar:

Merve Gençer | Özkan Ergene

Yayıncı:

Erciyes University

Ana Başlıklar:

Fen ve Matematik Alanları Eğitimi (Diğer)

Dergi:

Erciyes Journal of Education Vol.9 Issue 1, pp.47-77

Belge Tipi:

Makale

Yayın Tarihi:

5/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001349534

pISSN:

2602-3830