An Overview of the Epistemological Link between Mathematical Thinking and Computational Thinking from Theory to Practice

Year 2025, Issue: 64, 123 - 149, 19.05.2025

Behiye Dinçer Aksoy , Berna Cantürk Günhan , Filiz Mumcu

https://doi.org/10.9779/pauefd.1438401

Abstract

Mathematical thinking is critical to the maintenance of daily life and the development of science. This study examines the epistemological connection between mathematical and Computational Thinking (CT). Since CT involves the problem-solving process through thinking and computer science tools, it is thought to have an important relationship with mathematical thinking. In order to understand this relationship, mathematical modeling problems are addressed from a cognitive perspective in this study. Using a case study, a conceptual framework was developed by examining studies that attempt to integrate CT into mathematics education. In line with the framework, a professional development course was prepared and administered to a mathematics teacher. Subsequently, the relationship between the cognitive processes in the modeling process and the components of CT was examined. The study's findings revealed that (a) considering abstraction in the context of Piaget's abstraction theory is a more effective approach for understanding mathematical thinking, (b) more than one CT component can be identified at each stage of the modeling process, and no single component can be exclusively associated with a single stage, and (c) common and distinct thinking processes between mathematical thinking and CT were uncovered. These findings contribute to a more nuanced comprehension of the intricate interrelationships between mathematical thinking and cognitive flexibility.

Keywords

Mathematical thinking , Computational thinking , Mathematical modeling

Matematiksel Düşünme ve Bilgi İşlemsel Düşünmenin Epistemolojik Bağlantısına Kuramdan Uygulamaya Bir Bakış

Abstract

Matematiksel düşünme, günlük yaşamın sürdürülmesinde ve bilimin gelişiminde kritik bir öneme sahiptir. Bu çalışmada, matematiksel düşünme ile Bilgi İşlemsel Düşünme (BİD) arasındaki epistemolojik bağlantı incelenmektedir. Çünkü BİD, problem çözme sürecini düşünme biçimi ve bilgisayar bilimi araçlarıyla ele aldığı için, matematiksel düşünmeyle önemli bir ilişkiye sahip olduğu düşünülmektedir. Bu ilişkinin anlaşılması için, çalışmada matematiksel modelleme problemleri bilişsel perspektifle ele alınmıştır. Durum çalışması araştırma deseni kullanılarak, matematik eğitimine BİD'i entegre etmeye çalışan çalışmalar incelenmiş ve bir kavramsal çerçeve oluşturulmuştur. Oluşturulan çerçeve doğrultusunda bir mesleki gelişim kursu hazırlanmış ve bir matematik öğretmenine uygulanmıştır. Böylece modelleme sürecindeki bilişsel süreçler ile BİD bileşenleri arasındaki ilişki incelenmiştir. Araştırmanın bulgularına göre, (a) soyutlamanın Piaget’in soyutlama teorisi bağlamında ele alınmasının matematiksel düşünmeyi anlamada daha etkili olduğu, (b) modelleme sürecinde birden fazla BİD bileşeninin her aşamada açığa çıkabileceği ve herhangi bir bileşenin tek bir aşama ile ilişkilendirilemeyeceği belirlenmiş, (c) matematiksel düşünme ile BİD arasındaki ortak ve farklı düşünme süreçleri ortaya konmuştur. Bu bulgular, matematiksel düşünme ve BİD arasındaki karmaşık ilişkilerin daha derinlemesine anlaşılmasına katkı sağlamaktadır.

Keywords

Matematiksel düşünme , Bilgi işlemsel düşünme , Matematiksel modelleme

Ethical Statement

Bu araştırma, Dokuz Eylül Üniversitesi Bilimsel Araştırma ve Yayın Etiği Sosyal ve Beşeri Bilimler kurulunun 21/11/2023 tarihli E-87347630-659-806813 sayılı kararı ile alınan izinle yürütülmüştür.

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