CAN SYMBOLIC COMPUTATION AND FORMALIST SYSTEMS ENHANCE MATH EDUCATION WITH ARTIFICIAL INTELLIGENCE?

Yıl 2024, Cilt: 26 Sayı: 2, 487 - 504, 13.12.2024

Selçuk Yazar

https://doi.org/10.26468/trakyasobed.1435490

Öz

In recent years, a solution developed using deep learning methods has been used to solve difficult problems in a field. The capability of deep learning models is that they require large and heavily sampled data sets. Computer Algebra Systems developed over time have made significant progress, especially in the field of symbolic mathematics solutions solved by machine learning. It is a persistent problem how appropriate it is to use such formal systems in some aspects of algorithmic decision-making. In this paper, we discussed the suitability of artificial intelligence applications to formal propositions by evaluating a deep learning study conducted especially in the field of symbolic mathematics and Math education. Symbolic computation systems have a strong potential for enhancing math education. Furthermore, within the framework of the Incompleteness Theorem, to show why the construction of a mathematical grammar is not a complete solution for Mathematics education systems.

Anahtar Kelimeler

Symbolic Mathematics, Formal Systems, Computer Algebra Systems, Artificial Intelligence, Mathematics Learning.

SEMBOLİK HESAPLAMA VE FORMALİST SİSTEMLER MATEMATİK EĞİTİMİNİ YAPAY ZEKA İLE GELİŞTİREBİLİR Mİ?

Öz

Son yıllarda, derin öğrenme yöntemleri kullanılarak geliştirilen bir çözüm, bir alandaki zor problemleri çözmek için kullanılmaktadır. Derin öğrenme modellerinin özelliği, büyük ve yoğun örneklenmiş veri setlerine ihtiyaç duymalarıdır. Zaman içerisinde geliştirilen Bilgisayar Cebiri Sistemleri, özellikle makine öğrenmesi ile çözülen sembolik matematik çözümleri alanında önemli ilerlemeler kaydetmiştir. Bu tür biçimsel sistemlerin algoritmik karar vermenin bazı yönlerinde kullanılmasının ne kadar uygun olduğu süregelen bir sorundur. Bu bildiride özellikle sembolik matematik ve Matematik eğitimi alanında yapılan bir derin öğrenme çalışması değerlendirilerek yapay zeka uygulamalarının formal önermelere uygunluğu tartışılmıştır. Sembolik hesaplama sistemleri matematik eğitimini geliştirmek için güçlü bir potansiyele sahiptir. Ayrıca, Eksiklik teoremi çerçevesinde, matematiksel bir gramer yapısı oluşturmanın Matematik eğitim sistemleri için neden tam bir çözüm olamayacağının gösterilmesi amaçlanmıştır.

Anahtar Kelimeler

Sembolik Matematik, Biçimsel Sistemler, Bilgisayar Cebir Sistemleri, Yapay Zeka, Matematik Öğrenimi.

Kaynakça

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