Using Cognitive Tools to Enhance Understanding in Differential Equations

Abstract

Artikel ini melaporkan satu kajian yang bertujuan untuk memahami perkembangan konsep persamaan pembeza dalam suasana pembelajaran yang disokong oleh alat kognitif yang telah dibangunkan dan dinamakan DEgraf. Tahap kefahaman pelajar dianalisis melalui peta konsep yang diperkenalkan oleh Novak. Kerja bertulis beberapa masalah yang dihasilkan pelajar diteliti dan diterjemahkan kepada peta konsep untuk digunakan bagi memahami tahap kefahaman. Kajian menghasilkan struktur kognitif yang terdiri daripada pelbagai konsep dan hubungan antara konsep. Struktur kognitif dapat menggambarkan kualiti kefahaman relational pelajar. Kajian menunjukkan penggunaan alat kognitif dalam suasana pembelajaran yang aktif boleh membantu perkembangan kefahaman relational atau konseptual pelajar. Kata kunci: Pembelajaran bermakna; peta konsep; kefahaman relational; alat kognitif; persamaan pembeza This paper reports a research conducted to understand the development of concepts on differential equations in a learning environment supported with a cognitive tool developed known as DEgraf. The students’ levels of understanding were analyzed via concept mapping as introduced by Novak. Their written solutions on various problems were examined and transformed to concept maps which were used as tools to understand their levels of understanding. Results showed the cognitive structures in terms of mathematical relationships and the number of concepts made by the students. These cognitive structures illustrare the students quality of relational understanding. The study showed that active learning environments incorporating the use of a cognitive tool may lead to the development of relational or conceptual understanding. Key words: Meaningful learning; concept maps; relational understanding; cognitive tools; differential equations