Using Cognitive Tools to Enhance Understandingin Differential Equations

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.