Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

Summarizes theoretical and empirical aspects of research that is investigating how best to support conceptual learning and the critical role that representations have in complex scientific and mathematical domains. Explains Law Encoding Diagrams (LEDs) and considers how computers may further enhance the potential benefit of LEDs for conceptual…