Ranking the Difficulty Level of the Knowledge Units Based on Learning Dependency

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. Then they propose three hypotheses of factors influencing difficulty based on the correlation between the difficulty level of knowledge units and the learning dependency. Finally, the authors provide algorithms for ranking the knowledge units with objective and subjective difficulty scores. The experiment on the knowledge map of the “plane geometry” course shows that our algorithm can precisely calculate the difficulty level of knowledge units. ter, 2006). The following is an example of a definition type knowledge unit: “Definition of triangle: the plane figure formed by connecting three points not in a straight line by straight line segments”. An example of a theoric knowledge unit is as follows: “Triangle interior angles sum theorem: the sum of the measures of the interior angles of a triangle is 180°.” The knowledge unit “Triangle interior angles sum theorem” has a learning dependency on the knowledge unit “Definition of triangle”. This dependency means that “Definition of triangle” must be learned before the “Triangle interior angles DOI: 10.4018/jdet.2012010102 32 International Journal of Distance Education Technologies, 10(1), 31-43, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. sum theorem”. A knowledge map is defined as a directed graph composed of knowledge units and learning dependency relationships (Gordon, 2000; Lin & Hsueh, 2006). Knowledge maps have been employed in navigational learning as a knowledge representation tool (Lin et al., 2006; Han & Kim, 2005). A navigational learning path can be visually presented by making use of the knowledge map based on the learner’s cognition level. Personalized learning content and services can also be offered adaptively to avoid the learning disorientation problems (Adomavicius, 2005). In navigational learning, each knowledge unit has two properties (objective difficulty and subjective difficulty) that affect the efficiency of learning the objective difficulty level and the subjective difficulty level. Computing and ranking these properties are helpful in guiding learners to allocate their efforts and time appropriately. Currently, the navigational learning model does not have a standard to identify the difficulty level properties. Therefore, the efficiency of navigation learning is limited. This paper will address this problem by studying on how to rank the difficulty levels of the knowledge units based on these units’ learning dependencies. The difficult level of a knowledge unit correlates to the knowledge unit itself, and also is influenced by the learner’s cognition level (Cant, Jeffery, & Henderson-Sellers, 1995). We define the objective difficulty level as the complexity of the knowledge unit itself, and the subjective difficulty level as the degree to which an individual learner’s cognitive level affects the objective difficulty. We identified the correlations between a knowledge map’s topological properties and the objective difficulty levels of its knowledge units by building the knowledge maps of eight courses, including “Plane Geometry,” “Data Structure,” “Computer System Architecture”, “Principles of Computer Composition,” and others. We reached to three hypotheses after analyzing these correlations. According to these hypotheses, we propose an algorithm of ranking the objective and subjective difficulty level of the knowledge units. The algorithm is based on the learning dependency relationships among the knowledge units. The rest of the paper is organized as follows: we review the related researches in difficulty ranking; we elaborate on the hierarchical structure of the knowledge map, and presents the algorithm for ranking the difficulty level of the knowledge units; we then provide the experimental results of the proposed ranking algorithm; and end the paper with the conclusion and future work.