Analyzing problem's difficulty based on neural networks and knowledge map

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed in the problem construction process are also defined in this paper in order to formulate and calculate the difficulties. Beside the difficulty of the basic problem, four difficulty dimensions for problem solvers to realize what kinds of abilities they are lack of to deal with the problem, including Identification, Elaboration, Planning, and Execution, corresponding to the each step of problem solving process are also analyzed and designed by the artificial neural networks in this paper. By these difficulty measures learners can understand what kind of problems they meet and what sort of problem solving strategies they use in solving the problem. To verify our goals, an Item Generating System is constructed for demonstrating and supporting the difficulty calculation in the end of this paper.