Difficulty analysis for learners in problem solving process based on the knowledge map

We propose 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 problems is according to the process of building a problem, including concept selection, unknown designation, and proposition construction. Some necessary measures observed in the problem building process are also defined in order to formulate and calculate the difficulties. Beside the difficulty of the basic problem, four difficulty dimensions, identification, elaboration, planning, and execution, corresponding to the problem solving steps are also analyzed. With these difficulty measures learners can understand what kinds of problems they met and what sorts of problem solving strategies are emphasized in solving the problem. To reach our goal, an item generating system is constructed for demonstrating and supporting the difficulty calculation.