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Item State Transition Functions and Polytomous Knowledge Structures Based on Procedural Knowledge Learning

SUN Xiaoyan;LI Jinjin;School of Mathematical Sciences, Huaqiao University;School of Mathematics and Statistics, Minnan Normal University;  
In the assessment of procedural knowledge, skills refer to the operation paths relevant to the solution of an item. Based on the learning assessment of procedural knowledge, a method of delineating polytomous knowledge structure from the state structure of the item itself is proposed to establish a polytomous assessment system for problem solving. Firstly, the response values are set according to the solution or operation process of each item to obtain the item-specific response value set. The item state space is defined by item state transition function, and the problem space is extended to polytomous case. Then, the conjunctive skill maps are derived from the operation paths, and the polytomous knowledge structures delineated by the conjunctive skill maps are discussed. The results show that the polytomous knowledge structure delineated by a skill map based on the conjunctive model satisfies the item-wise intersection closure. Finally, the algorithm steps of delineating polytomous knowledge structure are given, and the effectiveness of the proposed algorithm is illustrated by an example.
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