Relationship between complexity of information and difficulty of example-oriented textbooks

A new method is proposed for rating the complexity of the information in an example-oriented textbook. Quantitative relations are studied between the proposed complexity and difficulty of understanding the textbook. The complexity of the information in the textbook is rated in terms of an information unit newly defined in this paper by the deformation of propositions. These information units are propositions that were previously unfamiliar to the learners using the textbook. In the case of causal relations among propositions, the number of preconditions affects the complexity of information and the number of preconditions is adopted as an attribute of the information unit (the `dimension' of the information unit) and are reflected in the rating of complexity of information. The difficulty of the textbook is indexed by the error rate of the answers to its exercises. A serial model is proposed in which the understanding of one learning item is achieved when every information unit included in the item is understood with no errors. We attempt to relate the complexity of the information and difficulty of learning quantitatively. By learning experiments using a C language textbook, the validity of the model and its usefulness are demonstrated. From the results of experiments, the difficulty increase corresponds to the increase in the number of information units and the number of preconditions.