Basic Knowledge Components And Knowledge Chains With Their Applications In ICAI

Knowledge space theories provide methods of describing the given structure of Knowledge Area. These methods are based on the science realm of cognition. The aim of the research on these theories is modeling for human knowledge in the process of study and use in any subject .This paper studies a new knowledge space theory based on knowledge points, analyses the framework of this knowledge space, and tries to use ICAI (Intelligent Computer Assisted Instruction) as its application target. A detailed introduction is as follows: establishing the knowledge space, making use of some mathematics tools such as aggregation, combination, etc, using interactive computer to evaluate study states of learners and feedback as quickly but accurately as possible, carrying out to instruct and control the study path of learners to attain the goal of study.At present,knowledge space theories are based on problems, i.e. knowledge is expressed as problems in those theories. For example, how do students master the knowledge is judged from how they answer the questions. Expressing knowledge as the form of problems is just one of the methods to figure it. Actually, in the case of teaching processes and teaching material arrangement, knowledge is imparted as the form of knowledge points which are divided by knowledge itself. Consequently, for improving these knowledge space theories, it is necessary to study a kind of knowledge space based on knowledge points in practice.In knowledge space theory which is based on knowledge points, it can form the Knowledge Point Relationship Networks according to the internal and external relationship among Knowledge Points. After that, vertical or horizontal studies can be made in the Knowledge Point Relationship Networks, and then obtain knowledge components and knowledge chains——which are erected as elements of a middle positions between knowledge points and knowledge space. Knowledge component is defined as a kind of block divided from its Knowledge Point Relationship Network by using the horizontal way, the frame of this block can incarnate the structure of knowledge and the progress in studying. Basic knowledge components are the knowledge components with certain character。This paper shows how to divide basic knowledge components. Knowledge chain is defined as a kind of vertical frame in terms of the structure of its Knowledge Point Relationship Network and the sequence of studying. It comes up with some concepts of the Knowledge Chain Cluster, the Underlay Set and the Underlaid Set, and finds the internal relationships between them and the Knowledge Point Relationship Network. This article investigates a kind of knowledge space based on basic knowledge components as middle positions, and then, takes some part of plane geometry in the book named THE THIRTEEN BOOKS OF EUCLUD'S ELEMENTS for instance, to verify the results from this investigation so as to offer approaches and reasons to develop ICAI systems.