Skills first - An alternative approach to construct knowledge spaces
|Basis of knowledge spaces; Free fans; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; Multiple items; Order operations; Psychology; Psychology, Mathematical; Set representations of partial orders; Social Sciences, Mathematical Methods
|ACADEMIC PRESS INC ELSEVIER SCIENCE
|JOURNAL OF MATHEMATICAL PSYCHOLOGY
This paper combines two aspects in the construction of knowledge spaces. The first is to utilize a partial order of skills which belong to a given domain of knowledge to find items or problems which finally constitute a knowledge space or a learning space. Secondly the orders of skills of different (related) areas are coalesced by well known order operations to construct larger spaces. In the first part a so called basic set representation of an order is utilized to considerably simplify the construction of knowledge spaces. In the second part the techniques to ``add'' and ``multiply'' orders are applied to given orders resulting in new orders to which the set representation theory of the first part is applied. Properties of the building blocks are identified which can be transferred to the combination and yield properties of the final knowledge space which make their handling a bit more convenient. In particular, places which proved useful in the construction of the first part are identified when these order operations are utilized. (C) 2021 Elsevier Inc. All rights reserved.
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checked on Mar 2, 2024