技能映射下学习空间判别定理

Discriminance theorems of learning spaces delineated by skill maps

在知识空间理论中,个体的知识状态不仅可以由个体能解决的问题确定,还可以由其掌握的技能确定.技能映射反映了问题和技能间的联系,但是技能映射下导出的知识结构一般都不是学习空间.由于无论是由技能映射导出知识结构的过程,还是判定知识结构是否是学习空间的过程都比较复杂,因此有必要直接在技能映射下研究导出学习空间的条件.本文首先给出了基于原子的学习空间判别定理.在此基础上,根据每项技能确定的知识状态与原子间的关系,提出了析取模型下学习空间判别定理.进一步地,利用合取模型和析取模型下导出的知识结构的对偶性,提出了合取模型下学习空间判别定理.

Based on knowledge space theory,the knowledge state can be established not only by the items an individual is capable of solving,but also by the skills one masters.Skill maps connect items and skills.However,knowledge structures delineated by skill maps are not learning spaces in general.Not only is it complex to delineate knowledge structures by skill maps,but also complex to identify whether the delineated knowledge structures are learning spaces.Therefore,it is necessary to investigate the conditions for delineating learning space directly from skill maps.Firstly,the discriminance theorem of learning spaces is established based on atoms in this paper.Then according to the relationship of atoms and knowledge states identified by each skill,the discriminance theorem of learning spaces delineated via disjunctive model is proposed.Further,we obtain the discriminance theorem of learning spaces delineated via conjunctive model by the duality of knowledge structures delineated by the two discussed models.