Steadiness analysis of means-end conceptual paths and problem-chains based on concept lattices and similarity measuring

Abstract

Formal concept analysis has shown much potential in supporting personalized learning. This paper is motivated by several application scenarios of concept lattices in supporting mathematics education. The aim of the paper is to develop a scheme for designing problem-chains based on concept lattices and provide evaluation methods towards steadiness of the corresponding learning processes. Particularly, a model is developed to study the sensitivity of conversion from effort on problems to efficacy on knowledge/skills. Then the notion of successive trails is introduced to describe means-end chains of learning states. Towards steadiness of the corresponding learning processes, evaluation methods are developed and data experiments are conducted from aspects of effort on problems, efficacy on knowledge/skills and conversion sensitivity. Moreover, the notion of conceptual paths is introduced in order to describe personalized learning strategies. Subsequently, a scheme for designing problem-chains is given based on conceptual paths and similarity measuring. Finally, a method of evaluating the steadiness of problem-chains is proposed by taking advantage of linear regression analysis on problem-chains.