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.

正式的概念分析已显示出在支持个性化学习方面的巨大潜力。本文受概念格在支持数学教育中的几种应用场景的启发。本文的目的是开发一种基于概念格的问题链设计方案，并为评估相应学习过程的稳定性提供评估方法。特别是，开发了一个模型来研究从问题上的努力转换为知识/技能的有效性的敏感性。然后引入连续轨迹的概念来描述学习状态的均值端链。为了使相应的学习过程保持稳定，从评估问题的努力，对知识/技能的有效性和转换敏感性的角度出发，开发了评估方法并进行了数据实验。而且，为了描述个性化的学习策略，引入了概念路径的概念。随后，基于概念路径和相似性度量给出了一种设计问题链的方案。最后，利用对问题链的线性回归分析，提出了一种评估问题链稳定性的方法。