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

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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.

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Acknowledgements

Thanks the support from Outstanding Youth Foundation of Hunan Scientific Committee (no. 2019JJ30016), Young Talents Program in Hunan Province (no. 2017RS3030), Key Programs of Hunan Education Committee (no. 20A301), National Natural Science Foundation of China (11771134, 61976089) and Construct Program of Key Discipline in Hunan Province.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Key Laboratory of High Performance Computing and Stochastic Information Processing, Hunan Normal University, Changsha, 410012, Hunan, People’s Republic of China

    Lankun Guo & Zhenhua Jia

  2. College of Mathematics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Qingguo Li

  3. College of Information Science and Engineering, Hunan Normal University, Changsha, 410012, Hunan, People’s Republic of China

    Jianhua Dai

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  1. Lankun Guo
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Appendices

Appendix 1

See Table 9.

Table 9 The weight on knowledges/skills
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Appendix 2

See Tables 10 and 11.

Table 10 Standard deviation and coefficient of variation of all successive trails from \(\alpha _{3}\) to \(\alpha _{9}\)
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Table 11 \(\widetilde{\mathcal {E}}(\gamma _{_{i}}, \gamma _{_{i+1}})\) and associated \(\sigma ^{{\rm T}}_{\mathcal {E}}\) of all successive trails from \(\alpha _{3}\) to \(\alpha _{9}\)
Full size table

Appendix 3

See Table 12.

Table 12 Average value, standard deviation and coefficient of variation of all paths from \(\alpha _{3}\) to \(\alpha _{9}\)
Full size table

Appendix 4

See Table 13.

Table 13 \(\widetilde{\mathcal {H}}(\gamma _{_{i-1}}, \gamma _{_{i}})\) and associated \(\sigma ^{{\rm P}}_{\mathcal {H}}\) of all successive trails from \(\alpha _{3}\) to \(\alpha _{9}\)
Full size table

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Guo, L., Jia, Z., Li, Q. et al. Steadiness analysis of means-end conceptual paths and problem-chains based on concept lattices and similarity measuring. Int. J. Mach. Learn. & Cyber. 13, 691–719 (2022). https://doi.org/10.1007/s13042-021-01309-5

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