Learning Paths and Skills Assessment in Formal Context
ZHOU Yinfeng1, LI Jinjin1,2, FENG Danlu1, YANG Taoli1
1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000; 2. Fujian Key Laboratory of Granular Computing and Application, Minnan Normal University, Zhangzhou 363000
Abstract：In the learning process, learners may learn and master some skills with their knowledge state unchanged. In this situation, learners' skills cannot be assessed accurately due to the unchanged knowledge state. In this paper, a method of formal concept analysis is employed based on the skill function to find learning paths and conduct skills assessment. Firstly, the concepts of subsequent state, effective skill and well-formed skill function are introduced. Secondly, based on the formal context, the conditions that the skill functions satisfy the well-formedness are discussed in two situations. The results of gradual effective learning and effective assessment are obtained under the well-formedness conditions, and the algorithms for obtaining the well-formed skill contexts and the well-formed skill functions and finding learning paths are designed. Finally, the effectiveness of the proposed algorithms is verified on two datasets. The learning paths diagram obtained by the well-formed skill function can not only guide the learners to study effectively but also evaluate whether the learners master the corresponding effective skills according to the change of the learners' knowledge states.
[1] WILLE R.Restructuring Lattice Theory: An Approach Based on Hie-rarchies of Concepts // Proc of the International Conference on Formal Concept Analysis. Berlin,Germany: Springer, 2009: 314-339. [2] 马垣,曾子维,迟呈英,等.形式概念分析及其新进展.北京:科学出版社, 2011. (MA Y, ZENG Z W, CHI C Y, et alFormal Concept Analysis and Its New Progress. Beijing, China: Science Press, 2011.) [3] ZUPA B, BOHANCE M, DEMŠAR J, et al.Learning by Discovering Concept Hierarchies. Artificial Intelligence, 1999, 109(1/2): 211-242. [4] 张云中,柳迪,张原铭.基于形式概念分析的知识发现研究态势.情报科学, 2018, 36(9): 153-158. (ZHANG Y Z, LIU D, ZHANG Y M.Research Trend of Know-ledge Discovery Based on Formal Concept Analysis. Information Science, 2018, 36(9): 153-158.) [5] VALTCHEV P, MISSAOUI R, GODIN R, et al. Generating Frequent Itemsets Incrementally: Two Novel Approaches Based on Galois Lattice Theory. Journal of Experimental and Theoretical Artificial Intelligence, 2002, 14(2/3): 115-142. [6] DOIGNON J P, FALMAGNE J C.Spaces for the Assessment of Knowledge. International Journal of Man Machine Studies, 1985, 23(2): 175-196. [7] HELLER J, MAYER B, HOCKEMEYER C,et al. Competence-Based Knowledge Structures for Personalised Learning. International Journal on E-learning, 2006, 5(1): 75-86. [8] STEINER C M, NUSSBAUMER A, ALBERT D.Supporting Self-Regulated Personalised Learning through Competence-Based Know-ledge Space Theory. Policy Futures in Education, 2009, 7(6): 645-661. [9] DOBLE C, MATAYOSHI J, COSYN E, et al. A Data-Based Simulation Study of Reliability for an Adaptive Assessment Based on Knowledge Space Theory. International Journal of Artificial Intelligence in Education, 2019, 29(2): 258-282. [10] REDDY A A, HARPER M.ALEKS-Based Placement at the University of Illinois // FALMAGNE J C, ALBERT D, DOBLE C, et al., eds. Knowledge Spaces: Applications in Education. Berlin, Germany: Springer, 2013: 51-68. [11] SITTHISAK O, GILBERT L, ALBERT D.Adaptive Learning Using an Integration of Competence Model with Knowledge Space Theory // Proc of the 2nd IIAI International Conference on Advanced Applied Informatics. Washington, USA: IEEE, 2013: 199-202. [12] RUSCH A, WILLE R.Knowledge Spaces and Formal Concept Ana-lysis // BOCK H H, POLASEK W, eds. Data Analysis and Information Systems. Berlin, Germany: Springer, 1996: 427-436. [13] YAO Y Y, MIAO D Q, XU F F.Granular Structures and Approximations in Rough Sets and Knowledge Spaces// ABRAHAM A, FALCÓN R, BELLO R, eds. Rough Set Theory: A True Landmark in Data Analysis. Berlin, Germany: Springer, 2009: 71-84. [14] 王国胤,姚一豫,于洪.粗糙集理论与应用研究综述.计算机学报, 2009, 32(7): 1229-1246. (WANG G Y, YAO Y Y, YU H.A Survey on Rough Set Theory and Applications. Chinese Journal of Computers, 2009, 32(7): 1229-1246.) [15] 李进金,孙文. 知识空间,形式背景和知识基.西北大学学报(自然科学版), 2019, 49(4): 517-526. (LI J J, SUN W.Knowledge Space, Formal Context and Know-ledge Base. Journal of Northwest University (Natural Science Edition), 2019, 49(4): 517-526.) [16] DOIGNON J P.Knowledge Spaces and Skill Assignments// FISCHER G H, LAMING D, eds. Contributions to Mathematical Psychology, Psychometrics, and Methodology. Berlin, Germany: Springer, 1994: 111-121. [17] DUNTSCH I, GEDIGA G.Skills and Knowledge Structures. British Journal of Mathematical and Statistical Psychology, 1995, 48(1) : 9-27. [18] HELLER J, AUGUSTIN T, HOCKEMEYER C, et al. Recent Developments in Competence-Based Knowledge Space Theory// FALMAGNE J C, ALBERT D, DOBLE C, et al., eds. Know-ledge Spaces. Berlin, Germany: Springer, 2013: 243-286. [19] STEFANUTTI L, DE CHIUSOLE D D. On the Assessment of Lear-ning in Competence Based Knowledge Space Theory. Journal of Mathematical Psychology, 2017, 80: 22-32. [20] DOIGNON J P, FALMAGNE J C. Knowledge Spaces. Berlin, Germany: Springer, 1999. [21] FALMAGNE J C, DOIGNON J P.Learning Spaces: Interdisciplinary Applied Mathematics. Berlin, Germany: Springer, 2011. [22] FALMAGNE J C, ALBERT D, DOBLE C, et al. Knowledge Spaces: Applications in Education. Berlin, Germany: Springer, 2013. [23] XU F F, MIAO D Q, YAO Y Y, et al. Analyzing Skill Sets with Or-Relation Tables in Knowledge Spaces // Proc of the 8th IEEE International Conference on Cognitive Informatics. Washington, USA: IEEE, 2009: 174-180. [24] 高纯,王睿智.知识空间理论析取模型下最小技能集的生成.计算机科学与探索, 2010, 4(12): 1109-1114. (GAO C, WANG R Z.The Formation of Minimal Skill Set in Disjunctive Model of Knowledge Space Theory. Journal of Frontiers of Computer Science and Technology, 2010, 4(12): 1109-1114.) [25] SPOTO A, STEFANUTTI L, VIDOTTO G.Knowledge Space Theo-ry, Formal Concept Analysis, and Computerized Psychological Assessment. Behavior Research Methods, 2010, 42(1): 342-350. [26] 周银凤,李进金.形式背景下的技能约简与评估[J/OL]. [2021-04-26]. https://kns.cnki.net/kcms/detail/11.5602.tp.20210128.0926.002.html. (ZHOU Y F, LI J J. Skill Reduction and Assessment in Formal ContextJ/OL]. [2021-04-26]. https://kns.cnki.net/kcms/detail/11.5602.tp.20210128.0926.002.html.) [27] HELLER J, ÜNLÜ A, ALBERT D.Skills, Competencies and Know-ledge Structures // FALMAGNE J C, ALBERT D, DOBLE C, et al., eds. Knowledge Spaces. Berlin, Germany: Springer, 2013: 229-242. [28] HELLER J, STEFANUTTI L, ANSELMI P, et al. On the Link Between Cognitive Diagnostic Models and Knowledge Space Theory. Psychometrika, 2015, 80: 995-1019. [29] HELLER J, STEFANUTTI L, ANSELMI P, et al. Erratum to: On the Link Between Cognitive Diagnostic Models and Knowledge Space Theory. Psychometrika, 2016, 81: 250-251. [30] HELLER J, ANSELMI P, STEFANUTTI L, et al. A Necessary and Sufficient Condition For Unique Skill Assessment. Journal of Mathematical Psychology, 2017, 79: 23-28. [31] HOCKEMEYER C, CONLAN O, WADE V, et al. Applying Competence Prerequisite Structures for eLearning and Skill Management. Journal of Universal Computer Science, 2003, 9(12): 1428-1436. [32] DE CHIUSOLE D D, STEFANUTTI L, ANSELMI P, et al. Stat-Knowlab. Assessment and Learning of Statistics with Competence-Based Knowledge Space Theory. International Journal of Artificial Intelligence in Education, 2020, 30: 668-700. [33] 李金海,闫梦宇,徐伟华,等.概念认知学习的若干问题与思考.西北大学学报(自然科学版), 2020, 50(4): 501-515. (LI J H, YAN M Y, XU W H, et al. Some Problems and Thoughts on Concept-Cognitive Learning. Journal of Northwest University(Natural Science Edition), 2020, 50(4): 501-515.) [34] 李金海,米允龙,刘文奇.概念的渐进式认知理论与方法.计算机学报, 2019, 42(10): 2233-2250. (LI J H, MI Y L, LIU W Q.Incremental Cognition of Concepts: Theories and Methods. Chinese Journal of Computers, 2019, 42(10): 2233-2250.) [35] KICKMEIER-RUST D M, STEINER C M, ALBERT D. Uncovering Learning Processes Using Competence-Based Knowledge Structuring and Hasse Diagrams[C/OL]. [2021-04-26]. http://ceur-ws.org/Vol-1518/paper7.pdf. [36] GANTER B, WILLE R.Formal Concept Analysis: Mathematical Foundations. Berlin, Germany: Springer, 1999. [37] DUNTSCH N, GEDIGA G.Modal-Style Operators in Qualitative Data Analysis // Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2002: 155-162. [38] SUN W, LI J J, GE X, et al. Knowledge Structures Delineated by Fuzzy Skill Maps. Fuzzy Sets and Systems, 2021, 407: 50-66.
2021, Vol. 34 
