Journal of Electronic Science and Technology, Volume. 22, Issue 2, 100262(2024)
Enhancing personalized exercise recommendation with student and exercise portraits
Figures & Tables(12)
Fig. 1. Exercise recommendation: (a) students’ mastery of knowledge with past response records and (b) difficulty of exercises pertinent to each knowledge concept and the exercises-knowledge concepts indication.
Fig. 2. Model framework of the presented PER, which consists of three main tasks: (a) finer-grained portrait of the student and the exercise construction of CSEG, (b) importance ranking of the exercises through a joint random walk, and (c) final list of exercise recommendations with multi-objective optimization.
Fig. 5. Impacts of the candidate, i.e., top-
Fig. 6. Performance comparison with the change in the student (exercise) similarity threshold .
Table 1. Several important mathematical notations.
View tableView in ArticleTable 1. Several important mathematical notations.
Notation Description S, E, K The set of students/exercises/knowledge concepts R Student exercise response matrix Q Exercise and knowledge concept incidence matrix ms The degree of student mastery of knowledge concept cs The knowledge concept coverage of student response de The exercise difficulty qe The knowledge association W s,W eThe student/exercise similarity matrix J The probability transition matrix D0 The set of candidate exercises D The final list of recommended exercises
Table 2. Description of PERP algorithm.
View tableView in ArticleTable 2. Description of PERP algorithm.
Algorithm 1: PERP algorithm Input: R, Q Output: Final recommendation list D 1. A, B $ \leftarrow $ training NeuralCD model;2. for i = 0 to N do 3. ${{\bf{m}}_{{s_i}}} = {{\mathrm{softmax}}} \left( {{\bf{x}}_{{s_i}}^{\mathrm{T}}{\bf{A}}} \right)$ 4. ${{\bf{c}}_{{s_i}}} = {{\mathrm{softmax}}} \left( {{{\bf{x}}_{{s_i}}}{\bf{RQ}}} \right)$ 5. end for 6. Ws $ \leftarrow $ student similarity matrix;7. for j = 0 to M do 8. ${{\bf{d}}_{{e_j}}} = {{\mathrm{sigmoid}}} \left( {{\bf{x}}_{{e_j}}^{\rm{T}}{\bf{B}}} \right)$ 9. ${{\bf{q}}_{{e_j}}} = {\bf{x}}_{{e_j}}^{\mathrm{T}}{\bf{Q}}$ 10. ${{\bf{e}}_j} = { {\bf{d} }_{ {e_j} } } \odot { {\bf{q} }_{ {e_j} } }$ 11. end for 12. We $ \leftarrow $ exercise similarity matrix;13. J $ \leftarrow $ transition probability matrix J by (7);14. for j = 0 to t do 15. ${\bf{v}}_s^{t + 1} = \beta {\bf{Jv}}_s^t + (1 - \beta ){\bf{v}}_s^0$ 16. end for 17. D0 $ \leftarrow $ choose exercises with the top-P largest scores;18. while termination criterion is not satisfied do 19. D1 $ \leftarrow $ the top-L exercises of D0;20. D2 $ \leftarrow $ replace some of the exercises in D1;21. $ {\bf{D}}_1' $ $ \leftarrow $ distance matrix of the exercises in D1;22. ${\bf{D}}_2' $ $ \leftarrow $ distance matrix of the exercises in D2;23. if ${\bf{D}}_1' $ >${\bf{D}}_2' $ 24. D1 $ \leftarrow $ D225. else 26. $\gamma = \exp \left( {\frac{ { - \left( { {{\rm{mean}}} \left( {{\bf{D}}_2^\prime } \right)} \right) - \left( { {{\rm{mean}}} \left( {{\bf{D}}_1^\prime } \right)} \right)} }{ { {k_B}T} } } \right)$ 27. r $ \leftarrow $ random(0, 1)28. if r > $\gamma $ 29. D1 $ \leftarrow $ D230. else 31. D1 $ \leftarrow $ D132. end if 33. end if 34. end while 35. D $ \leftarrow $ largest distance
Table 3. Real dataset statistics.
View tableView in ArticleTable 3. Real dataset statistics.
Dataset ASSISTments 2009-2010 Algebra 2006-2007 Students 4163 1338 Exercises 17746 91771 Knowledge concepts 123 491 Records 278607 222314
Table 4. Performance of all methods on all datasets.
View tableView in ArticleTable 4. Performance of all methods on all datasets.
Model ASSISTments 2009-2010 Algebra 2006-2007 Novelty Accuracy Diversity Novelty Accuracy Diversity KNN 0.934 0.888 0.254 0.783 0.747 0.407 KGEB-CF 0.912 0.879 0.524 0.676 0.631 0.674 MBHT 0.946 0.893 0.343 0.798 0.859 0.468 DKT 0.602 0.880 0.466 0.621 0.855 0.583 NeuralCD 0.583 0.894 0.495 0.645 0.859 0.668 DTransformer 0.713 0.892 0.452 0.661 0.861 0.516 HB-DeepCF 0.914 0.823 0.758 0.739 0.695 0.619 KCP-ER 0.957 0.895 0.765 0.818 0.863 0.743 PERP 0.959 0.897 0.781 0.821 0.865 0.758
Table 5. Right and wrong answer recommendations on the ASSISTments 2009-2010 dataset.
View tableView in ArticleTable 5. Right and wrong answer recommendations on the ASSISTments 2009-2010 dataset.
ASSISTments 2009-2010 PERP+ PERP– Novelty 0.959 0.961 Accuracy 0.897 0.887 Diversity 0.781 0.779
Table 6. Student with ID.219 answered and recommended the situation.
View tableView in ArticleTable 6. Student with ID.219 answered and recommended the situation.
Exercise number Knowledge concepts Actual answer records 7,33,960, 962,1098, 1831,3090, 3102,3145, 3151,7398, 7465,7516, 8724,8729, 10274,12339, 12358,12811, 17125,17162 Equation solving, Histogram as table or graph, Number line, Line plot, Stem and leaf plot, Table, Mode, Addition and subtraction fractions, Ordering fractions, Conversion of fraction decimals percents, Finding percents, Scale factor, Unit rate, Pattern finding KNN 8318,8306, 8304,8252, 14864,8254 Multiplication and division integers, Addition whole numbers, Division fractions NeuralCD 10224,52, 70,8286,37, 7380,8307 Equation solving, Stem and leaf plot, Addition and subtraction fractions, Circle graph, Finding percents PERP 196,246, 202,235, 184,200 Box and whisker, Congruence, Ordering integers, Square root, Equivalent fractions
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Wei-Wei Gao, Hui-Fang Ma, Yan Zhao, Jing Wang, Quan-Hong Tian. Enhancing personalized exercise recommendation with student and exercise portraits[J]. Journal of Electronic Science and Technology, 2024, 22(2): 100262
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Received: Jul. 3, 2023
Accepted: May. 31, 2024
Published Online: Aug. 8, 2024
The Author Email: Ma Hui-Fang (mahuifang@yeah.net)
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