Enhancing personalized exercise recommendation with student and exercise portraits

Wei-Wei Gao; Hui-Fang Ma; Yan Zhao; Jing Wang; Quan-Hong Tian

doi:10.1016/j.jnlest.2024.100262

Journals >Journal of Electronic Science and Technology >Volume 22 >Issue 2 >Page 100262 > Article

Journal of Electronic Science and Technology
Vol. 22, Issue 2, 100262 (2024)

Enhancing personalized exercise recommendation with student and exercise portraits

Wei-Wei Gao¹, Hui-Fang Ma^1,*, Yan Zhao¹, Jing Wang¹, and Quan-Hong Tian²

Author Affiliations

¹College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730070, China

²Computer Center of Gansu Province, Lanzhou, 730070, China

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DOI: 10.1016/j.jnlest.2024.100262 Cite this Article

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 Copy Citation Text

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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. 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.

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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. 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.

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Fig. 3. Influence of similar students (exercises).

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Fig. 4. Influence of portraits of students (exercises).

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Fig. 5. Impacts of the candidate, i.e., top-P (recommendation), i.e., top-L (exercise) number on performance.

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Fig. 6. Performance comparison with the change in the student (exercise) similarity threshold .

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Notation	Description
S, E, K	The set of students/exercises/knowledge concepts
R	Student exercise response matrix
Q	Exercise and knowledge concept incidence matrix
m^s	The degree of student mastery of knowledge concept
c^s	The knowledge concept coverage of student response
d^e	The exercise difficulty
q^e	The knowledge association
W^s, W^e	The student/exercise similarity matrix
J	The probability transition matrix
D₀	The set of candidate exercises
D	The final list of recommended exercises

Table 1. Several important mathematical notations.

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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 $D2
25. 　　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 $D2
30. 　　　else
31. 　　　　D1$ \leftarrow $D1
32. 　　　end if
33. 　　end if
34. 　end while
35. 　D$ \leftarrow $largest distance

Table 2. Description of PERP algorithm.

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Dataset	ASSISTments 2009-2010	Algebra 2006-2007
Students	4163	1338
Exercises	17746	91771
Knowledge concepts	123	491
Records	278607	222314

Table 3. Real dataset statistics.

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Model	ASSISTments 2009-2010			Algebra 2006-2007
Model	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 4. Performance of all methods on all datasets.

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ASSISTments 2009-2010	PERP+	PERP–
Novelty	0.959	0.961
Accuracy	0.897	0.887
Diversity	0.781	0.779

Table 5. Right and wrong answer recommendations on the ASSISTments 2009-2010 dataset.

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	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