1. 2023 55 4 Journal of South China Normal University Natural Science Edition 1 1． 81－86 doi 10．6054 / j．jscnun．2023052 1* 2 1 510631 2． 430062 DKT－DE 。 。 DKT－DE SISTments2017 。 5 3 ASSISTments2009、 ASSISTments2015、 AS- BKT、 DKT、 DKT+、 DKVMN、 SAKT DKT－DE DKT－DE DKT+ ASSISTments2009、 ASSISTments2015、 ASSISTments2017 AUC 2．78%、 2．44%、 1．5%。 。 TP391 A 1000－5463 2023 04－0081－06 Deep Knowledge Tracing Model by Integrating Problem Difficulty and Answering Experience LIANG Xiang 1 LIU Mengchi 1* HU Jie 2 FENG Jiamei 1 1． Department of Computer Science South China Normal University Guangzhou 510631 China 2． Department of Computer and Information Engineering Hubei University Wuhan 430062 China Abstract Aiming at the problem that the existing deep knowledge tracking model lacks comprehensive considera- tion of exercises and student characteristic information． A deep knowledge tracking model by integrating problem difficulty and answering experience DKT －DE is proposed． The model evaluates the difficulty of the exercises and the students' answering experience by analyzing the answer sequence to enrich the feature information of the input layer of the model thereby improving the prediction performance of the model． Finally the DKT － DE model was compared with five baseline models BKT DKT DKT + DKVMN SAKT model through comparative experiments and ablation experiments on three public datasets ASSISTments2009 ASSISTments2015 ASSISTments2017 ． The comparative experiment results demonstrate that the DKT －DE model can more accurately assess students' knowledge mastery． Compared with the best －performing baseline model DKT + the DKT －DE model achieves an average AUC improvement of 2． 78% 2． 44% and 1． 5% on the ASSISTments2009 ASSISTments2015 and ASSISTments2017 datasets respectively． The ablation experiment results further confirm the positive contributions of incorporating question difficulty and student response experience to enhance the predictive capability of the model． Keywords educational data mining knowledge tracking deep learning student model intelligent education 、 。 gent Tutoring Systems ITS ITS 。 2021－10－11 《 》 61672389 * Email liumengchi@ scnu．edu．cn http ∥journal －n．scnu．edu．cn 201905010009 1 Intelli- 。

2. 55 8 2 2 ITS Knowledge Tra- 。 cing KT ITS Deep Knowledge Tracing Model by Integrating Problem Difficulty and Answering Experience DKT － DE 。 。 Bayesian Knowledge Tracing Hidden Markov BKT 3 Model HMM 。 DKT －DE 1 1．1 。2015 PIECH Ｒecurrent Neu- 4 ral Network ＲNN Deep Knowledge Tracing DKT 。 ＲNN DKT BKT DKT 。 DKT 。 x 0 … x t s t Q i 1 1．2 。 5 WANG DKT archical Knowledge Tracing DHKT Deep Knowledge Tracing PDKT 。 MINN i 0 ＲNN 。 One － Hot = x t q t r t t x t y t h t 。 h t Deep Hier- 6 CHEN DKT Prerequisite Driven 。 2 PIECH DKT DKT 。 r t+ 1 。 DKT 2015 。 q t+ 1 = Q x i = q i r i q i = Q id r i = 0 1 。 t h t－ 1 t t 1．3 10 。 7 。 K － mean DKT NAGATANI 。 8 。 10 9 LFKT 。 D q j = { 。 φ q j a a [ Σ N j φ q j a = i= 0 。 D q j | N j | ≥ 10 | N j | ＜10 | r ij = 0 | N j q j = Q ] 1 a － 1 Q

3. 4 8 3 d j =R a One － Hot q j D q j N j r ij i 0 D q j DKT r ij = q j 。 10 a。 a 。 DKT － DE 、 。 q j q j 2 e t d t =R a 1 z = Σ c jt = 1 t= 1 z 1 z = Σ c jt = 0 t= 1 E c j 1 z = Correct c j F c j 1 z 1 z Correct c j 1 z b { = － b b 1 z 1 z －Incorrect c j 1 z | F c j 1 z | ＜b F c j 1 z ≤ － b F c j 1 z ≥ b Incorrect c j 1 z c j = C C b =N + 2 E c j 1 z t －1 。x' t x t =R x' t = Embedding q t r t F c j 1 z E c j 1 z = － b One － Hot 3 1 q t 1 t h t = LSTM x t h t－1 。 4 m c j e jz =R 2b+1 c t 2b+1 x t = Concat x' t d t e t t－1 x' t Embedding t q t t id r t = 0 1 0 c t t id t － 1。 LSTM h t =R k k 。h t x t h t－ 1 z F c j x' t =R g 、 t 。 Incorrect c j 、 x t q t Correct c j 3 。 y t =R t Q 。y t y t = σ W yh h t + b y m m × k 2 ASSISTments2009、 ASSISTments2015、 AS- SISTments2017 b 8。 1 。 W yh =R σ · Sigmoid 5 b y =R 。 m y t r t 。 L =－ Σ r t log y t + 1 － r t log 1 － y t 。 t 1 Figure 1 The relationship between the answer experience value and the correct rate 1．4 DKT 。DKT －DE 2 Figure 2 DKT－DE Structure diagram of DKT－DE model 6

4. 55 8 4 Embedding size 2 m 。 a DKT － DE 3 5 log 2 m 10 b 8。 2．3 AUC DKT －DE 16 Area Under the ＲOC Curve 。 。AUC ＲOC 2．1 0 ～ 1。 ASSITments2009 SITments2015 12 ASSITments2017 13 11 、 AS- AUC 0．5 AUC 1 。 。 2．4 1 ASSISTments2009 ments ASSIST- 3 2009—2010 5 skill － builder 325 637 DKT － DE 。 4 151 5 。 2 ASSISTments2015 AUC AS- 。 1 2015—2016 SISTments BKT、 DKT、 DKVMN、 DKT + 、 SAKT 。 、 110 DKT － DE 2．4．1 1 。 0 1 19 840 、 100 683 801 BKT 。 2 DKT 3 17 DKVMN 。 18 － 19 20 。 3 DKT + ASSISTments2009 。 3 ASSISTments2017 DKT + ASSISTments 686 942 816 DKT ASSITments2009、ASSITments2015、ASSITments2017 、 102 AUC 。 、 0．80%、 1．79% 1．67%。 4 。 DKT、 DKVMN DKT － DE DKT 8∶2 5 mini － batch 32 Dropout batch － size AUC ASSITments2009、 ASSITments2015、 ASSITments2017 AUC 0． 005 15 2．78%、 2． 44%、 DKT － DE 1．50% 0．4。 ASSITments2009、 3．60%、 4．28%、 3．19% DKT + DKT － DE 。 14 200 。 5 ASSITments2015、 ASSITments2017 80% 20% 18 SAKT 2．2 Adam DKT 。 Embedding 1 Table 1 3 AUC Average AUC of each model on the test set AUC BKT DKT DKVMN DKT+ SAKT DKT－DE ASSISTments2009 0．624 0．749 0．747 0．755 0．742 0．776 ASSISTments2015 0．642 0．723 0．721 0．736 0．719 0．754 ASSISTments2017 0．635 0．719 0．711 0．731 0．678 0．742

5. 4 8 5 2．4．2 ASSIT- 3 ments2009、 ASSITments2015、 ASSITments2017 DKT － 。 DE DKT DKT DKT － Diff DKT DKT －Exp 。 DKT －DE 。 2 。 DKT － DE 2 DKT － DE DKT － Diff DKT －Exp 。 。 2 Table 2 Ｒesults of ablation experiments DKT － DE AUC DKT－Diff DKT－Exp 。 DKT－DE ASSISTments2009 0．758 0．763 0．776 ASSISTments2015 0．730 0．746 0．754 ASSISTments2017 0．733 0．734 0．742 。 2．5 1 Assistments2009 DKT － DE 。 M ． San Francisco Margan Kaufmann 2010． 3 2 t t +1 r t WOOLF B P． Building intelligent interactive tutors student－centered strategies for revolutionizing e－learning q t PIECH C HUANG J NGUYEN A et al． Learning pro- gram embeddings to propagate feedback on student code C ∥ Proceedings of the 32nd International Conference 。 on Machine Learning． Lille PMLＲ 2015 1093－1102． 3 COＲBETT A T ANDEＲSON J Ｒ． Knowledge tracing mode- lling the acquisition of procedural knowledge J ． User 。 Modeling and User － Adapted Interaction 1995 4 253 － 278． 。 4 PIECH C SPENCEＲ J HUANG J et al． Deep knowledge tracing J ． Computer Science 2015 3 3 5 19－23． WANG T MA F GAO J． Deep hierarchical knowledge tracing C ∥ Proceedings of the 12th International Con- ference on Educational Data Mining． Worcester IEDMS 2019 1－4． 6 CHEN P LU Y ZHENG V W et al． Prerequisite－driven deep knowledge tracing C ∥ Proceedings of the 2018 IEEE International Conference on Data Mining． Piscata- way IEEE 2018 39－48． 7 MINN S YU Y DESMAＲAIS M C et al． Deep knowledge tracing and dynamic student classification for knowledge 3 Figure 3 tracing C ∥Proceedings of the 2018 IEEE International Heat map of knowledge mastery Conference on Data Mining． Piscataway IEEE 2018

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