Neural-Symbolic Knowledge Tracing: Injecting Educational Knowledge into Deep Learning for Responsible Learner Modelling
Authors: Danial Hooshyar, Gustav Šír, Yeongwook Yang, Tommi Kärkkäinen, Raija Hämäläinen, Ekaterina Krivich, Mutlu Cukurova, Dragan Gašević, Roger Azevedo
Organizations: School of Digital Technologies Tallinn University, Estonia · Faculty of Information Technology University of Jyväskylä Finland · Faculty of Education and Psychology University of Jyväskylä Finland · Department of Computer Science Czech Technical University Czech Republic · Department of Computer Science and Engineering Kangwon National University Republic of Korea · School of Digital Technologies Tallinn University Estonia · UCL Knowledge Lab UCL Centre for Artificial Intelligence University College London UK · Faculty of Education School of Computing and Data Science The University of Hong Kong · Centre for Learning Analytics Monash University Australia · School of Modeling Simulation and Training University of Central Florida US
The growing use of artificial intelligence (AI) in education, particularly large language models (LLMs), has increased interest in intelligent tutoring systems. However, LLMs often show limited adaptivity and struggle to model learners' evolving knowledge over time, highlighting the need for dedicated learner modelling approaches. Although deep knowledge tracing methods achieve strong predictive performance, their opacity and susceptibility to bias can limit alignment with pedagogical principles. To address this, we propose Responsible-DKT, a neural-symbolic deep knowledge tracing approach that integrates symbolic educational knowledge (e.g., mastery and non-mastery rules) into sequential neural models for responsible learner modelling. Experiments on a real-world dataset of students' math interactions show that Responsible-DKT outperforms both a neural-symbolic baseline and a fully data-driven PyTorch DKT model across training settings. The model achieves over 0.80 AUC with only 10% of training data and up to 0.90 AUC, improving performance by up to 13%. It also demonstrates improved temporal reliability, producing lower early- and mid-sequence prediction errors and the lowest prediction inconsistency rates across sequence lengths, indicating that prediction updates remain directionally aligned with observed student responses over time. Furthermore, the neural-symbolic approach offers intrinsic interpretability via a grounded computation graph that exposes the logic behind each prediction, enabling both local and global explanations. It also allows empirical evaluation of pedagogical assumptions, revealing that repeated incorrect responses (non-mastery) strongly influence prediction updates. These results indicate that neural-symbolic approaches enhance both performance and interpretability, mitigate data limitations, and support more responsible, human-centered AI in education.
Figures & tables
Figure 1: Architecture of the proposed Responsible-DKT approach.
Symbol
Meaning
D
Student interaction dataset
U∈{u1,u2,…,u∣U∣}
Set of students
Q∈{q1,q2,…,q∣Q∣}
Set of quizzes
S∈{s1,s2,…,s∣S∣}
Set of skills
t
Discrete timestep within a student’s interaction sequence
xt=(st,qt,yt)
Input tuple with skill, quiz, and correctness at timestep t
Table 1: Notation.
Statistic
Original
Train
Val
Test
# of records (interactions)
21471.0
14057.0
2969.0
4428.0
# of students
167.0
105.0
15.0
30.0
# of quizzes
1058.0
939.0
565.0
647.0
# of skills
13.0
13.0
12.0
13.0
Avg. interactions per student
128.57
133.88
197.93
147.6
Avg. interactions per quiz
20.29
14.97
5.25
6.84
Table 2: Descriptive statistics of the dataset.
Sequence length statistic
Value
Min
1
Q1
5.0
Median
46.0
Mean
128.57
Q3
193.0
Max
1437
Table 3: Summary statistics of student interaction sequence lengths.
Figure 2: Cumulative distribution function of student interaction sequence lengths.
Models
Training ratio (%)
N
Metrics
AUC
Accuracy
Precision
Recall
F1-score
Low
High
Low
High
Low
High
BaseNS-DKT
10
10
0.56
0.76
0.10
0.79
0.02
0.95
0.03
0.86
50
0.68
0.79
0.09
0.80
0.01
0.99
0.01
0.88
100
0.71
0.76
0.55
0.77
0.08
0.98
0.14
0.86
Full
0.77
0.82
0.62
0.84
0.27
0.96
0.38
0.89
Table 4: Performance comparison of the models across varying sequence lengths and training ratios.
Models
Sequence length
Early
Middle
Late
BaseNS-DKT
10
22.97
20.78
24.69
50
24.03
18.27
19.16
100
22.25
21.11
27.82
Full
21.15
16.12
16.56
Responsible-DKT
10
17.57
10.39
18.52
50
15.58
13.46
11.98
Table 5: Early-, middle-, and late-stage prediction error rates (%) across different sequence lengths.
Models
Sequence length
Volatility
Inconsistency
BaseNS-DKT
10
0.12
0.48
50
0.09
0.46
100
0.11
0.43
Full
0.11
0.44
Responsible-DKT
10
0.18
0.41
50
0.17
0.40
Table 6: Volatility and inconsistency of predicted mastery trajectories across different sequence lengths.
Figure 3: Step-wise predicted probabilities for repeated attempts of a single skill ( Addition and subtraction of fractions ) by one student. Each column represents a quiz interaction involving the same skill, with ✓ indicating a correct response and × an incorrect response.
Figure 4: Grounded neural-symbolic computation graph for predicting correct(t1,q954) . House nodes denote grounded input facts (quiz, skill, and prior correctness), which are first integrated into a unified representation via combined_embed(T) , where quiz, skill, and outcome embeddings are merged. The yellow-highlighted nodes indicate the three main predictive pathways contributing to the target: the recurrent neural pathway (left), the symbolic mastery pathway (right), and the historical aggregation pathway (middle). These components are aggregated at the final output node to produce the predicted probability of correctness.
Figure 5: Local explanation of Responsible-DKT predictions for a student sequence on skill s3 ( addition and subtraction of fractions ), showing contributions of previous interactions to predictions at timesteps 5 and 10 (left and right, respectively).
Figure 6: Global explanation of the Responsible-DKT model predictions.
Rule
Avg ∣val∣∗
Avg ∣grad∣∗∗
Count
avg_embed
1.9947
0.0008
284
mastered
1.6692
0.0004
219
not_mastered
1.8557
0.0016
49
∗∣val∣ : average absolute rule activation (strength of contribution during forward computation).
∗∗∣grad∣ : average absolute gradient (sensitivity of model predictions to that rule).
Table 7: Global importance of symbolic rules in the Responsible-DKT model.
1Shanghai Institute of AI Education, East China Normal University, Shanghai, 200241, China · 2Shool of Computer Sicence and Technology, East China Normal University, Shanghai, 200241, China