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Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations

Sein MinnJill-Jênn VieKoh TakeuchiHisashi KashimaFeida Zhu

article2022AAAI61 citations

Proposes an interpretable knowledge tracing model that combines skill mastery, cross-skill learning transfer, and problem difficulty within a Tree-Augmented Naive Bayes classifier to outperform deep learning approaches while providing clear causal explanations of student learning.

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Online and intelligent tutoring platforms rely heavily on knowledge tracing—the ability to model a learner's skill mastery over time and predict whether they will answer future exercises correctly. While modern deep-learning models achieve strong predictive accuracy, they function as complex "black boxes" with tens of thousands of opaque parameters. This lack of interpretability prevents educators and system designers from understanding why a student succeeded or failed, hindering the delivery of meaningful, diagnostic instructional interventions.

The article demonstrates a novel student modeling framework called Interpretable Knowledge Tracing (IKT). The main objective is to evaluate whether a transparent, probabilistic graphical model can outperform complex neural networks in predicting student performance while providing clear, psychologically grounded causal explanations.

To achieve this, the approach uses standard data mining methods to extract three interpretable latent factors from student interaction logs: individual skill mastery (estimated via traditional sequential modeling), dynamic ability profiles that capture cross-skill learning transfer (grouped via clustering algorithms over rolling 20-attempt windows), and problem difficulty (scaled from 1 to 10 based on historical first-attempt failure rates). These features are integrated into a Tree-Augmented Naive Bayes classifier, which captures the dependencies among features to forecast future answers. The approach was tested against established baseline models across three large public tutoring datasets comprising up to 28,834 students and over 2.5 million interaction records.

The evaluation produced several key findings. First, IKT consistently outperformed or matched all state-of-the-art deep-learning models across the benchmark datasets, reaching an average Area Under the Curve (AUC) of 0.805 and lower error rates. Second, ablation analysis revealed that problem difficulty is by far the most influential factor in forecasting success, driving an absolute predictive improvement of 11.2% to 15.7% in AUC. Third, tracking dynamic student ability profiles provided modest additional predictive gains (up to 1.4% in AUC) by accounting for general learning transfer across different skills.

These results demonstrate that organizations deploying intelligent tutoring systems do not need to sacrifice model interpretability to achieve cutting-edge predictive power. By replacing resource-heavy deep neural networks with probabilistic graphical models, educational platforms can significantly reduce computational training costs, lower infrastructure overhead, and improve operational transparency. Furthermore, the model's conditional probability structure provides clear causal pathways, allowing systems to diagnose whether a student's incorrect answer stemmed from a genuine skill deficiency or an exceptionally difficult problem.

For educational technology leaders and system developers, the article supports adopting feature-driven probabilistic models like IKT within personalized curriculum engines. Future work should focus on field-testing these causal insights in live instructional environments to guide real-time adaptive interventions. Platform managers should, however, note the primary operational limitation: the model requires discrete data bins, relies on having at least a few prior student attempts to reliably estimate item difficulty, and initiates ability profiling only after an initial baseline of student activity.

intelligent tutoring systemstudent modelinginterpretable knowledge tracingstudent modelingcausal relations
arXiv: 2112.11209
  • Paper: The Mythos of Model Interpretability, Zachary C. Lipton (2016). This paper establishes the foundational conceptual framework distinguishing transparent, interpretable-by-design models from post-hoc explanations, motivating the design philosophy behind Interpretable Knowledge Tracing.
  • Paper: Concept Bottleneck Models, Pang Wei Koh et al. (2020). This work introduces the methodology of using interpretable intermediate latent concepts to drive final predictions, directly informing how student mastery and difficulty profiles are extracted for transparent modeling.
Cover for Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations

Abstract

Intelligent Tutoring Systems have become critically important in future learning environments. Knowledge Tracing (KT) is a crucial part of that system. It is about inferring the skill mastery of students and predicting their performance to adjust the curriculum accordingly. Deep Learning-based KT models have shown significant predictive performance compared with traditional models. However, it is difficult to extract psychologically meaningful explanations from the tens of thousands of parameters in neural networks, that would relate to cognitive theory. There are several ways to achieve high accuracy in student performance prediction but diagnostic and prognostic reasoning are more critical in learning sciences. Since KT problem has few observable features (problem ID and student's correctness at each practice), we extract meaningful latent features from students' response data by using machine learning and data mining techniques. In this work, we present Interpretable Knowledge Tracing (IKT), a simple model that relies on three meaningful latent features: individual skill mastery, ability profile (learning transfer across skills) and problem difficulty. IKT's prediction of future student performance is made using a Tree-Augmented Naive Bayes Classifier (TAN), therefore its predictions are easier to explain than deep learning-based student models. IKT also shows better student performance prediction than deep learning-based student models without requiring a huge amount of parameters. We conduct ablation studies on each feature to examine their contribution to student performance prediction. Thus, IKT has great potential for providing adaptive and personalized instructions with causal reasoning in real-world educational systems.

Topics

intelligent tutoring systemstudent modeling

Keywords

interpretable knowledge tracingstudent modelingcausal relationsstudent performance predictioneducational data miningintelligent tutoring systemsknowledge tracingBayesian networksadaptive learning

Table of Contents

  • Introduction
  • Background
  • Interpretable Knowledge Tracing
  • Interpretation through Feature Engineering
  • Interpretable Student Performance Prediction
  • Experiments
  • Datasets
  • Results
  • Ablation Studies
  • Conclusion
  • References

Knowls

  1. Knowl 1 — Interpretable Knowledge Tracing architecture

    model/method

    Interpretable Knowledge Tracing (IKT) predicts whether a student will answer the next problem correctly by replacing a high-dimensional neural hidden state with three engineered, semantically meaningful features: (1) individual mastery of the skill associated with the problem, (2) the student’s ability profile, representing learning transfer across skills, and (3) the difficulty level of the problem. The model also uses the current skill ID as an evidence variable. Skill mastery is extracted with one Bayesian Knowledge Tracing (BKT) model per skill, ability profiles are obtained by clustering cumulative per-skill success-rate vectors, and problem difficulty is estimated from other students’ first-attempt outcomes. These features are combined in a discretized Tree-Augmented Naive Bayes (TAN) classifier whose class node is the correctness of the next response. The resulting conditional-probability tables provide an intended diagnostic interpretation of predictions, such as whether a predicted failure is associated with low mastery, a weak transfer profile, or a difficult problem.

  2. Knowl 2 — TAN classifier for interpretable response prediction

    model/method

    IKT uses a Tree-Augmented Naive Bayes classifier to estimate the probability that the next response is correct. Let y∈{0,1}y\in\{0,1\} denote correctness, where 11 means a correct response, and let ftf_t contain the current skill ID sts_t, skill-mastery feature, ability-profile label, and problem-difficulty level. The posterior prediction is

    P(y∣ft)=P(y)P(ft∣y)∑y′∈{0,1}P(y′)P(ft∣y′).P(y\mid f_t)=\frac{P(y)P(f_t\mid y)}{\sum_{y'\in\{0,1\}}P(y')P(f_t\mid y')}.

    Unlike ordinary Naive Bayes, the TAN graph connects every evidence node to the correctness class and also allows each evidence node to have at most one additional parent among the other evidence nodes. The additional evidence-node edges form a tree, allowing dependencies among skill ID, mastery, ability profile, and difficulty to be represented. IKT learns this tree with the paper’s minimum-weighted-spanning-tree procedure in WEKA using training data only, then estimates conditional-probability tables after discretizing the feature values. The class node yields the predicted correctness probability, while the graph and its conditional tables are used for diagnostic and prognostic reasoning. The paper interprets the directed dependencies as causal relations for explanation, but it does not estimate causal effects of interventions.

  3. Knowl 3 — Skill-mastery feature extracted with Bayesian Knowledge Tracing

    model/method

    For every skill ss, IKT independently fits a two-state Bayesian Knowledge Tracing model. The latent event LtL_t means that a student has mastered skill ss at attempt time tt, and qt=P(Lt)q_t=P(L_t) is the mastery probability before observing the current response. The skill-specific parameters are P(L0)P(L_0), the initial mastery probability; P(T)P(T), the probability of learning the skill after an opportunity when it was not mastered; P(G)P(G), the probability of guessing correctly without mastery; and P(S)P(S), the probability of slipping and answering incorrectly despite mastery. For an observed response ot∈{0,1}o_t\in\{0,1\}, the posterior mastery probabilities are

    P(Lt∣ot=1)=qt(1−P(S))qt(1−P(S))+(1−qt)P(G),P(L_t\mid o_t=1)=\frac{q_t(1-P(S))}{q_t(1-P(S))+(1-q_t)P(G)}, P(Lt∣ot=0)=qtP(S)qtP(S)+(1−qt)(1−P(G)).P(L_t\mid o_t=0)=\frac{q_tP(S)}{q_tP(S)+(1-q_t)(1-P(G))}.

    After either observation, the next prior is updated as

    qt+1=P(Lt∣ot)+(1−P(Lt∣ot))P(T).q_{t+1}=P(L_t\mid o_t)+(1-P(L_t\mid o_t))P(T).

    The skill-mastery feature supplied to IKT is the estimated probability of having learned the queried skill, rather than the probability of applying it correctly on a particular problem. Each skill model uses only responses to that skill; attempts involving other skills are ignored, so this feature alone does not model cross-skill transfer.

  4. Knowl 4 — Ability-profile extraction for learning transfer

    algorithm

    IKT represents a student’s changing cross-skill ability by clustering cumulative performance vectors. Let there be nn skills, let xjx_j denote skill jj, and let xjt∈{0,1}x_{jt}\in\{0,1\} be the correctness indicator used for skill xjx_j in time interval tt. For student ii, the cumulative success ratio for skill xjx_j through interval zz is defined as

    Ri(xj)1:z=∑t=1zxjt∣Njt∣,R_i(x_j)_{1:z}=\frac{\sum_{t=1}^{z}x_{jt}}{|N_{jt}|},

    where ∣Njt∣|N_{jt}| is the total number of attempts on skill xjx_j through interval zz. The performance vector is

    d1:zi=(Ri(x1)1:z,Ri(x2)1:z,…,Ri(xn)1:z).\mathbf d^i_{1:z}=\big(R_i(x_1)_{1:z},R_i(x_2)_{1:z},\ldots,R_i(x_n)_{1:z}\big).

    If a student has no attempt for a skill in the available history, IKT assigns that skill a ratio of 0.50.5. K-means clustering is fitted on training-student performance vectors, and the resulting centroids are used to assign each student-time point to the nearest cluster by Euclidean distance. The cluster ID is the student’s ability-profile feature abzab_z. In the experiments, a time interval contains 20 attempts, seven clusters are learned, and every student starts with profile 1 before the first profile evaluation; profiles are then recomputed after each additional 20 attempts. For prediction at interval zz, the profile is based on history through interval z−1z-1, preventing the current response from entering its own ability label.

  5. Knowl 5 — Problem-difficulty estimation from first-attempt success

    equation

    IKT assigns difficulty to problems rather than to skills and assumes that each problem is associated with one skill. For problem pjp_j, let NjN_j be the set of students who attempted it and let Oi(pj)∈{0,1}O_i(p_j)\in\{0,1\} be student ii’s outcome on the first attempt. If at least four students attempted the problem, the average first-attempt success rate is mapped to a ten-level difficulty scale using

    δ(pj)=⌊10∑i∈NjOi(pj)∣Nj∣⌋,\delta(p_j)=\left\lfloor 10\frac{\sum_{i\in N_j}O_i(p_j)}{|N_j|}\right\rfloor,

    and the assigned level is

    difficulty level⁡(pj)={δ(pj),∣Nj∣≥4,5,∣Nj∣<4.\operatorname{difficulty\ level}(p_j)= \begin{cases} \delta(p_j), & |N_j|\ge 4,\\ 5, & |N_j|<4. \end{cases}

    Problems with no records and problems attempted by fewer than four students therefore receive the default level 5. This feature is computed from aggregate student outcomes and is separate from the student-specific skill-mastery and ability-profile features.

  6. Knowl 6 — Comparative knowledge-tracing experiment

    experimental setup

    IKT was evaluated for next-problem correctness prediction on three public datasets: ASSISTments 2009–2010, ASSISTments 2012–2013, and Cognitive Tutor Algebra 2005–2006. Only first correct attempts to original problems were retained; records with missing skill IDs and duplicate problem records were removed.

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    Five-fold cross-validation split students into 80% training and 20% testing within each fold. The evaluation metrics were area under the ROC curve (AUC) and root mean squared error (RMSE). IKT used 20 attempts per temporal interval, seven learned ability-profile clusters plus the initial profile, and a TAN tree learned from training data. Baselines were BIRT, PFA, BKT, DKT, DKT-DSC, DKVMN, and AKT-R. Neural baselines were implemented with an embedding size of 200, batch size 32, learning rate 0.01, dropout, and 100 epochs; training used mini-batch stochastic gradient descent. BKT was fit separately for each skill, with skill-level results averaged. The experiments therefore compare IKT with both traditional probabilistic models and deep sequential models under the same student-level train/test splits.

  7. Knowl 7 — AUC performance of IKT against existing models

    data/table

    Across the three datasets, the full IKT configuration, IKT-3, achieved the highest AUC on ASS-09 and Algebra and matched or exceeded most baselines on ASS-12. Its AUC was 0.7970.797 on ASS-09, 0.7670.767 on ASS-12, and 0.8510.851 on Algebra, with an average of 0.8050.805. AKT-R was the strongest competing model overall, with a higher score than IKT-3 on ASS-12 (0.7770.777 versus 0.7670.767) but lower scores on ASS-09 and Algebra. The results show that the interpretable feature-based model outperformed the tested deep models without using a large neural parameterization.

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  8. Knowl 8 — RMSE performance of IKT against existing models

    data/table

    The RMSE results support the AUC comparison: lower values favor better calibrated prediction errors. IKT-3 had the lowest RMSE on ASS-09 (0.4110.411), tied AKT-R on Algebra (0.3540.354), and was slightly worse than AKT-R on ASS-12 (0.4130.413 versus 0.4090.409). Its average RMSE was 0.3920.392, compared with 0.3950.395 for AKT-R. The paper reports that IKT-3 improved RMSE over the second-best model by up to 2.84%2.84\% on ASS-09.

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  9. Knowl 9 — Ablation identifies problem difficulty as the dominant feature

    empirical result

    The ablation study defines IKT-1 as using skill ID and skill mastery, IKT-2 as adding the ability profile, and IKT-3 as adding problem difficulty to IKT-2. The results show that the ability profile provides only a mild AUC improvement from IKT-1 to IKT-2, smaller than 1.4%1.4\% across the reported datasets. Adding problem difficulty produces the largest gain: the paper reports increases of approximately 11.2%11.2\% to 15.7%15.7\% in AUC from IKT-1 to IKT-3. For example, Algebra rises from 0.7310.731 to 0.8460.846. IKT-3 also has the lowest RMSE in every dataset within the ablation comparison.

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  10. Knowl 10 — Scope and stated limitations

    limitation

    The contribution is evaluated only on predictive performance and does not establish the causal effect of changing a student’s mastery, ability profile, or exposure to problem difficulty. The authors identify the need for future experiments on knowledge acquisition and learning behavior, including the trade-off between prediction accuracy and causal explanation. The method also assumes one skill per problem, uses independently trained BKT models for mastery, represents continuous evidence through discretized TAN conditional tables, and assigns a default difficulty of 5 to sparsely observed or unseen problems.

Coverage note — The paper’s compact comparison of model characteristics and the illustrative diagrams were not made separate knowls because their content is subsumed by the IKT architecture, feature-extraction, and experimental knowls.

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Citation

MLA
Minn, S., et al. “Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations”. arXiv, 2021, http://arxiv.org/abs/2112.11209v1.
APA
Minn, S., Vie, J.-J., Takeuchi, K., Kashima, H., & Zhu, F. (2021). Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations. arXiv. http://arxiv.org/abs/2112.11209v1
Chicago
Minn, S., J.-J. Vie, K. Takeuchi, H. Kashima, and F. Zhu. 2021. “Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations”. arXiv. http://arxiv.org/abs/2112.11209v1.
Harvard
Minn, S. et al. (2021) “Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2112.11209v1.
Vancouver
1. Minn S, Vie J-J, Takeuchi K, Kashima H, Zhu F (2021) Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations. arXiv

BibTeX

@article{minn2021interpretable,
  title = {Interpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations},
  author = {Minn, Sein and Vie, Jill-Jenn and Takeuchi, Koh and Kashima, Hisashi and Zhu, Feida},
  year = {2021},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2112.11209v1},
  eprint = {2112.11209}
}
Metadata:arXiv

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