Knowledge Tracing: Models & Advancements

• Knowledge Tracing (KT) is a framework that estimates hidden skill mastery by analyzing time-ordered student interactions.
• KT models span from Bayesian methods to deep neural approaches like DKT and self-attention, each balancing interpretability and accuracy.
• Recent advances address challenges like label leakage and recency bias while integrating LLMs to enhance explainability and personalization.

Knowledge Tracing (KT) is the modeling paradigm focused on inferring and predicting a learner’s evolving mastery of latent knowledge concepts (“KCs” or skills) from their sequence of interactions with educational material. At its core, KT algorithms estimate the probability that a student will answer future exercises correctly by dynamically updating a hidden knowledge state based on observable responses. KT forms the analytical backbone of modern intelligent tutoring systems, curriculum sequencing engines, and adaptive educational interventions.

1. Formal Problem Definition and Early Approaches

In KT, each student engages in a time-ordered history of interactions, yielding data of the form

$\mathcal{S}_i = \{(q_t, c_t, r_t)\}_{t=1}^T$

where $q_t$ is a question ID, $c_t$ is the set (or ID) of associated knowledge concepts, and $r_t\in\{0,1\}$ indicates response correctness. The canonical KT task is to predict

$$\hat{r}_{t+1} = P(r_{t+1}=1 \mid q_{1:t}, c_{1:t}, r_{1:t})$$

so as to quantify latent mastery and inform personalized feedback or curriculum sequencing (Shen et al., 2021, Abdelrahman et al., 2022).

Classical approaches include:

• Bayesian Knowledge Tracing (BKT): Each KC is modeled as an independent two-state HMM (unlearned/learned), with parameters for prior mastery, learning/transitions, slip, and guess. State update and prediction are recursive, with parameter learning by EM (Shen et al., 2021, Abdelrahman et al., 2022).
• Item Response Theory (IRT), Performance Factor Analysis (PFA), and Factorization Machines: Logistic models parameterize success probability as a function of person and item skill embeddings and practice counts (Shen et al., 2021, Abdelrahman et al., 2022).

While these models provided interpretable constructs, they were limited to simple Markovian transitions, independence assumptions, and inflexibility regarding multi-KC exercises and transfer.

2. Deep and Neural Approaches: Expressivity and Challenges

Advances in deep learning led to state-of-the-art KT models that capture non-linear, long-range temporal dependencies:

• Deep Knowledge Tracing (DKT): A recurrent neural network (usually LSTM) takes as inputs one-hot or embedded (KC, response) pairs and outputs, at each timestep, the probabilities of correct responses for each KC. Knowledge state is encoded as the hidden state of the RNN (Shen et al., 2021, Abdelrahman et al., 2022, Pandey et al., 2021).
• Dynamic Key-Value Memory Networks (DKVMN): Each KC's knowledge state is stored in a memory cell; the network reads and writes to this memory using content-based addressing (Shen et al., 2021, Abdelrahman et al., 2022).
• Self-Attention KT Models: Replace recurrence with dot-product (e.g., SAKT) or monotonic (AKT) attention over past interactions, offering superior performance on long sequences and efficient context modeling (Pandey et al., 2021, Hicke, 2023).

These models surpass classical methods in predictive AUC (e.g., SAKT: 0.81 vs. DKT: 0.75 on EdNet (Pandey et al., 2021)), but face challenges in interpretability, robustness, and reproducibility.

3. Key Technical Challenges: Label Leakage and Recency Bias

Modern KT pipelines often expand each (question, response) into multiple (KC, response) pairs to address sparsity from multi-KC exercises. This process introduces label leakage, wherein the repeated use of the same response value across KCs associated with a single question allows models to “cheat” by exploiting intra-question dependencies, inflating training and validation performance while impairing real-world generalization (Badran et al., 23 Aug 2025).

Additionally, traditional models often overlook recency effects, despite their foundational role in learning and forgetting. Pedagogically, the time since a KC was last encountered heavily impacts mastery decay and reinforcement, a fact underused in most KT architectures (Badran et al., 23 Aug 2025).

4. State-of-the-Art Solutions and Methodological Advances

4.1 Leakage-Free and Recency-Aware KT

To address leakage, (Badran et al., 23 Aug 2025) proposes a leakage-free MASK strategy: when expanding a multi-KC exercise, all but the final KC–response pair in the expansion have their labels replaced by a dedicated MASK label (analogous to masked language modeling). Embedding matrices are correspondingly augmented with MASK rows and integrated at the input level, preserving general applicability across KT architectures. Empirically, DKT-ML and AKT-ML close the leakage-induced generalization gap (e.g., AKT AUC: 0.7334 → 0.7543 on ASSIST09).

Recency is incorporated via learnable Fourier-feature-based encodings that represent, for each interaction, the stepwise distance since the same KC was last seen and update the embedding accordingly. This recency signal subsumes (and empirically outperforms) traditional positional encodings, enabling the model to capture forgetting and reinforcement effects. The recency extension (e.g., AKT-ML$^d$) produced further AUC gains: 0.7566 (ASSIST09), 0.8325 (Algebra05) (Badran et al., 23 Aug 2025).

4.2 LLMs and Explainable KT

Emerging methods integrate pre-trained LLMs (PLMs) directly into KT. LKT (Lee et al., 2024) encodes each interaction as a textual token sequence—questions, KC descriptions, and correctness—feeding it into a PLM (e.g., BERT, RoBERTa). This setup enhances semantic grounding, addresses cold start by leveraging linguistic similarity for unseen items, and supports natural language explainability via LIME and attention map analysis. LKT achieved superior AUC and accuracy over previous numeric KT models on large datasets (e.g., DeBERTa-v3 LKT AUC 0.8513 vs. AKT 0.8207 on XES3G5M-T).

4.3 Automated Knowledge Concept Annotation

KCQRL (Ozyurt et al., 2024) replaces expert-driven question–KC annotation with an LLM-prompted, chain-of-thought, step-wise annotation process, further learning semantically-informed embeddings for questions/solution-steps/KCs via a contrastive, false-negative-elimination loss. These representations then serve as plug-in replacements for randomly initialized embeddings in downstream KT models, boosting performance in both data-abundant and low-data regimes (absolute AUC gains up to +5.7).

4.4 Hybrid and Interpretable Models

GRKT (Cui et al., 2024) ties cognitive psychology and graph neural modeling, introducing a three-stage process (retrieval, memory strengthening, learning/forgetting) mapped directly onto graph-structured KC relations. It achieves not only superior AUC but also perfect monotonicity and consistency metrics.

AAKT (Zhou et al., 17 Feb 2025) recasts KT as a generative, alternate autoregressive process, interleaving question-side and response-side encoding in a causal Transformer and enforcing structural regularization via auxiliary skill and time signals.

KT-PSP/StatusKT (Park et al., 29 Nov 2025) incorporates problem-solving process data (handwritten solution steps) and extracts fine-grained mathematical proficiency (MP) signals via a teacher–student–teacher LLM pipeline, injecting per-dimension MP ratios as auxiliary features for better interpretability and modest accuracy gains.

5. Practical Impact, Empirical Results, and Application Contexts

Empirical studies consistently demonstrate that:

• Masked leakage-free embeddings and recency encoding yield robust, architecture-agnostic improvements with negligible computational cost (Badran et al., 23 Aug 2025).
• Automated semantic annotation and LLM-based embeddings outperform human-labeled or randomly initialized representations, especially in data-scarce settings (Ozyurt et al., 2024).
• PLM-based frameworks address cold start and zero-shot generalization, while affording natural language explanations (Lee et al., 2024).
• Application-driven evaluation on large-scale benchmarks (EdNet, ASSISTments, XES3G5M) and task-specific datasets (KT-PSP-25 for math proficiency) confirms that recent advances deliver both higher predictive accuracy and enhanced pedagogical interpretability.
• Models like SQKT (Kim et al., 22 Jan 2025) for programming education that leverage student-generated questions and code-based feature fusion show significant generalization gains (+33.1% in some AUC metrics) in cross-domain low-data regimes.

KT models are core to adaptive recommender systems, curriculum sequencing, and the feedback engine in ITSs, realizing the objective of personalized learning by dynamically identifying concept mastery gaps and optimizing intervention strategies.

6. Open Challenges and Future Research

Despite significant progress, current research points to ongoing challenges:

• Interpretability: Most deep KT models still lack transparent mechanisms for educators to diagnose or audit predicted student trajectories or concept mastery shifts (Shen et al., 2021, Cui et al., 2024).
• Data Scarcity and Cold Start: While PLMs and LLMs have improved cold-start handling, further work is needed on robust adaptation in extremely low-data or lifelong learning regimes (Lee et al., 2024, Li et al., 2024).
• Multi-modal and Unstructured Inputs: Integration of richer input data—open-ended responses, hand-written codes, explanations, question text, and even process data (pen trajectory, speech)—remains an open technical challenge (Park et al., 29 Nov 2025, Kim et al., 22 Jan 2025).
• Generalizability and Domain Transfer: Most public datasets are in K-12 mathematics; further validation is required on broader subjects and task structures, including health, language, and professional education (Abdelrahman et al., 2022).

Emergent frontiers include graph-based hybrid architectures that integrate cognitive constraints, continual and lifelong KT models, reinforcement learning–augmented curriculum sequencing, and explainable AI (XAI) for trustworthy educational analytics.

7. Summary Table: Recent KT Advances

Method/Theme	Key Advancement	Reported AUC Gains
MASK/Recency Embedding (Badran et al., 23 Aug 2025)	Leakage-free, recency-aware	+0.02–0.12 per dataset
LKT (PLM-based KT) (Lee et al., 2024)	Semantic text input, cold start	+0.03 (AKT→LKT)
KCQRL (Ozyurt et al., 2024)	Auto KC annotation, semantic rep.	+0.2–5.7 (all models)
SQKT (Kim et al., 22 Jan 2025)	Student question, code, auto-skill	up to +33.1 compared to baseline
GRKT (Cui et al., 2024)	Psychologically grounded GNN	+0.19–0.57% ACC, perfect Consistency
KT-PSP/StatusKT (Park et al., 29 Nov 2025)	Solution process, MP extraction	+0.3–1.3 AUC
AAKT (Zhou et al., 17 Feb 2025)	Autoregressive, causal trans.	+0.02–0.05 vs. best

Together, these developments mark the field’s ongoing shift toward more robust, interpretable, and generalizable knowledge tracing—delivering accurate mastery inference while closely aligning with real cognitive processes and the demands of modern adaptive education systems.