# Knowledge Tracing for Complex Problem Solving: Granular Rank-Based Tensor Factorization

arXiv: https://arxiv.org/abs/2210.09013 · HTML: https://mlsanity.com/paper/2210.09013/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [Context-Aware Attentive Knowledge Tracing](https://mlsanity.com/paper/2007.12324/) (2020)
- [Dynamic Key-Value Memory Networks for Knowledge Tracing](https://mlsanity.com/paper/1611.08108/) (2016)
- [Towards an Appropriate Query, Key, and Value Computation for Knowledge Tracing](https://mlsanity.com/paper/2002.07033/) (2020)
- [Addressing Two Problems in Deep Knowledge Tracing via Prediction-Consistent Regularization](https://mlsanity.com/paper/1806.02180/) (2018)
- [Back to the Basics: Bayesian extensions of IRT outperform neural networks for proficiency estimation](https://mlsanity.com/paper/1604.02336/) (2016)
- [Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics](https://mlsanity.com/paper/1412.5967/) (2014)
- [Modeling Knowledge Acquisition from Multiple Learning Resource Types](https://mlsanity.com/paper/2006.13390/) (2020)

## Built on by (most cited first, 5 of 5)

- [3DG: A Framework for Using Generative AI for Handling Sparse Learner Performance Data From Intelligent Tutoring Systems](https://mlsanity.com/paper/2402.01746/) (2024)
- [Predicting Learning Performance with Large Language Models: A Study in Adult Literacy](https://mlsanity.com/paper/2403.14668/) (2024)
- [Data Augmentation for Sparse Multidimensional Learning Performance Data Using Generative AI](https://mlsanity.com/paper/2409.15631/) (2024)
- [Generative Data Imputation for Sparse Learner Performance Data Using Generative Adversarial Imputation Networks](https://mlsanity.com/paper/2503.18982/) (2025)
- [Improving Group Fairness in Tensor Completion via Imbalance Mitigating Entity Augmentation](https://mlsanity.com/paper/2507.20542/) (2025)

## Abstract (arXiv)

Knowledge Tracing (KT), which aims to model student knowledge level and predict their performance, is one of the most important applications of user modeling. Modern KT approaches model and maintain an up-to-date state of student knowledge over a set of course concepts according to students' historical performance in attempting the problems. However, KT approaches were designed to model knowledge by observing relatively small problem-solving steps in Intelligent Tutoring Systems. While these approaches were applied successfully to model student knowledge by observing student solutions for simple problems, they do not perform well for modeling complex problem solving in students.M ost importantly, current models assume that all problem attempts are equally valuable in quantifying current student knowledge.However, for complex problems that involve many concepts at the same time, this assumption is deficient. In this paper, we argue that not all attempts are equivalently important in discovering students' knowledge state, and some attempts can be summarized together to better represent student performance. We propose a novel student knowledge tracing approach, Granular RAnk based TEnsor factorization (GRATE), that dynamically selects student attempts that can be aggregated while predicting students' performance in problems and discovering the concepts presented in them. Our experiments on three real-world datasets demonstrate the improved performance of GRATE, compared to the state-of-the-art baselines, in the task of student performance prediction. Our further analysis shows that attempt aggregation eliminates the unnecessary fluctuations from students' discovered knowledge states and helps in discovering complex latent concepts in the problems.