# The Continuous Hint Factory - Providing Hints in Vast and Sparsely Populated Edit Distance Spaces

arXiv: https://arxiv.org/abs/1708.06564 · HTML: https://mlsanity.com/paper/1708.06564/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

## Built on by (most cited first, 12 of 12)

- [Next-Step Hint Generation for Introductory Programming Using Large Language Models](https://mlsanity.com/paper/2312.10055/) (2023)
- [Giving Feedback on Interactive Student Programs with Meta-Exploration](https://mlsanity.com/paper/2211.08802/) (2022)
- [Navigating the Landscape of Hint Generation Research: From the Past to the Future](https://mlsanity.com/paper/2404.04728/) (2024)
- [Play to Grade: Testing Coding Games as Classifying Markov Decision Process](https://mlsanity.com/paper/2110.14615/) (2021)
- [Generating Feedback-Ladders for Logical Errors in Programming using Large Language Models](https://mlsanity.com/paper/2405.00302/) (2024)
- [Simulating Student-Tutor Interactions with LLMs for Multilingual Math Feedback](https://mlsanity.com/paper/2506.04920/) (2025)
- [Automatic Assessment of the Design Quality of Python Programs with Personalized Feedback](https://mlsanity.com/paper/2106.01399/) (2021)
- [Automatic Creativity Measurement in Scratch Programs Across Modalities](https://mlsanity.com/paper/2211.05227/) (2022)
- [Learning Code-Edit Embedding to Model Student Debugging Behavior](https://mlsanity.com/paper/2502.19407/) (2025)
- [ast2vec: Utilizing Recursive Neural Encodings of Python Programs](https://mlsanity.com/paper/2103.11614/) (2021)
- [Efficient Feedback and Partial Credit Grading for Proof Blocks Problems](https://mlsanity.com/paper/2204.04196/) (2022)
- [Designing and Evaluating Chain-of-Hints for Scientific Question Answering](https://mlsanity.com/paper/2510.21087/) (2025)

## Abstract (arXiv)

Intelligent tutoring systems can support students in solving multi-step tasks by providing hints regarding what to do next. However, engineering such next-step hints manually or via an expert model becomes infeasible if the space of possible states is too large. Therefore, several approaches have emerged to infer next-step hints automatically, relying on past students' data. In particular, the Hint Factory (Barnes & Stamper, 2008) recommends edits that are most likely to guide students from their current state towards a correct solution, based on what successful students in the past have done in the same situation. Still, the Hint Factory relies on student data being available for any state a student might visit while solving the task, which is not the case for some learning tasks, such as open-ended programming tasks. In this contribution we provide a mathematical framework for edit-based hint policies and, based on this theory, propose a novel hint policy to provide edit hints in vast and sparsely populated state spaces. In particular, we extend the Hint Factory by considering data of past students in all states which are similar to the student's current state and creating hints approximating the weighted average of all these reference states. Because the space of possible weighted averages is continuous, we call this approach the Continuous Hint Factory. In our experimental evaluation, we demonstrate that the Continuous Hint Factory can predict more accurately what capable students would do compared to existing prediction schemes on two learning tasks, especially in an open-ended programming task, and that the Continuous Hint Factory is comparable to existing hint policies at reproducing tutor hints on a simple UML diagram task.