Mathematical framework of edit-based hint policies¶

Theory · All theories
Evidence · no claims cited

Description¶

The article provides "precise definitions of key concepts in the field of edit-based hint policies and integrate them into a mathematical framework". It defines the edit set (functions on a state space, ideally symmetric so every edit is reversible), the hint policy as a function from states to edits, the legal move graph whose edges are edits, and the edit distance as the shortest-path distance in that graph under an edit cost function. This framework contextualizes existing approaches and forms the basis for the CHF.

Design Implications¶

Context¶

Requirements¶

• A symmetric edit set and a symmetric edit cost function so that any student action can be reversed and distances are well-defined

Constraints¶

• Edit distances on unordered trees are NP-hard, making some distances infeasible in practice

Target Learners¶

• students solving multi-step tasks such as programming problems

Target Learning Objectives¶

• next-step guidance toward correct and complete task solutions

Claims¶

Related Theories¶

• Edit distance space: Euclidean embedding of states under a symmetric edit distance

Examples¶

• Continuous Hint Factory (CHF)
• Select hint-training data from successful students using a goal-directedness criterion

Key Sources¶

• Benjamin Paaßen, Barbara Hammer, Thomas W. Price, Tiffany Barnes, Sebastian Gross, Niels Pinkwart. (2018). The Continuous Hint Factory - Providing Hints in Vast and Sparsely Populated Edit Distance Spaces. Journal of Educational Data Mining, Volume 10, No 1. https://jedm.educationaldatamining.org/index.php/JEDM/article/view/158