Towards the Pedagogical Steering of Large Language Models for Tutoring: A Case Study with Modeling Productive Failure

One-to-one tutoring is one of the most efficient methods of teaching. Following the rise in popularity of Large Language Models (LLMs), there have been efforts to use them to create conversational tutoring systems, which can make the benefits of one-to-one tutoring accessible to everyone. However, current LLMs are primarily trained to be helpful assistants and thus lack crucial pedagogical skills. For example, they often quickly reveal the solution to the student and fail to plan for a richer multi-turn pedagogical interaction. To use LLMs in pedagogical scenarios, they need to be steered towards using effective teaching strategies: a problem we introduce as Pedagogical Steering and believe to be crucial for the efficient use of LLMs as tutors. We address this problem by formalizing a concept of tutoring strategy, and introducing StratL, an algorithm to model a strategy and use prompting to steer the LLM to follow this strategy. As a case study, we create a prototype tutor for high school math following Productive Failure (PF), an advanced and effective learning design. To validate our approach in a real-world setting, we run a field study with 17 high school students in Singapore. We quantitatively show that StratL succeeds in steering the LLM to follow a Productive Failure tutoring strategy. We also thoroughly investigate the existence of spillover effects on desirable properties of the LLM, like its ability to generate human-like answers. Based on these results, we highlight the challenges in Pedagogical Steering and suggest opportunities for further improvements. We further encourage follow-up research by releasing a dataset of Productive Failure problems and the code of our prototype and algorithm.

Mathematical Optimization-Based Period Estimation with Outliers and Missing Observations

We consider the frequency estimation of periodic signals using noisy time-of-arrival (TOA) information with missing (sparse) data contaminated with outliers. We tackle the problem from a mathematical optimization standpoint, formulating it as a linear regression with an unknown increasing integer independent variable and outliers. Assuming an upper bound on the variance of the noise, we derive an online, parallelizable, near-CRLB optimization-based algorithm amortized to a linear complexity. We demonstrate the outstanding robustness of our algorithm to noise and outliers by testing it against diverse randomly generated signals. Our algorithm handles outliers by design and yields precise estimations even with up to 20% of contaminated data.