Towards the Pedagogical Steering of Large Language Models for Tutoring: A Case Study with Modeling Productive Failure (2025)

Abstract: One-to-one tutoring is one of the most efficient methods of teaching. With the growing popularity of Large Language Models (LLMs), there have been efforts to create LLM-based conversational tutors which can expand the benefits of one-to-one tutoring to everyone. However, current LLMs are trained primarily to be helpful assistants and 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 settings, they need to be steered to use effective teaching strategies: a problem we introduce as Pedagogical Steering. We develop StratL, an algorithm to optimize LLM prompts and steer it to follow a predefined multi-turn tutoring plan represented as a transition graph.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 and show that StratL succeeds in steering the LLM to follow the PF tutoring strategy. Finally, we highlight challenges in Pedagogical Steering of LLMs and offer opportunities for further improvements by publishing a dataset of PF problems and our code.

## introduction one-to-one tutoring is an effective teaching method @xcite . because of the efficiency of tutoring and its prohibitive cost, the challenge of finding scalable and affordable one-to-one tutoring solutions is considered as one of the greatest problems in education: the so-called two-sigma problem @xcite . following the rising popularity of large language 1 dataset 2 code models (llms), there has been a growing interest in using them to make tutoring affordable by building conversational tutoring systems @xcite . however, previous research has highlighted the lack of pedagogical properties of llms @xcite . most llms are instruction-tuned to optimize for a broad set of human preferences @xcite , leading to assistantlike responses. however, a tutor's goal is to maximize learning, not user satisfaction. these two goals can be contradictory. for example, if a student asks for help, providing them directly with the solution would likely maximize their satisfaction and be the response preferred by llms @xcite ). yet, it is more efficient from a learning standpoint to promote students' active engagement and let them cognitively engage with the problem, for example, by providing an indirect hint or asking a guiding question @xcite . moreover, existing llm tutors are optimized and mostly evaluated for single-turn requests, while a tutoring dialog should be envisioned as a multiturn teacher-student interaction where the teacher uses various pedagogical cues @xcite . as llms are not natively made for tutoring, we introduce the shift from their user-serving goal to a pedagogically suitable one as the pedagogical steering problem. we present and evaluate stratl, an algorithm to model a multi-turn tutoring strategy with llms. we define a multi-turn strategy as a succession of single-turn pedagogical goals called tutoring intents. stratl uses a transition graph to dynamically redefine the tutoring intents after every student utterance and prompts the llm to follow these intents for the next turn. we partner with learning scientists to integrate a strategy based on an advanced learning design known as productive failure (pf) @xcite , which is more tutoring dialog history @xmath0... can you give me the solution? sure! here is how to proceed: (gives solution directly) tutor non-pedagogically steered let's start intuitively! describe in your words... (promotes learning) tutor pedagogically steered i. student state tracing multi-label classification of student utterance i am lost... can you give me the solution? selected assessments features s n : [m] "the student lacks confidence." [g] "the student directly asks for help." iii. intent dependent steering act as an experienced tutor... the exercise @xmath1. give a hint. do not give the solution. i 1 i 3 p n+1 base @xmath2. tutor intent selection learning sciences-based transition conditioned on s n from current dialogue intents i n to next i n+1 i n+1 =[i 1 ,i 3 ] i 0 i 3 i 4 i 1 i 2 i @xmath3 we summarize our contributions as follows: we introduce the stratl algorithm to model the concept of tutoring strategy and to prompt an llm towards a given strategy using a sequence of single-turn intents. ## methodology tutoring strategy modeling we define a tutoring strategy function as a function ϕ that takes as input (k, @xmath4, the grounding information and dialog history up to any turn t, and that outputs a set i t+1 ⊆ i of single-turn tutoring intents for turn t + 1. abstractly, ϕ represents the decision process by which an expert tutor, given the context of the conversation, selects the best possible intents from a pedagogical standpoint to react to the student's last utterance. this function will be replaced in practice by an approximation φ introduced in the next paragraph. the resulting conditional tutor model generates y n+1 according to: student state tracing expert tutors base their interventions on observations about (1) the student's emotional or knowledge state @xcite , and (2) the state of the conversation and their previous interventions @xcite . for example, a tutor does not react the same way to a computational mistake as to a reasoning one. therefore, we use state features (1) we define in the next paragraph, and the previous tutoring intents (2) as inputs to our intent selection function φ. each student turn is associated with a set s t of state features describing the state of the student and of the conversation at turn t. the state features are chosen from a set s of possible features. a feature in s could, for example, be 'the student is confused' or 'the student made a computational mistake'. we denote ψ a classifier that provides these features based on the dialog history and grounding. our intent selection function thus writes ϕ(i n , s n ) = i n+1 ⊆ i. as previously noted, ϕ depends on the student state features s n and previous tutor intents i n . our final conditional generation model produces output: ## conclusion we present the pedagogical limitations of llms in tutoring as the pedagogical steering problem. we introduce stratl, an algorithm addressing this problem. stratl integrates ideas from learning sciences with llms, utilizing a student state tracing and a tutoring intent selection procedure based on expert-defined transition graphs to dynamically steer the llm to follow a modeled pedagogy. a field study with high school students demonstrates stratl's ability to follow the productive failure learning design.