Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors (2024)

Abstract: Large language models (LLMs) offer many opportunities to scale high-quality personalized tutoring. A promising approach is to build dialog tutoring models to scaffold students’ problem-solving. However, even though existing models perform well in solving reasoning questions, they can struggle to precisely detect student’s errors and tailor their feedback to these errors. Inspired by real-world teaching practice where teachers identify student errors and customize their response based on them, we focus on verifying student solutions and show how grounding to such verification improves the overall quality of tutor response generation. We collect a dataset of 1,002 stepwise math reasoning chains with the first error step annotated by teachers. We show empirically that finding the mistake in a student solution is challenging for current models. We propose and evaluate several verifiers for detecting these errors. Using both automatic and human evaluation we show that the student solution verifiers steer the generation model towards highly targeted responses to student error which are more often correct with less hallucinations compared to existing baselines. The benchmark dataset and code will be released openly.

## introduction the field of dialog tutoring aims to build systems that can teach students by holding a conversation with them @xcite . dialog tutors hold the potential to make personalized teaching available to learners anywhere anytime. the increasing capabilities of llms have brought renewed hope to this field @xcite . however, realtime tutoring is quite complex, and human teachers bring various intricate capabilities when teaching, * equal contribution. yet, although research on effective human tutors shows they perform these steps sequentially by first reasoning about the error, then picking a strategy, and then responding @xcite , many tutoring models perform all of them in one forward pass. recent studies @xcite have shown that this can lead to several deficiencies that can be detrimental to student learning, for example, in math tutoring. despite impressive performance on math reasoning benchmarks @xcite , dialog tutors often generate hallucinated outputs and present erroneous information to students, for example, because they assess an incorrect solution as correct. we show an example of this in figure 1 . in this paper, we alleviate this problem by decoupling the verification of student solutions from response generation with a modular approach. as opposed to the common approach, the model does not directly generate the tutor response from the students' utterances, whereby solution assessment is done implicitly in the models' activations, but rather receives the output of an additional verification model that assesses solutions and can therefore also be more specialized. we hypothesize that this increases the correctness of the model as well as makes the response more targeted to the error because the response generation module is already aware of the exact student error. furthermore, this architecture more closely mimics human tutors. to test our approach and train verifiers, we collect a dataset of ca. 1k student solutions and their stepwise reasoning chains in the domain of multistep math problem-solving, which we released publicly. this dataset augments the math dialog tu-problem dialogue history justin has a box that is 6 inches in height and the width is 4 inches. the length of the box is double its height. what is the volume of the box? ## verification-based response generation we first introduce the task of verification and different verifiers in section 3.1. afterwards, in section 3.2, we combine verification and response generation for modular tutor response generation. ## data collection we propose and evaluate various verifiers in this work. since some of them require training data and to evaluate their performance, we collect a dataset of 1,002 human-produced verification outputs to train and evaluate them. this is similar in size to a related corpus @xcite . in this section, we describe the annotation task and data collection. incorrect student solutions source our work extends mathdial @xcite ) by having teachers annotate incorrect student solutions from the dataset with their first error step. there, these incorrect student solutions were used to condition a student model (instructgpt) to generate responses in a dialogue with a human teacher. mathdial uses names and genders randomly sampled from a diverse set of cultural and ethnical backgrounds and reasoning errors sourced from learning sciences literature during data collection. specifically, the problems in mathdial are based on the gsm8k @xcite dataset of multistep math word problems. in mathdial, the reasoning chains are generated using a 2-shot cot prompt with gpt-3.5-turbo, and temperature sampling (@xmath0.7) is used to get multiple reasoning paths (@xmath1. finally, the most common incorrect solution is chosen. subsequently, their student model is prompted to respond to a human teacher as a student who tries to solve a problem with a particular incorrect solution. to not skew our dataset to errors, we balance it with rephrased reference solutions from the student model. we reproduce the student model prompt from mathdial to generate student responses using the reference solutions. all reference solutions and student responses with incorrect solutions are part of the dataset. details are in appendix a. ## experiments we evaluate different verifiers on our dataset and use them to inform response generation models to improve their correctness. since we extend math-dial with additional annotations we use mathdial dialogues for evaluating tutor response generation. besides math problem and student solution in a dialog, we either use a model-generated cot reference solution if marked by "solution" or no reference solution as input to the models. next, we detail metrics and models. ## results we first show the performance of different verification models in section 6.1 and then use verification models in response generation in section 6.2. ## ablation studies next, we provide further ablations, first on the utility function used in the nw algorithm (section 7.1) and then on the impact of verification before response generation based on its correctness and problem difficulty (section 7.2). ## discussion student errors are key learning opportunities. tutors should recognize them and precisely guide students with targeted feedback without telling the full solution. our results show that even state-ofthe-art llms can struggle with this but that adding a separate verification step can help. still, while verification can make responses more targeted, they sometimes tend to be less actionable (cf. ## conclusion motivated by effective teaching practice, we split the task of tutor response generation into two separate steps of verifying the student solution and generating a response. to evaluate our approach, we collect a dataset of around 1k teacher-annotated solutions to augment an existing math tutoring corpus. our results show that splitting response generation into two steps can result in more targeted and correct responses that better scaffold human learning. we showcase this using both automatic evaluation and human evaluation annotated by teachers, both for prompted and finetuned models.