Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in assessments and practices. One of the most important aspects of MCQs is the distractors, i.e., incorrect options that are designed to target common errors or misconceptions among real students. To date, the task of crafting high-quality distractors largely remains a labor and time-intensive process for teachers and learning content designers, which has limited scalability. In this work, we study the task of automated distractor generation in the domain of math MCQs and explore a wide variety of large language model (LLM)-based approaches, from in-context learning to fine-tuning. We conduct extensive experiments using a real-world math MCQ dataset and find that although LLMs can generate some mathematically valid distractors, they are less adept at anticipating common errors or misconceptions among real students.

Improving the Validity of Automatically Generated Feedback via Reinforcement Learning

Automatically generating feedback via large language models (LLMs) in intelligent tutoring systems and online learning platforms has the potential to improve the learning outcomes of many students. However, both feedback generation and evaluation are challenging: feedback content has to be valid especially in subjects like math, which requires models to understand the problem, the solution, and where the student's error lies. Feedback also has to be pedagogically valid to reflect effective tutoring strategies, such as explaining possible misconceptions and encouraging the student, among other desirable features. In this work, we address both problems of automatically generating and evaluating feedback while considering both correctness and alignment. First, we propose a rubric for evaluating math feedback and show that GPT-4 is able to effectively use it to annotate human-written and LLM-generated feedback. Second, we propose a framework for feedback generation that optimizes both correctness and alignment using reinforcement learning (RL). Specifically, we use GPT-4's annotations to create preferences over feedback pairs in an augmented dataset for training via direct preference optimization (DPO). We show that our methods significantly increase the correctness and alignment of generated feedback with Llama 2, an open-source LLM, qualitatively analyze our generation and evaluation systems using case studies, and outline several areas for future work.

Improving Socratic Question Generation using Data Augmentation and Preference Optimization

The Socratic method is a way of guiding students toward solving a problem independently without directly revealing the solution to the problem. Although this method has been shown to significantly improve student learning outcomes, it remains a complex labor-intensive task for instructors. Large language models (LLMs) can be used to augment human effort by automatically generating Socratic questions for students. However, existing methods that involve prompting these LLMs sometimes produce invalid outputs, e.g., those that directly reveal the solution to the problem or provide irrelevant or premature questions. To alleviate this problem, inspired by reinforcement learning with AI feedback (RLAIF), we first propose a data augmentation method to enrich existing Socratic questioning datasets with questions that are invalid in specific ways. Next, we propose a method to optimize open-source LLMs such as LLama 2 to prefer ground-truth questions over generated invalid ones, using direct preference optimization (DPO). Our experiments on a Socratic questions dataset for student code debugging show that a DPO-optimized 7B LLama 2 model can effectively avoid generating invalid questions, and as a result, outperforms existing state-of-the-art prompting methods.

Using Large Language Models for Student-Code Guided Test Case Generation in Computer Science Education

In computer science education, test cases are an integral part of programming assignments since they can be used as assessment items to test students' programming knowledge and provide personalized feedback on student-written code. The goal of our work is to propose a fully automated approach for test case generation that can accurately measure student knowledge, which is important for two reasons. First, manually constructing test cases requires expert knowledge and is a labor-intensive process. Second, developing test cases for students, especially those who are novice programmers, is significantly different from those oriented toward professional-level software developers. Therefore, we need an automated process for test case generation to assess student knowledge and provide feedback. In this work, we propose a large language model-based approach to automatically generate test cases and show that they are good measures of student knowledge, using a publicly available dataset that contains student-written Java code. We also discuss future research directions centered on using test cases to help students.

Exploring Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learning

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in both assessments and practices. An important aspect of MCQs is the distractors, i.e., incorrect options that are designed to target specific misconceptions or insufficient knowledge among students. To date, the task of crafting high-quality distractors has largely remained a labor-intensive process for teachers and learning content designers, which has limited scalability. In this work, we explore the task of automated distractor and corresponding feedback message generation in math MCQs using large language models. We establish a formulation of these two tasks and propose a simple, in-context learning-based solution. Moreover, we explore using two non-standard metrics to evaluate the quality of the generated distractors and feedback messages. We conduct extensive experiments on these tasks using a real-world MCQ dataset that contains student response information. Our findings suggest that there is a lot of room for improvement in automated distractor and feedback generation. We also outline several directions for future work

Improving Reading Comprehension Question Generation with Data Augmentation and Overgenerate-and-rank

Reading comprehension is a crucial skill in many aspects of education, including language learning, cognitive development, and fostering early literacy skills in children. Automated answer-aware reading comprehension question generation has significant potential to scale up learner support in educational activities. One key technical challenge in this setting is that there can be multiple questions, sometimes very different from each other, with the same answer; a trained question generation method may not necessarily know which question human educators would prefer. To address this challenge, we propose 1) a data augmentation method that enriches the training dataset with diverse questions given the same context and answer and 2) an overgenerate-and-rank method to select the best question from a pool of candidates. We evaluate our method on the FairytaleQA dataset, showing a 5% absolute improvement in ROUGE-L over the best existing method. We also demonstrate the effectiveness of our method in generating harder, "implicit" questions, where the answers are not contained in the context as text spans.

Modeling and Analyzing Scorer Preferences in Short-Answer Math Questions

Automated scoring of student responses to open-ended questions, including short-answer questions, has great potential to scale to a large number of responses. Recent approaches for automated scoring rely on supervised learning, i.e., training classifiers or fine-tuning language models on a small number of responses with human-provided score labels. However, since scoring is a subjective process, these human scores are noisy and can be highly variable, depending on the scorer. In this paper, we investigate a collection of models that account for the individual preferences and tendencies of each human scorer in the automated scoring task. We apply these models to a short-answer math response dataset where each response is scored (often differently) by multiple different human scorers. We conduct quantitative experiments to show that our scorer models lead to improved automated scoring accuracy. We also conduct quantitative experiments and case studies to analyze the individual preferences and tendencies of scorers. We found that scorers can be grouped into several obvious clusters, with each cluster having distinct features, and analyzed them in detail.

Interpretable Math Word Problem Solution Generation Via Step-by-step Planning

Solutions to math word problems (MWPs) with step-by-step explanations are valuable, especially in education, to help students better comprehend problem-solving strategies. Most existing approaches only focus on obtaining the final correct answer. A few recent approaches leverage intermediate solution steps to improve final answer correctness but often cannot generate coherent steps with a clear solution strategy. Contrary to existing work, we focus on improving the correctness and coherence of the intermediate solutions steps. We propose a step-by-step planning approach for intermediate solution generation, which strategically plans the generation of the next solution step based on the MWP and the previous solution steps. Our approach first plans the next step by predicting the necessary math operation needed to proceed, given history steps, then generates the next step, token-by-token, by prompting a language model with the predicted math operation. Experiments on the GSM8K dataset demonstrate that our approach improves the accuracy and interpretability of the solution on both automatic metrics and human evaluation.

RetICL: Sequential Retrieval of In-Context Examples with Reinforcement Learning

Many recent developments in large language models focus on prompting them to perform specific tasks. One effective prompting method is in-context learning, where the model performs a (possibly new) generation/prediction task given one (or more) examples. Past work has shown that the choice of examples can make a large impact on task performance. However, finding good examples is not straightforward since the definition of a representative group of examples can vary greatly depending on the task. While there are many existing methods for selecting in-context examples, they generally score examples independently, ignoring the dependency between them and the order in which they are provided to the large language model. In this work, we propose Retrieval for In-Context Learning (RetICL), a learnable method for modeling and optimally selecting examples sequentially for in-context learning. We frame the problem of sequential example selection as a Markov decision process, design an example retriever model using an LSTM, and train it using proximal policy optimization (PPO). We validate RetICL on math problem solving datasets and show that it outperforms both heuristic and learnable baselines, and achieves state-of-the-art accuracy on the TabMWP dataset. We also use case studies to show that RetICL implicitly learns representations of math problem solving strategies.

A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing

In this paper, we take a preliminary step towards solving the problem of causal discovery in knowledge tracing, i.e., finding the underlying causal relationship among different skills from real-world student response data. This problem is important since it can potentially help us understand the causal relationship between different skills without extensive A/B testing, which can potentially help educators to design better curricula according to skill prerequisite information. Specifically, we propose a conceptual solution, a novel causal gated recurrent unit (GRU) module in a modified deep knowledge tracing model, which uses i) a learnable permutation matrix for causal ordering among skills and ii) an optionally learnable lower-triangular matrix for causal structure among skills. We also detail how to learn the model parameters in an end-to-end, differentiable way. Our solution placed among the top entries in Task 3 of the NeurIPS 2022 Challenge on Causal Insights for Learning Paths in Education. We detail preliminary experiments as evaluated on the challenge's public leaderboard since the ground truth causal structure has not been publicly released, making detailed local evaluation impossible.