Math Operation Embeddings for Open-ended Solution Analysis and Feedback

by   Mengxue Zhang, et al.

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually constructing cognitive models and anticipating student errors for each question. This process requires significant human effort and does not scale to most questions used in homework and practices that do not come with this information. In this paper, we analyze students' step-by-step solution processes to equation solving questions in an attempt to scale up error diagnostics and feedback mechanisms developed for a small number of questions to a much larger number of questions. Leveraging a recent math expression encoding method, we represent each math operation applied in solution steps as a transition in the math embedding vector space. We use a dataset that contains student solution steps in the Cognitive Tutor system to learn implicit and explicit representations of math operations. We explore whether these representations can i) identify math operations a student intends to perform in each solution step, regardless of whether they did it correctly or not, and ii) select the appropriate feedback type for incorrect steps. Experimental results show that our learned math operation representations generalize well across different data distributions.


Algebra Error Classification with Large Language Models

Automated feedback as students answer open-ended math questions has sign...

Few-shot Question Generation for Personalized Feedback in Intelligent Tutoring Systems

Existing work on generating hints in Intelligent Tutoring Systems (ITS) ...

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 ...

Mathematical Language Processing: Automatic Grading and Feedback for Open Response Mathematical Questions

While computer and communication technologies have provided effective me...

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

Solutions to math word problems (MWPs) with step-by-step explanations ar...

Deep Discourse Analysis for Generating Personalized Feedback in Intelligent Tutor Systems

We explore creating automated, personalized feedback in an intelligent t...

Leveraging Human Feedback to Scale Educational Datasets: Combining Crowdworkers and Comparative Judgement

Machine Learning models have many potentially beneficial applications in...

Please sign up or login with your details

Forgot password? Click here to reset