@inproceedings{d211c471854d4b39b4b03dbe3381fdbc,
title = "Math Operation Embeddings for Open-ended Solution Analysis and Feedback",
abstract = "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 homeworks and practices that do not come with this information. In this paper, we analyze students{\textquoteright} 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.",
keywords = "Embeddings, Feedback, Math expressions, Math operations",
author = "Mengxue Zhang and Zichao Wang and Richard Baraniuk and Andrew Lan",
note = "Funding Information: Math education is of crucial importance to a competitive future science, technology, engineering, and mathematics (STEM) workforce since math knowledge and skills are required in many STEM subjects [11]. One important way ∗This work is supported by the National Science Foundation under grant IIS-1917713. Publisher Copyright: {\textcopyright} EDM 2021.All rights reserved.; 14th International Conference on Educational Data Mining, EDM 2023 ; Conference date: 29-06-2021 Through 02-07-2021",
year = "2021",
language = "English (US)",
series = "Proceedings of the 14th International Conference on Educational Data Mining, EDM 2021",
publisher = "International Educational Data Mining Society",
pages = "216--227",
editor = "I-Han Hsiao and Shaghayegh Sahebi and Francois Bouchet and Jill-Jenn Vie",
booktitle = "Proceedings of the 14th International Conference on Educational Data Mining, EDM 2021",
}