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Teachers often use open-ended questions to promote students' deeper understanding of the content. These questions are particularly useful in K–12 mathematics education, as they provide richer insights into students' problem-solving processes compared to closed-ended questions. However, they are also challenging to implement in educational technologies as significant time and effort are required to qualitatively evaluate the quality of students' responses and provide timely feedback. In recent years, there has been growing interest in developing algorithms to automatically grade students' open responses and generate feedback. Yet, few studies have focused on augmenting teachers' perceptions and judgments when assessing students' responses and crafting appropriate feedback. Even fewer have aimed to build empirically grounded frameworks and offer a shared language across different stakeholders. In this paper, we propose a taxonomy of feedback using data mining methods to analyze teacher-authored feedback from an online mathematics learning platform. By incorporating qualitative codes from both teachers and researchers, we take a methodological approach that accounts for the varying interpretations across coders. Through a synergy of diverse perspectives and data mining methods, our data-driven taxonomy reflects the complexity of feedback content as it appears in authentic settings. We discuss how this taxonomy can support more generalizable methods for providing pedagogically meaningful feedback at scale. 

This paper was written with the help of ChatGPT. Recent advancements in the development and deployment of large generative language models to power generative AI tools, including OpenAIż˝fs ChatGPT, have led to their broad usage across virtually all fields of study. While the tools have been trained to generate human-like-dialogue in response to questions or prompts, they are similarly used to compose larger, more complex artifacts, including social media posts, essays, and even research articles. Although this abstract has been written entirely by a human without any input, consultation, or revision from a generative language model, it would likely be difficult to discern any difference as a reader. In light of this, there is growing debate and concern regarding using these models to aid the writing process, particularly concerning publication. Aside from some notable risks, including the unintentional generation of false information, citation of non-existing research articles, or plagiarism by generating text that is sampled from another source without proper citation, there are additional questions pertaining to the originality of ideas expressed in a work has been partially-written or revised by a generative language model. We present this paper as both a case study into the usage of generative models to aid in the writing of academic research articles but also as an example of how transparency and open science practices may help in addressing several issues that have been raised in other contexts and communities. While this paper neither attempts to promote nor contest the use of these language models in any writing task, it is the goal of this work to provide insight and potential guidance into the ethical and effective usage of these models within this domain. 

With the support of digital learning platforms, synchronous and collaborative learning has become a prominent learning paradigm in mathematics education. Computer-Supported Collaborative Learning (CSCL) has emerged as a valuable tool for enhancing mathematical discourse, problem solving, and ultimately learning outcomes. This paper presents an innovative examination of Graspable Math (GM), a dynamic mathematic notation and learning online platform, to enable synchronous, collaborative learning between pairs of students. Through analyzing students' online log data, we adopt a data-driven method to better understand the intricate dynamics of collaborative learning in mathematics as it happens. Specifically, we apply frequency distributions, cluster analysis to present students' dynamic interaction patterns and identify distinctive profiles of collaboration. Our findings reveal several collaboration profiles that emerge through these analyses. This research not only bridges the gap in current CSCL tools for mathematics, but also provides empirical insights into the effective design and implementation of such tools. The insights gained from this research offer implications for the design of digital learning tools that support effective and engaging collaborative learning experiences.