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Human-conducted rating tasks are resource-intensive and demand significant time and financial commitments. As Large Language Models (LLMs) like GPT emerge and exhibit prowess across various domains, their potential in automating such evaluation tasks becomes evident. In this research, we leveraged four prominent LLMs: GPT-4, GPT-3.5, Vicuna, and PaLM 2, to scrutinize their aptitude in evaluating teacher-authored mathematical explanations. We utilized a detailed rubric that encompassed accuracy, explanation clarity, the correctness of mathematical notation, and the efficacy of problem-solving strategies. During our investigation, we unexpectedly discerned the influence of HTML formatting on these evaluations. Notably, GPT-4 consistently favored explanations formatted with HTML, whereas the other models displayed mixed inclinations. When gauging Inter-Rater Reliability (IRR) among these models, only Vicuna and PaLM 2 demonstrated high IRR using the conventional Cohen’s Kappa metric for explanations formatted with HTML. Intriguingly, when a more relaxed version of the metric was applied, all model pairings showcased robust agreement. These revelations not only underscore the potential of LLMs in providing feedback on student-generated content but also illuminate new avenues, such as reinforcement learning, which can harness the consistent feedback from these models. 

We present a conversational AI tutor (CAIT) for the purpose of aiding students on middle school math problems. CAIT was created utilizing the CLASS framework, and it is an LLM fine-tuned on Vicuna using a conversational dataset created by prompting ChatGPT using problems and explanations in ASSISTments. CAIT is trained to generate scaffolding questions, provide hints, and correct mistakes on math problems. We find that CAIT identifies 60% of correct answers as correct, generates effective sub-problems 33% of the time, and has a positive sentiment 72% of the time, with the remaining 28% of interactions being neutral. This paper discusses the hurdles to further implementation of CAIT into ASSISTments, namely improved accuracy and efficacy of sub-problems, and establishes CAIT as a proof of concept that the CLASS framework can be applied to create an effective mathematics tutorbot. 

This exploratory study delves into the complex challenge of analyzing and interpreting student responses to mathematical problems, typically conveyed through image formats within online learning platforms. The main goal of this research is to identify and differentiate various student strategies within a dataset comprising image-based mathematical work. A comprehensive approach is implemented, including various image representation, preprocessing, and clustering techniques, each evaluated to fulfill the study’s objectives. The exploration spans several methods for enhanced image representation, extending from conventional pixel-based approaches to the innovative deployment of CLIP embeddings. Given the prevalent noise and variability in our dataset, an ablation study is conducted to meticulously evaluate the impact of various preprocessing steps, assessing their potency in eradicating extraneous backgrounds and noise to more precisely isolate relevant mathematical content. Two clustering approaches—k-means and hierarchical clustering—are employed to categorize images based on student strategies that underlies their responses. Preliminary results underscore the hierarchical clustering method could distinguish between student strategies effectively. Our study lays down a robust framework for characterizing and understanding student strategies in online mathematics problem-solving, paving the way for future research into scalable and precise analytical methodologies while introducing a novel open-source image dataset for the learning analytics research community. 

The development and measurable improvements in performance of large language models on natural language tasks opens the opportunity to utilize large language models in an educational setting to replicate human tutoring, which is often costly and inaccessible. We are particularly interested in large language models from the GPT series, created by OpenAI. In the original study we found that the quality of explanations generated with GPT-3.5 was poor, where two different approaches to generating explanations resulted in a 43% and 10% successrate. In a replication study, we were interested in whether the measurable improvements in GPT-4 performance led to a higher rate of success for generating valid explanations compared to GPT-3.5. A replication of the original study was conducted by using GPT-4 to generate explanations for the same problems given to GPT-3.5. Using GPT-4, explanation correctness dramatically improved to a success rate of 94%. We were further interested in evaluating if GPT-4 explanations were positively perceived compared to human-written explanations. A preregistered, follow-up study was implemented where 10 evaluators were asked to rate the quality of randomized GPT-4 and teacher-created explanations. Even with 4% of problems containing some amount of incorrect content, GPT-4 explanations were preferred over human explanations. 

There is a growing need to empirically evaluate the quality of online instructional interventions at scale. In response, some online learning platforms have begun to implement rapid A/B testing of instructional interventions. In these scenarios, students participate in series of randomized ex- periments that evaluate problem-level interventions in quick succession, which makes it difficult to discern the effect of any particular intervention on their learning. Therefore, dis- tal measures of learning such as posttests may not provide a clear understanding of which interventions are effective, which can lead to slow adoption of new instructional meth- ods. To help discern the effectiveness of instructional in- terventions, this work uses data from 26,060 clickstream se- quences of students across 31 different online educational experiments exploring 51 different research questions and the students’ posttest scores to create and analyze different proximal surrogate measures of learning that can be used at the problem level. Through feature engineering and deep learning approaches, next problem correctness was deter- mined to be the best surrogate measure. As more data from online educational experiments are collected, model based surrogate measures can be improved, but for now, next prob- lem correctness is an empirically effective proximal surrogate measure of learning for analyzing rapid problem-level exper- iments. 

Despite increased efforts to assess the adoption rates of open science and robustness of reproducibility in sub-disciplines of education technology, there is a lack of understanding of why some research is not reproducible. Prior work has taken the first step toward assessing reproducibility of research, but has assumed certain constraints which hinder its discovery. Thus, the purpose of this study was to replicate previous work on papers within the proceedings of the International Conference on Educational Data Mining to accurately report on which papers are reproducible and why. Specifically, we examined 208 papers, attempted to reproduce them, documented reasons for reproducibility failures, and asked authors to provide additional information needed to reproduce their study. Our results showed that out of 12 papers that were potentially reproducible, only one successfully reproduced all analyses, and another two reproduced most of the analyses. The most common failure for reproducibility was failure to mention libraries needed, followed by non-seeded randomness. 

Teachers often rely on the use of a range of open-ended problems to assess students’ understanding of mathematical concepts. Beyond traditional conceptions of student open- ended work, commonly in the form of textual short-answer or essay responses, the use of figures, tables, number lines, graphs, and pictographs are other examples of open-ended work common in mathematics. While recent developments in areas of natural language processing and machine learning have led to automated methods to score student open-ended work, these methods have largely been limited to textual an- swers. Several computer-based learning systems allow stu- dents to take pictures of hand-written work and include such images within their answers to open-ended questions. With that, however, there are few-to-no existing solutions that support the auto-scoring of student hand-written or drawn answers to questions. In this work, we build upon an ex- isting method for auto-scoring textual student answers and explore the use of OpenAI/CLIP, a deep learning embedding method designed to represent both images and text, as well as Optical Character Recognition (OCR) to improve model performance. We evaluate the performance of our method on a dataset of student open-responses that contains both text- and image-based responses, and find a reduction of model error in the presence of images when controlling for other answer-level features. 

The use of Bayesian Knowledge Tracing (BKT) models in predicting student learning and mastery, especially in math- ematics, is a well-established and proven approach in learn- ing analytics. In this work, we report on our analysis exam- ining the generalizability of BKT models across academic years attributed to ”detector rot.” We compare the gen- eralizability of Knowledge Training (KT) models by com- paring model performance in predicting student knowledge within the academic year and across academic years. Models were trained on data from two popular open-source curric- ula available through Open Educational Resources. We ob- served that the models generally were highly performant in predicting student learning within an academic year, whereas certain academic years were more generalizable than other academic years. We posit that the Knowledge Tracing mod- els are relatively stable in terms of performance across aca- demic years yet can still be susceptible to systemic changes and underlying learner behavior. As indicated by the evi- dence in this paper, we posit that learning platforms lever- aging KT models need to be mindful of systemic changes or drastic changes in certain user demographics. 

Similar content has tremendous utility in classroom and online learning environments. For example, similar content can be used to combat cheating, track students’ learning over time, and model students’ latent knowledge. These different use cases for similar content all rely on different notions of similarity, which make it difficult to determine contents’ similarities. Crowdsourcing is an effective way to identify similar content in a variety of situations by providing workers with guidelines on how to identify similar content for a particular use case. However, crowdsourced opinions are rarely homogeneous and therefore must be aggregated into what is most likely the truth. This work presents the Dynamically Weighted Majority Vote method. A novel algorithm that combines aggregating workers’ crowdsourced opinions with estimating the reliability of each worker. This method was compared to the traditional majority vote method in both a simulation study and an empirical study, in which opinions on seventh grade mathematics problems’ similarity were crowdsourced from middle school math teachers and college students. In both the simulation and the empirical study the Dynamically Weighted Majority Vote method outperformed the traditional majority vote method, suggesting that this method should be used instead of majority vote in future crowdsourcing endeavors.