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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. 

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. 

Open-ended questions in mathematics are commonly used by teachers to monitor and assess students’ deeper conceptual understanding of content. Student answers to these types of questions often exhibit a combination of language, drawn diagrams and tables, and mathematical formulas and expressions that supply teachers with insight into the processes and strategies adopted by students in formulating their responses. While these student responses help to inform teachers on their students’ progress and understanding, the amount of variation in these responses can make it difficult and time-consuming for teachers to manually read, assess, and provide feedback to student work. For this reason, there has been a growing body of research in developing AI-powered tools to support teachers in this task. This work seeks to build upon this prior research by introducing a model that is designed to help automate the assessment of student responses to open-ended questions in mathematics through sentence-level semantic representations. We find that this model outperforms previously published benchmarks across three different metrics. With this model, we conduct an error analysis to examine characteristics of student responses that may be considered to further improve the method. 

Online education technologies, such as intelligent tutoring systems, have garnered popularity for their automation. Whether it be automated support systems for teachers (grading, feedback, summary statistics, etc.) or support systems for students (hints, common wrong answer messages, scaffolding), these systems have built a well rounded support system for both students and teachers alike. The automation of these online educational technologies, such as intelligent tutoring systems, have often been limited to questions with well structured answers such as multiple choice or fill in the blank. Recently, these systems have begun adopting support for a more diverse set of question types. More specifically, open response questions. A common tool for developing automated open response tools, such as automated grading or automated feedback, are pre-trained word embeddings. Recent studies have shown that there is an underlying bias within the text these were trained on. This research aims to identify what level of unfairness may lie within machine learned algorithms which utilize pre-trained word embeddings. We attempt to identify if our ability to predict scores for open response questions vary for different groups of student answers. For instance, whether a student who uses fractions as opposed to decimals. By performing a simulated study, we are able to identify the potential unfairness within our machine learned models with pre-trained word embeddings. 

The use of computer-based systems in classrooms has provided teachers with new opportunities in delivering content to students, supplementing instruction, and assessing student knowledge and comprehension. Among the largest benefits of these systems is their ability to provide students with feedback on their work and also report student performance and progress to their teacher. While computer-based systems can automatically assess student answers to a range of question types, a limitation faced by many systems is in regard to open-ended problems. Many systems are either unable to provide support for open-ended problems, relying on the teacher to grade them manually, or avoid such question types entirely. Due to recent advancements in natural language processing methods, the automation of essay grading has made notable strides. However, much of this research has pertained to domains outside of mathematics, where the use of open-ended problems can be used by teachers to assess students’ understanding of mathematical concepts beyond what is possible on other types of problems. This research explores the viability and challenges of developing automated graders of open-ended student responses in mathematics. We further explore how the scale of available data impacts model performance. Focusing on content delivered through the ASSISTments online learning platform, we present a set of analyses pertaining to the development and evaluation of models to predict teacher-assigned grades for student open responses. 

Sensor-free affect detectors can detect student affect using their activities within intelligent tutoring systems or other online learning environments rather than using sensors. This technology has made affect detection more scalable and less invasive. However, existing detectors are either interpretable but less accurate (e.g., classical algorithms such as logistic regression) or more accurate but uninterpretable (e.g., neural networks). We investigate the use of a new type of neural networks that are monotonic after the first layer for affect detection that can strike a balance between accuracy and interpretability. Results on a real- world student affect dataset show that monotonic neural networks achieve comparable detection accuracy to their non-monotonic counterparts while offering some level of interpretability. 

There is a long history of research on the development of models to detect and study student behavior and affect. Developing computer-based models has allowed the study of learning constructs at fine levels of granularity and over long periods of time. For many years, these models were developed using features based on previous educational research from the raw log data. More recently, however, the application of deep learning models has often skipped this feature-engineering step by allowing the algorithm to learn features from the fine-grained raw log data. As many of these deep learning models have led to promising results, researchers have asked which situations may lead to machine-learned features performing better than expert-generated features. This work addresses this question by comparing the use of machine-learned and expert-engineered features for three previously-developed models of student affect, off-task behavior, and gaming the system. In addition, we propose a third feature-engineering method that combines expert features with machine learning to explore the strengths and weaknesses of these approaches to build detectors of student affect and unproductive behaviors. 

We present and evaluate a machine learning based system that automatically grades audios of students speaking a foreign language. The use of automated systems to aid the assessment of student performance holds great promise in augmenting the teacher’s ability to provide meaningful feedback and instruction to students. Teachers spend a significant amount of time grading student work and the use of these tools can save teachers a significant amount of time on their grading. This additional time could be used to give personalized attention to each student. Significant prior research has focused on the grading of closed-form problems, open-ended essays and textual content. However, little research has focused on audio content that is much more prevalent in the language-study education. In this paper, we explore the development of automated assessment tools for audio responses in a college-level Chinese language-learning course. We analyze several challenges faced while working with data of this type as well as the generation and extraction of features for the purpose of building machine learning models to aid in the assessment of student language learning.