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Research spanning nearly a century has found that math plays an important role in the learning of chemistry. Here, we use a large dataset of student interactions with online courseware to investigate the details of this link between math and chemistry. The activities in the courseware are labeled against a list of knowledge components (KCs) covered by the content, and student interactions are tracked over a full semester of general chemistry at a range of institutions. Logistic regression is used to model student performance as a function of the number of opportunities a student has taken to engage with a particular KC. This regression analysis generates estimates of both the initial knowledge and the learning rate for each student and each KC. Consistent with results from other domains, the initial knowledge varies substantially across students, but the learning rate is nearly the same for all students. The role of math is investigated by labeling each KC with the level of math involved. The overwhelming result from regressions based on these labels is that only the initial knowledge varies strongly across students and across the level of math involved in a particular topic. The student learning rate is nearly independent of both the level of math involved in a KC and the prior mathematical preparation of an individual student. The observation that the primary challenge for students lies in initial knowledge, rather than learning rate, may have implications for course and curriculum design. 

A model that maps the requisite skills, or knowledge components, to the contents of an online course is necessary to implement many adaptive learning technologies. However, developing a skill model and tagging courseware contents with individual skills can be expensive and error prone. We propose a technology to automatically identify latent skills from instructional text on existing online courseware called Smart (Skill Model mining with Automated detection of Resemblance among Texts). Smart is capable of mining, labeling, and mapping skills without using an existing skill model or student learning (aka response) data. The goal of our proposed approach is to mine latent skills from assessment items included in existing courseware, provide discovered skills with human-friendly labels, and map didactic paragraph texts with skills. This way, mapping between assessment items and paragraph texts is formed. In doing so, automated skill models produced by Smart will reduce the workload of courseware developers while enabling adaptive online content at the launch of the course. In our evaluation study, we applied Smart to two existing authentic online courses. We then compared machine-generated skill models and human-crafted skill models in terms of the accuracy of predicting students’ learning. We also evaluated the similarity between machine-generated and human-crafted skill models. The results show that student models based on Smart-generated skill models were equally predictive of students’ learning as those based on human-crafted skill models— as validated on two OLI (Open Learning Initiative) courses. Also, Smart can generate skill models that are highly similar to human-crafted models as evidenced by the normalized mutual information (NMI) values. 

It has been shown that answering questions contributes to students learning effectively. However, generating questions is an expensive task and requires a lot of effort. Although there has been research reported on the automa- tion of question generation in the literature of Natural Language Processing, these technologies do not necessarily generate questions that are useful for educational purposes. To fill this gap, we propose QUADL, a method for generating questions that are aligned with a given learning objective. The learning objective reflects the skill or concept that students need to learn. The QUADL method first identifies a key concept, if any, in a given sentence that has a strong connection with the given learning objective. It then converts the given sentence into a question for which the predicted key concept becomes the answer. The results from the survey using Amazon Mechanical Turk suggest that the QUADL method can be a step towards generating questions that effectively contribute to students’ learning.