In educational applications, knowledge tracing refers to the problem of estimating students’ time-varying concept/skill mastery level from their past responses to questions and predicting their future performance.One key limitation of most existing knowledge tracing methods is that they treat student responses to questions as binary-valued, i.e., whether they are correct or incorrect. Response correctness analysis/prediction is straightforward, but it ignores important information regarding mastery, especially for open-ended questions.In contrast, exact student responses can provide much more information.In this paper, we conduct the first exploration int open-ended knowledge tracing (OKT) by studying the new task of predicting students’ exact open-ended responses to questions.Our work is grounded in the domain of computer science education with programming questions. We develop an initial solution to the OKT problem, a student knowledge-guided code generation approach, that combines program synthesis methods using language models with student knowledge tracing methods. We also conduct a series of quantitative and qualitative experiments on a real-world student code dataset to validate and demonstrate the promise of OKT.

We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical computation and a context that specifies the problem scenario. Existing approaches are prone to generating MWPs that are either mathematically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem template, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that leverages i) pre-trained language models and a context keyword selection model to improve the language quality of generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantitative and qualitative experiments on three real-world MWP datasets demonstrate the superior performance of our approach compared to various baselines.

Word embedding models learn semantically rich vector representations of words and are widely used to initialize natural processing language (NLP) models. The popular continuous bag-of-words (CBOW) model of word2vec learns a vector embedding by masking a given word in a sentence and then using the other words as a context to predict it. A limitation of CBOW is that it equally weights the context words when making a prediction, which is inefficient, since some words have higher predictive value than others. We tackle this inefficiency by introducing the Attention Word Embedding (AWE) model, which integrates the attention mechanism into the CBOW model. We also propose AWE-S, which incorporates subword information. We demonstrate that AWE and AWE-S outperform the state-of-the-art word embedding models both on a variety of word similarity datasets and when used for initialization of NLP models.