Scalable and Equitable Math Problem Solving Strategy Prediction in Big Educational Data
Scalable and Equitable Math Problem Solving Strategy Prediction in Big Educational Data
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DOI：
10.5281/zenodo.8115669
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
Anup Shakya;V. Rus;D. Venugopal
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作者：
Anup Shakya;V. Rus;D. Venugopal
了解学生的问题解决策略可以对使用智能辅导系统 (ITS) 和自适应教学系统 (AIS) 进行有效的数学学习产生重大影响。例如，ITS/AIS 可以更好地进行个性化，以纠正不正确策略所表明的特定误解，可以设计特定问题来改进策略，并且可以通过适应学生的自然思维方式而不是试图适应所有人的标准策略来最大程度地减少挫败感。虽然人类专家可以在课堂环境中通过充分的学生互动手动识别策略，但不可能将其扩展到大数据。因此，我们利用机器学习和人工智能方法的进步来执行可扩展的策略预测，这对所有技能水平的学生来说也是公平的。具体来说，我们开发了一种名为 MVec 的嵌入，根据学生的掌握程度来学习表示。然后，我们使用非参数聚类方法对这些嵌入进行聚类，逐步学习聚类，以便将具有近似对称策略的实例分组在一起。策略预测模型是根据从这些集群中采样的实例进行训练的。这确保了我们在不同的策略上训练模型，并且特定组的策略不会对 DNN 模型产生偏见，从而允许它在所有组上优化其参数。使用来自 MATHia 的真实世界大规模学生交互数据集，我们使用 Transformer 和 Node2Vec 来实现我们的方法，以学习掌握嵌入和 LSTM 来预测策略。我们表明，我们的方法可以通过对大数据集的小样本进行训练来扩大规模以实现高精度，并且还具有预测平等性，即它可以为不同技能水平的学习者同样出色地预测策略。
Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.