Predicting learner actions and intentions is crucial for providing personalized real-time support and early intervention in programming education. This approach enables proactive, context-aware assistance that is difficult for human instructors to deliver by foreseeing signs of potential struggles and misconceptions, or by inferring a learner's understanding and coding intent through early prediction of their intended solution. Traditional frameworks such as Knowledge Tracing are limited to predicting student performance on subsequent tasks, focusing only on how learners will perform in the next task rather than modeling progress within the current task. Existing approaches to single-task prediction primarily aim to generate the final submitted code. Consequently, the development of models capable of predicting the step-by-step evolution of the code within a single task remains underexplored. This paper proposes a generative model that traces the historical evolution of a learner's code to predict the next code snapshot in a task. Specifically, we develop a deep learning model that encodes "learner context" by feeding a time-series of code snapshots into an LSTM. This context, combined with the current code, is used to decode the next code. In our evaluation using real-world data collected from programming exercise classes, our model achieves a BLEU score of 0.639. The results confirm that incorporating learner context is essential for improving prediction accuracy, yielding up to a 7.5% improvement over a baseline model. We also identify effective model architectures and fine-tuning techniques that contribute to performance gains. [For the complete proceedings, "Proceedings of the International Association for Development of the Information Society (IADIS) International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA) (22nd, Porto, Portugal, November 1-3, 2025)," see ED677812.]