AI modeling for source code understanding tasks has been making significant progress, and is being adopted in production development pipelines. However, reliability concerns, especially whether the models are actually learning task-related aspects of source code, are being raised. While recent model-probing approaches have observed a lack of signal awareness in many AI-for-code models, i.e. models not capturing task-relevant signals, they do not offer solutions to rectify this problem. In this paper, we explore data-driven approaches to enhance models' signal-awareness: 1) we combine the SE concept of code complexity with the AI technique of curriculum learning; 2) we incorporate SE assistance into AI models by customizing Delta Debugging to generate simplified signal-preserving programs, augmenting them to the training dataset. With our techniques, we achieve up to 4.8x improvement in model signal awareness. Using the notion of code complexity, we further present a novel model learning introspection approach from the perspective of the dataset.