Educational technology designs in developing countries mostly focus on making knowledge resources widely available, through MOOCs, repositories and computer-based tutoring. The use of digital media for cognitive augmentation, particularly interactive designs that help learners understand modelling topics in STEM, is underexplored. We report a 3-year design study examining this potential in the Indian context, testing two iterations of an interactive system, Touchy-Feely Vectors (TFV). The design supports learning vectors, a modelling topic pre-university students struggle with. Virtual lesson-plans were co-designed with teachers to augment -- but not replace -- their existing practices, and to address classroom and resource constraints. Pre-post testing of TFV-1 (a computer-based prototype) showed that it helped students develop a more integrated vector concept, and improved their reasoning. Field-implementation of TFV-2 (a textbook-linked touch-screen based design) in 6-classrooms (3-Control, N=135; 3-Experimental, N=131) showed that it fostered cognitive engagement in average-students and geometry-algebra integration (model-based reasoning) in good-students. These results, along with a requirements analysis based on textbooks, indicate that the interaction possibilities supported by different representational media critically shape student reasoning. The study also illustrates a systematic approach to design and test digital media systems that support cognitive augmentation in developing countries.