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Computational thinking is a key skill for space science graduates, who must apply advanced problem-solving skills to model complex systems, analyse big data sets, and develop control software for mission-critical space systems. We describe our work using Design Thinking to understand the challenges that students face in learning these skills. In the MSc Space Science & Technology at University College Dublin, we have used insights from this process to develop new teaching strategies, including improved assessment rubrics, supported by workshops promoting collaborative programming techniques. We argue that postgraduate level space science courses play a valuable role in developing more advanced computational skills in early-career space scientists.