Background: Recently human-centred design plays an increasing role in learning analytics, however this approach is mostly lacking in the design and evaluation of Intelligent Tutoring Systems (ITSs). A potential way to incorporate human-centred design principles in ITS development is by adopting a service design approach. Objectives: This article aims to identify how a service design approach can contribute to ITS development. Methods: A specific case study is implemented on "Waterproof," a system for helping students learn how to write mathematical proofs. Three substudies are conducted, namely a co-creative service blueprinting session; a usability test which focuses on the broad usage timeline; and an analysis of trace data. Results and Conclusions: The case study's results showed several concrete steps to improve the system and its embedding in the course, including for the onboarding process and the presentation of feedback in the form of error messages. Service design was shown to be useful in providing more a comprehensive design and evaluation of the ITS, going beyond the mere tool, by incorporating multiple stakeholders as well as the educational context.