Waterproof as students' personal proof assistant
Background information
Students often experience difficulties when learning how to construct and understand mathematical proofs, particularly in the transition from secondary school to university-level mathematics. These formal reasoning skills are essential for success in mathematics-intensive study programs, but they are also a known barrier contributing to early dropout. To support students in acquiring these skills, the digital tool Waterproof was developed at TU/e. It allows students to build formal proofs step by step using natural language, with the system checking the correctness of each step.
While initial experiences with Waterproof have been promising, the current implementation has limitations. Activities are sometimes too complex, feedback may be hard to interpret, and the learning goals are not always transparent to students. As a result, many students do not fully benefit from the tool’s potential. This project focuses on improving the design and integration of Waterproof within a foundational mathematics course. The aim is to support students in building their proof skills more effectively through a clear learning trajectory, adaptive feedback, and structured reflection. It also seeks to support teachers by creating shared resources and reducing the individual burden of developing proof-based instruction from scratch.
Figure 1: A screenshot of how Waterproof could be used as an assistant
Aim of the project
The goal of this project is to enhance the development of formal reasoning in an introductory mathematics course by redesigning the way Waterproof is used in teaching. The project will create a step-by-step learning trajectory that gradually builds students’ proof skills, starting with individual reasoning tasks and culminating in complete, structured proofs. Each activity will be closely tied to specific learning goals and supported by improved feedback mechanisms.
In addition to reworking the exercises, the project introduces reflection moments to help students connect their digital proof work to conventional written proofs. This is intended to strengthen both understanding and transfer of learning. The feedback provided by Waterproof will be redesigned to highlight key reasoning strategies and help students interpret the output more effectively.
The project also promotes collaboration among instructors using Waterproof, creating shared materials and reducing the need for duplicated effort. The overall aim is to improve student performance, reduce frustration in learning formal mathematics, and lay the groundwork for wider use of Waterproof in future courses that involve formal proofs.
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