Treffer: Cryptography in Organizing Online Collaborative Math Problem Solving

The aim of this study is to examine the potential of cryptographic techniques in enhancing the organization of online group work for solving mathematical problems, while applying differentiated instruction. Engaging students in mathematics often requires additional motivational strategies and compelling incentives for sustained effort. Online group work presents a valuable opportunity for collaboration and intensive communication in solving mathematical problems. However, it also poses challenges, particularly concerning academic integrity and the risk of unauthorized copying. To address these issues, this study proposes the integration of cryptographic protocols with differentiated instruction in online collaborative tasks. Specifically, various levels of problem-solving assistance are made accessible only when the majority of the group members reach a consensus. Assistance is unlocked through the submission of individual cryptographic key segments, assigned by the instructor. A group password-required to access incremental guidance-can be generated only when a sufficient number of key segments have been submitted. This mechanism facilitates progress monitoring and fosters group accountability. The paper illustrates this approach with an example from mathematics instruction, supported by a Python-based software tool designed to aid collaborative learning. The software employs Lagrange interpolation to generate unique key parts for each participant. The method was piloted with six pre-service teachers in Serbia, and the qualitative findings are discussed alongside implications for educational research and practice.