Elementary cryptography games for primary school students through WIMS

The importance of an active engagement of students in the learning process is nowadays recognised as a central aspect for a successful teaching practice. Many researchers highlight that teaching through games is a very effective way to involve pupils, especially in primary school. Indeed, the methodology of Game Based Learning not only stimulates students’ interest, but increases their motivation and satisfaction, making it easier to understand and remember new concepts. This is particularly relevant for Mathematics, where learning a new rule through experimentation leads to a better understanding. Such a methodology becomes even more powerful when combined with the use of the so-called “new technologies”. We developed a proposal for a web-based mathematical “turnkey” game environment for primary school pupils, using the WIMS system. The WIMS system (WWW Interactive Multipurpose Server, https://wims.matapp.unimib.it/), conceived by Xiao Gang and made public in 1998, is now in widespread use throughout France and is slowly spreading to other countries. It is available in various languages, and it is recognized for its vitality and effectiveness as a server for publishing interactive learning objects. One of its advantages is that its activities can be offered to the user with no need to install any additional software on the local pc (or on any mobile device) other than a standard web browser. Also, teachers can create virtual classes to propose activities to students and actively monitor their works. Obviously, WIMS can be a very useful tool for distance learning. The aim of this work is to present an activity on elementary cryptography through games. Our proposal consists of essentially two parts. The first activity challenges the students with the problem of ciphering and deciphering secret messages, taking inspiration from Caesar code. The second part involves a game inspired by modern cryptography techniques, such as Hamming codes for error correction. It is presented as a magic trick: one volunteer is asked to think about a number from 0 to 15 and to answer 7 yes/no questions regarding it. The interesting part is that the volunteer is allowed to lie once. The “mathe-magician” will then guess not only the number, but also the eventual lie. It is a very intriguing game (for adults as much as for kids), that stimulates pupils in asking the question “How does it work?”. This is enough to capture the students’ attention, enabling the teacher to introduce them to the inner mathematical motivations of the game, such as the binary code. The applets we will present are publicly available on any WIMS server (e.g. at the URL https://wims.matapp.unimib.it/test/wims.cgi?module=E4/game/oefcesare.it) in Italian and French (and will soon be available in English as well). In our presentation we will also share the outcomes of a trial testing of such activity with four classes of Italian students, for a total of 74 pupils of 8 and 9 years old, focusing on a qualitative analysis of the reactions of the pupils and their teachers. Moreover we will outline how the WIMS contents were designed to support the explanation of how the mathematics behind the magic works.