A criptografia como tema motivador para o ensino de matrizes

Abstract

The constant lack of motivation with the students' learning of Mathematics generates a certain frustration in the teaching of Mathematics on the part of the teachers. Traditional teaching, based on theoretical and expository teaching, is no longer sufficient for school needs, requiring other teaching methods to complement and motivate learning. With that in mind, cryptography was considered a motivating theme in the learning of mathematical content, as it is an interesting and challenging subject that can be used in various educational activities. Cryptography is part of the history of mathematics, as much of the development of cryptography is due to mathematics, which studies and devises strategies to make cryptography more complex to decipher. Encryption uses techniques that transform a readable message into an unreadable one, so that only the sender and recipient can understand it, ensuring the confidentiality of information associated with the message. This qualitative investigation aims to observe, analyze and report the results obtained in applications that relate cryptography and mathematics, attributing meaning to the mathematical concept studied, thus highlighting the importance of bringing current topics that relate mathematics to the student's reality to the classroom, motivating you to learn in an enjoyable and profitable way. The research is exploratory in nature and involves a bibliographic survey on cryptography, its historical aspects and mathematical concepts related to the cryptographic environment. For the elaboration of the data of this research, didactic proposals were applied with activities that use mathematics, more specifically second and third order matrices, to encrypt and decipher messages. The activities were carried out by students from a second-year high school class at a state public school, located in the city of Esteio, in the state of Rio Grande do Sul. Subsequently, the students answered a questionnaire in order to analyze the beneficial aspects, or not, of these applications. It stands out among the perceptions, after analyzing the activities, that this theme motivated and made the class react positively to the didactic proposal. This study can be used by elementary and high school teachers to review, correct, deepen and exercise the mathematical content taught, and other versions of these activities can be prepared, adapting them to the target audience, or using other encryption techniques, or other mathematical contents, making mathematics classes more attractive and meaningful.