Evmorfia-Iro Bartzia, Michael Lodi, M. Sbaraglia, Simon Modeste, Viviane Durand-Guerrier, S. Martini
{"title":"An Unplugged Didactical Situation on Cryptography between Informatics and Mathematics","authors":"Evmorfia-Iro Bartzia, Michael Lodi, M. Sbaraglia, Simon Modeste, Viviane Durand-Guerrier, S. Martini","doi":"10.15388/infedu.2024.06","DOIUrl":null,"url":null,"abstract":"In this paper, we present an activity to introduce the idea of public-key cryptography and to make pre-service STEM teachers explore fundamental informatics and mathematical concepts and methods. We follow the Theory of Didactical Situations within the Didactical Engineering methodology (both widely used in mathematics education research) to design and analyse a didactical situation about asymmetric cryptography using graphs. Following the phases of Didactical Engineering, after the preliminary analysis of the content, the constraints and conditions of the teaching context, we conceived and analysed the situation a priori, with a particular focus on the milieu (the set of elements students can interact with) and on the choices for the didactical variables. We discuss their impact on the problem-solving strategies the participants need to elaborate to decrypt an encrypted message. We implemented our situation and collected qualitative data. We then analysed a posteriori the different stategies that participants used. The comparison of the a posteriori analysis with the a priori analysis showed the learning potential of the activity. To elaborate on different problem-solving strategies, the participants need to explore and understand several concepts and methods from mathematics, informatics, and the frontier of the two disciplines, also moving between different semiotic registers.","PeriodicalId":45270,"journal":{"name":"Informatics in Education","volume":"7 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Informatics in Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/infedu.2024.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present an activity to introduce the idea of public-key cryptography and to make pre-service STEM teachers explore fundamental informatics and mathematical concepts and methods. We follow the Theory of Didactical Situations within the Didactical Engineering methodology (both widely used in mathematics education research) to design and analyse a didactical situation about asymmetric cryptography using graphs. Following the phases of Didactical Engineering, after the preliminary analysis of the content, the constraints and conditions of the teaching context, we conceived and analysed the situation a priori, with a particular focus on the milieu (the set of elements students can interact with) and on the choices for the didactical variables. We discuss their impact on the problem-solving strategies the participants need to elaborate to decrypt an encrypted message. We implemented our situation and collected qualitative data. We then analysed a posteriori the different stategies that participants used. The comparison of the a posteriori analysis with the a priori analysis showed the learning potential of the activity. To elaborate on different problem-solving strategies, the participants need to explore and understand several concepts and methods from mathematics, informatics, and the frontier of the two disciplines, also moving between different semiotic registers.
期刊介绍:
INFORMATICS IN EDUCATION publishes original articles about theoretical, experimental and methodological studies in the fields of informatics (computer science) education and educational applications of information technology, ranging from primary to tertiary education. Multidisciplinary research studies that enhance our understanding of how theoretical and technological innovations translate into educational practice are most welcome. We are particularly interested in work at boundaries, both the boundaries of informatics and of education. The topics covered by INFORMATICS IN EDUCATION will range across diverse aspects of informatics (computer science) education research including: empirical studies, including composing different approaches to teach various subjects, studying availability of various concepts at a given age, measuring knowledge transfer and skills developed, addressing gender issues, etc. statistical research on big data related to informatics (computer science) activities including e.g. research on assessment, online teaching, competitions, etc. educational engineering focusing mainly on developing high quality original teaching sequences of different informatics (computer science) topics that offer new, successful ways for knowledge transfer and development of computational thinking machine learning of student''s behavior including the use of information technology to observe students in the learning process and discovering clusters of their working design and evaluation of educational tools that apply information technology in novel ways.