An Unplugged Didactical Situation on Cryptography between Informatics and Mathematics

IF 2.1 Q1 EDUCATION & EDUCATIONAL RESEARCH
Evmorfia-Iro Bartzia, Michael Lodi, M. Sbaraglia, Simon Modeste, Viviane Durand-Guerrier, S. Martini
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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.
信息学与数学之间不插电的密码学教学情境
在本文中,我们提出了一个介绍公钥密码学思想的活动,并使职前STEM教师探索基础信息学和数学概念和方法。我们遵循教学工程方法论中的教学情境理论(在数学教育研究中广泛使用)来设计和分析使用图的非对称密码学的教学情境。在教学工程阶段之后,在对教学内容、教学环境的约束和条件进行初步分析之后,我们设想和分析了先验的情况,特别关注环境(学生可以与之互动的一组元素)和教学变量的选择。我们将讨论它们对参与者需要精心设计解密加密消息的解决问题策略的影响。我们实施了我们的情况并收集了定性数据。然后,我们对参与者使用的不同策略进行了事后分析。后验分析与先验分析的比较显示了该活动的学习潜力。为了阐述不同的问题解决策略,参与者需要探索和理解来自数学、信息学和这两个学科前沿的几个概念和方法,并在不同的符号学域之间移动。
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来源期刊
Informatics in Education
Informatics in Education EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
6.10
自引率
3.70%
发文量
20
审稿时长
20 weeks
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.
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