This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…

This research paper explores the integration of ChatGPT as a tool for interactive learning of numerical methods in a differential equations (DEs) course. DE course is crucial for engineering students to model real-world phenomena. However, many DE courses focus only on analytical solutions and neglect important numerical solutions. To overcome…

The aim of the study is to teach the concept of function using cryptology and to investigate whether it provides support to students who have difficulty integrating this topic into everyday life. The study's research group consisted of 50 elementary school teachers in the department of mathematics education at a public college in Ankara. Since the…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

This paper presents a case study that is part of a research studying how university statistics teachers integrate digital tools in their practice. The case study is of a teacher who claims to follow constructionist ideas for her teaching of statistics, using the R programming language. The teacher developed a series of activities with R, aiming to…

Prospective teachers and cryptography students use programming, statistics and guile to enrich both their courses.

The importance of computational thinking skills in mathematics has been recognized in educational research for a long time. More recently, this recognition has materialized in formal international recommendations (e.g., by PISA's 2022 Mathematics Framework) and in national or provincial curricular reforms (e.g., in France, Sweden, and Canada) that…

Despite the benefits of teaching computational thinking (CT) and applying coding tools in schools, many teachers feel unprepared to use these technologies. Hence, we introduced CT concepts and coding tools to pre-service teachers (n=36; 17 in online class and 19 in in-person class), equipping them with digital competencies through activities with…

This paper analyzed Scratch projects developed by undergraduate students. The sample consisted of 22 child development students (18 women and four men) in the 2018-2019 academic year. The study adopted an action research design within the scope of a course titled "Teaching Science and Mathematics in Preschool Education." The research was…

Effective collaboration between student peers is not spontaneous. A system that can measure collaboration in real-time may be useful, as it could alert an instructor to pairs that need help in collaborating effectively. We tested whether superficial measures of speech and user interface actions would suffice for measuring collaboration. Pairs of…

This article presents findings from research about a practice teaching course designed to help mathematics pre-service teachers to learn from the practices of school teachers and supervisors. For this reason, the aim of this study is to research the contribution of the practicum course to the teacher candidates understanding of the teaching…

This paper describes a framework for identifying, classifying, and coding student proofs, modified from existing proof-grading rubrics. The framework includes 20 common errors, as well as categories for interpreting the severity of the error. The coding scheme is intended for use in a classroom context, for providing effective student feedback. In…

Problem-solving is regarded as a major component of mathematical performance, and well-designed problem-solving-based learning environments have the potential to assist students in developing a meaningful understanding of mathematical concepts and procedures. In this respect, given its various features, dynamic mathematics software has been…