Creative Mathematical Sciences Communication

When students start learning the basic concepts of computer science (CS), they quickly find opportunities to demonstrate their skills, share interests, and compare their work with others. Attraction, innovation, techniques, and surprise should be desirable features of each task presented to learners. This paper discusses Bebras-like tasks that are designed to convey basic CS concepts to all age of students. Bebras is an international initiative aimed at promoting informatics and computational thinking among K-12 students, as well as teachers. Solving these tasks can be considered a systematic process that involves students in a deeper understanding of computing concepts and supports a pedagogical shift in the classroom, fostering students’ engagement and motivation to learn. Short tasks covering CS concepts can be solved in a few minutes and can be presented either on a computer or printed on cards in an attractive design. Another way to introduce Bebras-like problems is through unplugged activities, where a hands-on approach using physical objects, components, or their own bodies helps students to better grasp CS concepts.

It is entirely interesting, and profoundly important to science, that efforts to communicate science have often led scientists to new perspectives on their own work and their scientific fields and specialties. This two-way street in science communication was a founding impulse and inspiration of the Creative Mathematical Sciences Communication (CMSC) conference series. The vigor of that impulse continues in this paper via a few new game horizons. This paper uses well-quasi-ordering of trees and other mathematical objects to create games that are easy to understand, addictive, and engage some powerful mathematical fundamentals.

Graphs are a fundamental concept in computer science, effectively modeling diverse scenarios such as social networks, protein interactions, and mobility. Dijkstra’s algorithm is crucial for computing single-source shortest path in graphs and is a key component of graph processing. This paper presents an educational activity designed to “unplug” graphs and Dijkstra’s algorithm, making these topics accessible to a broad audience. The activity utilizes a physical graph with chains as edges and key rings with retractable badge holders as nodes. By pulling two nodes of this graph apart, it is possible to find a shortest path between these nodes. This can be used to visualize how Dijkstra’s algorithm works, including how the graph models the world. It invites for discussing how much more efficient this is compared to enumerating all paths, and what additional insights computer scientists had to achieve impressive speedups over plain Dijkstra, allowing for route planning to be perceived as a solved problem, where we use the packaged solution without further thought. We discuss the implementation of this activity in public outreach events, such as Culture Nights and primary school classrooms.

Artificial intelligence (AI) is now deeply ingrained in young peoples’ everyday lives. They need low-threshold learning opportunities to understand what AI is and how it works. Unplugged learning activities can offer such opportunities but must first manage to break down the topic’s complexities. This contribution presents such an activity giving students hands-on experience in training an actual machine learning (ML) model - all without a computer! ‘Actual’ here refers to the fact that the model students train ends up being an exact copy of what a standard Python implementation would produce. Three tools are presented that make this feasible in an unplugged two-hour workshop setting. We report our experience piloting the activity including questionnaire responses we collected from 56 upper secondary school students.

Kolam is a south Indian artform of drawing patterns on the ground in front of houses for decoration purposes. Relating these cultural designs as illustrations in mathematics classroom facilitates the learning enjoyable. This paper connects the aspects such as (i) representation and exploration of kolam patterns in terms of kolam moves that are similar to Turtle moves, (ii) accessibility of kolam patterns for vision impaired people as tactile diagrams (iii) relevance of a few elementary mathematical concepts and (iv) expression of simple kolam patterns with an inclusive tool, Tactile Kolam Cube. With an ethnomathematics perspective this paper provides scope to appreciate the cultural aspect on one hand and the mathematical properties on the other. We propose the tactile kolam sheets as teaching aids and tactile kolam cube as an assistive tool, and hence the focus of this paper is on these as classroom resources in mathematics pedagogy. Two types of kolam patterns viz. Kambi kolam and Hridhaya kamalam are referred in this paper.

We introduce a visual representation of qubits to assist in explaining quantum computing to students who lack the formal mathematics, and to a broad audience. The representation follows from physical devices that we developed to explain superposition, entanglement, measurement, phases, interference, and quantum gates. We have developed several hands-on teaching kits for students to manipulate objects that use this representation and to explain some applications, including quantum teleportation, quantum cryptography, and quantum nonlocality.

The engagement with a fascinating geometric problem involving the creation of a three-dimensional solid model can be traced back to the 18th century: The goal is to find a solid that has a circular base, looks like a triangle from one side, and like a square from the other. This problem has inspired many mathematicians, such as Georg Pólya in 1966. The appeal of the problem has not diminished over the years, mathematicians and mathematics educators are still engaged with analog or slightly modified versions of the problem. As with historical examples, the problem suggests a unique solution, but many descriptions of solutions to the problem are incomplete, as there are infinitely many solids that meet the required properties.

This paper explores how to find different solutions that meet the specified conditions of the geometric problem. It will determine and compare the volumes of two solids that meet these conditions. Furthermore, the advantages of creating analog solid models, as were made in the 18th century, will be discussed in comparison to 3D printed models. This approach can be utilized in various learning environments, leading to an understanding of the problem according to modern problem solving theory in mathematics education.

The Algorithm Experience is an activity for students of algorithms, in which they take on the role of a computer, and execute an algorithm by hand on a paper machine: an unplugged machine that uses envelopes for memory cells and paper cards for values. The experience was initially targeted at high school or university students.

In this experience report, we report on using the activity with primary school children in Louisiana in 2022 and 2023. We discuss several adaptation to the activity that were tried for this purpose and evaluate their success.

The Indian National Education Policy 2020 advocates the introduction of Computational Thinking (CT) and coding in school, and the National Curriculum Framework 2023 follows through on this. Undoubtedly, given the scale of this effort (reaching a quarter billion children), the challenges are aplenty.

As it happens, India already has some CS Unplugged style experience with large-scale initiatives in introducing CT in low-resource environments, necessarily working with the educational machinery of state governments. We discuss these experiences, focusing on the three dimensions of large-scale, low-resource, and state-run nature of CT education programmes. We identify some core challenges in the introduction of CT in schools that are specific to these contexts and articulate some questions on curricular choices.

This position paper considers the inclusion of binary number representation in school curricula. There can be resistance to this because it is seen as a mathematically advanced concept that isn’t explicitly visible in digital technologies, and that there may be better things to spend curriculum time on. We argue that the key concepts are valuable for digitally literate students to understand, they exercise aspects of Computational Thinking, and that it is very easily introduced to young students. Binary digits (abbreviated by Claude Shannon to “bits”) underpin all aspects of digital technology; importantly, they are the digits that make the technology digital, and therefore explain many of the benefits and limitations of digital devices. To reinforce this, we collect examples of where these digits are encountered in our digital society.

Education is about supporting humans in their growth, with a special focus on exploring their intellectual potential. Learning to act following a given (even complex) pattern is losing its educational value very fast, because all well described activities can be automized. Education therefore should focus on developing those cognitive process dimensions of pupils where technology cannot compete with humans. This means teaching how to describe and discover the world, how to verify own imaginations and models, how to think and how to design, analyze and evaluate new products of science and technology instead of learning the products of science and technology, and their applications.

In this article we claim that teaching numbers and fundamental arithmetic operations in schools starts on a too high abstract level resulting in learning algorithms of symbol manipulations without understanding the nature of the fundamental calculations.

In this paper we show that starting with the historical development of number representations (not with the decimal positional system) offers a natural, more understandable way for teaching mathematics in primary schools. We show, that going consequently from concrete to abstract empowers pupils to be able to design own representations of numbers and rediscover the execution of arithmetic operations on their own. We take the operation of division of integers to exemplary illustrate how a successful process of rediscovery of arithmetic algorithms can be designed.

In this article, we focus on the use of mental tools of computational thinking (CT) to solve selected problems in school mathematics. We suggest how to expand and enrich some of the traditional school mathematics topics through the use of CT, and as a result, obtain solutions that use and are supported by the power of informatics as a discipline and computers as computational tools. We show how addressing the computational complexity of problems can help also with developing mathematical thinking (MT). Although the problems are mathematical in nature, they do not appear in teaching mathematics in Poland according to the actual core curriculum, but they do appear in selected informatics classes (All references to the core curriculum in this paper are to the National Core Curriculum approved by the Ministry of National Education of Poland in 2017/2018). In the first part of the work, we briefly refer to computational thinking, mathematical thinking and general problem-solving strategies.

Making large-scale STEM exhibits can be a very engaging group activity for students across all ages. Apart from giving them a sense of accomplishment from completing the mammoth task of exhibit making, it also inspires them to think about the underlying algorithm that generated the design. In this paper, we describe exhibit designs based on pixel art using materials such as dice, bindis, Rubik’s cubes, strings, tessellation tiles, sticky notes, push-pins etc. We also share our experience and learnings from making 25+ different large scale portraits with students from elementary school to undergraduates. Affordable raw-materials and open-source tools make the designs accessible for use by educators in their schools.

The Bebras challenge is an international initiative to engage school pupils with computer science and computational thinking via an annual challenge designed by computer science experts and educators. BeLLE is an international consortium focusing on international comparisons of standard challenge task banks. The consortium uses the ViLLE platform to manage the challenge as it offers a digital exercise-based learning environment with comprehensive learning analytics. The goal is to learn more about students’ knowledge in computer science and computational thinking in order to provide information for curriculum development and other educational planning and research. BeLLE started in 2021 with a pilots in Hungary and India. After the successful pilot, the consortium expanded substantially in the following year, many multiple choice questions were transformed into interactive tasks, and the process of organizing the challenge in ViLLE was refined. In this paper, we present some results of the challenge conducted within the BeLLE consortium in 2022. Over 90,000 students (47 % girls, 53 % boys) participated in the challenge in total through BeLLE. The results show that most students across countries and age groups get less than half of the maximum scores. The difference between girls and boys become apparent in Hungary and Lithuania: in the two oldest age groups (14–16 and 16–19 years old) boys score higher than girls. The time spent on the challenge is often 30 to 40 min with a difference between girls and boys in Hungary and Lithuania: boys use either less or more time than girls.

We present a proposal for a learning path for children to teach them cryptography during visits to the MuMa Science Centre. As the goal of the Math Museum (MuMa) for which the track is being developed is to make youngsters enthusiastic about mathematics and computer science, we have decided to focus on cryptography. In our past experience this proved to be very effective – children love secrets and spy games. We will prepare a set of CS-unplugged-like activities which will cover the broad range from the simplest, historical ciphers up to the Enigma cipher. In contrast to previously described CS-unplugged activities, we will focus on methods of breaking those ciphers, not on merely using them. Breaking of Enigma deserves attention thanks both to clever use of pure mathematics, but also due to its historical significance in ending WWII. In this paper we will present ideas for activities to teach cryptanalysis of the simplest ciphers, starting from Caesar and Vigenère ciphers, as well as the design for a simple, paper teaching aid that simulates the simplified Enigma to show its properties. We share pertinent feedback we have received after several presentations we had already made to small groups of children and adults.

This paper presents two innovative extensions of the classic Human Sorting Network (HSN) activity from the CS Unplugged program. First, we describe the implementation of a large-scale HSN with 50 input nodes, realized with high school students in Vienna, Austria. We detail the logistical challenges and solutions for creating an HSN of this magnitude, including location selection, network layout, and participant coordination. Second, we report on using parallel 6-input HSNs, which introduce a competitive element and enhance engagement. This parallel setup allows for races between teams and can be adapted for various age groups and knowledge levels. Both extensions aim to increase the educational impact and enjoyment of the HSN activity. We provide comprehensive insights into our experiences, enabling other educators and researchers to replicate or further develop these HSN variants.

The experience of distance learning during COVID-19 has become invaluable for continuing lifelong learning process under the war conditions in Ukraine. That experience was especially helpful for the survival of universities relocated from the occupied territories, where distance learning became the only possible format. The main problem for Ukrainian universities during the war is that students often cannot attend online meetings due to poor communication, blackouts, or air alarms. The task is to organize the educational process to ensure its effectiveness. Ideally, the teacher should create a learning environment accessible from anywhere in the world at any time convenient for the student.

This paper analyzes and systematizes the authors’ experience in teaching mathematical and computer disciplines remotely during a full-scale invasion. We have identified four main criteria that a course should satisfy: completeness, self-sufficiency, finality, and relevance. The teacher must create high-quality course content that is accessible for students’ independent learning. This includes creating a syllabus, preparing and recording short video lectures, conducting consultations, organizing control activities (such as forming tests and assignments), and holding retrospectives where the author’s solutions are reviewed and analyzed, especially for computer disciplines and programming.

The authors believe that this model of interaction between the teacher and students during the war is key, as it allows students, in addition to communicating directly with the teacher in class, to have well-prepared and structured material for independent work and quick feedback from the teacher through messengers.