Introducing Golden Section in the Mathematics Class to Develop Critical Thinking from the STEAM Perspective

The Golden Section is a mathematical concept that is one of the most famous examples of connections between mathematics and the arts. Despite its widespread references in various areas of nature, art, architecture, literature, music, or aesthetics, discussions of the golden ratio often turn out to be false or misleading. Most of the incorrect statements are based on approximations or stem from the lack of checking the facts, making scientific mistakes in verifying the original scientific, historical, cultural context, or performing arbitrary operations in the measurements. This article offers geometric data and measurements, which allow the students to explore the golden ratio in various co…

Dionysian biopolitics : Karl Kerényi's concept of indestructible life

Scholar of religion Karl Kerényi’s last book, Dionysos, is a grand attempt at reinterpreting ζωη (zoe), the Greek concept of indestructible life, which he distinguishes from βίος (bios), finite life. In Kerényi’s view, the meaning and sensual experience of zoe was expressed in its richest form in the Cretan beginnings of the cult of Dionysos. The major characteristics of this cult, as Kerényi describes, were beyond the cultural, political, and sexual limits of the Christian interpretations of life and nature. Searching for modern analogies to zoe, Kerényi explains the idea in relation to molecular biology’s minimum definition of life. Despite the fact that Kerényi’s book contains only minor…

In the Footsteps of Daedalus: Labyrinth Studies Meets Visual Mathematics.

Karl Kerényi, the internationally renowned Hungarian classical philologist and scholar of religion, carried out significant mythological research on the labyrinth, both as a cultural symbol and a specific geometrical structure. In this paper, we summarize Ker´nyi's main findings and connect his mythological studies with visual-mathematical and ethno-mathematical research to provide a geometrical and topological analysis of these symbolic structures. In our visual mathematical analysis, we propose a very simple “cut and paste” construction of labyrinths based on a system of parallel black and white strips. Then we generalize the concept of the labyrinth and extend it to arbitrary graphs. Fin…

Válság és kultúra : Összeállítás a Nemzetközi Magyarságtudományi Társaság Doktorjelölt Konferenciájának anyagából

Renewable Energy Resources for Mathematics Learning : Windmills and Water Wheels at the Math Class

The Finnish National Core Curriculum has been renewed in 2014 and the National Core Curriculum of Korea has been renewed in 2015. Although, the Finnish and the Korean educational culture is radically different from each other, they are both producing top results in international educational assessments and their renewed curricula contain some very similar components. The "multidisciplinary learning module" in Finland and the "STEAM framework" in Korea are both emphasizing the complexity of phenomena, which can be understood only in context and by employing multiple perspectives based on the combination of various subjects. In this workshop, we introduce how to construct windmills and water …

Enhancing Digital Skills of Early Childhood Teachers Through Online Science, Technology, Engineering, Art, Math Training Programs in Estonia

Teacher professional development programs, including mid- and long-term Science, Technology, Engineering, Art, Math (STEAM) courses, have recently moved from in person learning at university premises to an online environment. Whether it is a temporary change in learning methods caused by the COVID-19 restrictions or whether it will become a new normal is currently under discussion in many teacher training institutions around the world. The aim of this study was to design and implement time- and money-saving synchronous online teacher training format for conducting co-design courses for early childhood teachers in the theme of STEAM integrated learning activities. Based on Tallinn University…

Individual Creativity and Career Choices of Pre-teens in the Context of a Math-Art Learning Event

A sample of 392 students (aged 12-13 years, M± SD: 12. 52% girls) completed a learning module integrating informal hands-on mathematics and arts activity (extending STEM to STEAM). Within a 140 minute workshop period participants worked with commercially available ‘4Dframe’ Math and STEAM learning toolkits to design and create original, personal and individual geometrical structures. Two science pedagogues acted as tutors supervising the process and intervened only when needed. A pre-/post-test design monitored individual creativity, relative autonomy, and career choice preference. Path analysis elaborated the role of creativity (measured with two subscales: act and flow), and it showed tha…

Hands-on math and art exhibition promoting science attitudes and promoting science attitudes

The current science, technology, engineering, art, math education (STEAM) approach emphasizes integration of abstract science and mathematical ideas for concrete solutions by art.The main aim was to find out how experience of learning mathematics differed between the contexts of school and an informal Math and Art Exhibition. The study participants (𝑁 = 256) were 12-13 years old from Finland. Several valid questionnaires and tests were applied (e.g., SRQ-A, RAVEN) in pre- and postdesign showing a good reliability.The results based on General Linear Modeling and Structural Equation Path Modeling underline the motivational effects. The experience of the effectiveness of hands-on learning at …

Mathematical monuments in Finland

With “mathematical monuments” we mean either monuments for famous mathematicians and their achievements or works of art representing mathematical objects in public places. We present a panoply of such monuments in Finland for the purposes of the mathematical tourist visiting our country. As we are interested in symbolic representations of science, we take a broad view of the notion of “monument” and take into account also some minor artefacts, such as portraits, medals and stamps, and other semiotic signs, such as street names and commemorative plates, illustrating some highlights of the history of mathematics in Finland. Peer reviewed

Mathematical and Coding Lessons Based on Creative Origami Activities

AbstractThis paper considers how creativity and creative activities can be encouraged in regular mathematical classes by combining different teaching approaches and academic disciplines. We combined origami and paper folding with fractals and their mathematical properties as well as with coding in Scratch in order to facilitate learning mathematics and computer science. We conducted a case study experiment in a Serbian school with 15 high school students and applied different strategies for learning profound mathematical and coding concepts such as fractals dimension and recursion. The goal of the study was to employ creative activities and examine students’ activities during this process i…

Educational Robotics: Evaluating the Role of Computational Thinking in Attaining 21st Century Skills

Abstract Educational Robotics (ER) has gained prominence in the literature on Computational Thinking (CT) because of its modularity, a feature that potentially facilitates the development of abstract thinking through complex robotic parts. The field of robotics encompasses the characteristics of technology, intelligence, embodiment, and interaction, and these characteristics can serve as means of instruction for CT. Essential 21st Century Skills include decomposition, pattern recognition, abstraction, and the use of algorithms; which are fundamental to effective problem-solving skills. Although CT is believed to be the key to developing 21st Century Skills, its role in doing so is significa…

Learning Mathematical Concepts as a Whole-Body Experience

Finnország reprezentációi a magyar irodalomban : a finn téli háború témája Márai Sándornál

Pedagogical framework, design principles, recommendations and guidelines for a STEM learning environment design

Developing a Pedagogical Framework and Design Principles for STEM Learning Environment Design

The need for effective and attractive learning environments (LEs) for science, technology, engineering, and mathematics (STEM) has been internationally recognized. Additionally, the connection between STEM learning and cross-curricular skills such as creativity, innovation, and entrepreneurship has garnered attention. A deep theoretical and empirical understanding is required when designing STEM LEs. In this study, a pedagogical framework for STEM LEs has been developed based on feedback from students, aged 10–18 years old, teachers, school directors, parents, and STEM professionals, and supported by the literature. First, representatives of key stakeholder groups in Belarus, Finland, Germa…

GeoMaTech: Integrating Technology and New Pedagogical Approaches Into Primary and Secondary School Teaching to Enhance Mathematics Education in Hungary

During the past decades, technology has been becoming an integral part of everyday life and slowly shaping mathematics and science teaching and learning (e.g. Heid & Blume, 2008). Although there have been enormous investments on educational technologies in many countries technology has yet to make a sizable impact on education (e.g. Drijvers et al., 2010). On the one hand students are becoming increasingly proficient users of technology while on the other hand opportunities offered by technologies have still little been utilized. Nevertheless, as technologies are becoming more integrated into education, they are providing new opportunities for pedagogical approaches and classroom organizati…

Omnidirectional Robot Construction at the Math Class

The goal for this workshop is to expose participants to an example of the Experience Workshop Math-Art Movement’s implementation of robot-design and construction in the mathematics classroom. While participants experiment with solving the problem of how to build an omnidirectional robot—a vehicle capable of driving in any direction in a 2D plane—several physical phenomena and properties can be discovered through geometrical measurements and mathematical calculations. After the mechanical problems have been resolved, the participating students can develop individual character to their robots by improving the aesthetics of their design, while also considering practical and technological quest…

DIONYSIAN BIOPOLITICS: KARL KERÉNYI’S CONCEPT OF INDESTRUCTIBLE LIFE

Scholar of religion Karl Kerenyi's last book, Dionysos, is a grand attempt at reinterpreting ζωη (zoe), the Greek concept of indestructible life, which he distinguishes from βίος (bios), finite life. In Kerenyi's view, the meaning and sensual experience of zoe was expressed in its richest form in the Cretan beginnings of the cult of Dionysos. The major characteristics of this cult, as Kerenyi describes, were beyond the cultural, political, and sexual limits of the Christian interpretations of life and nature. Searching for modern analogies to zoe, Kerenyi explains the idea in relation to molecular biology's minimum definition of life. Despite the fact that Kerenyi's book contains only minor…

Developing Primary School Students’ Formal Geometric Definitions Knowledge by Connecting Origami and Technology

In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11-12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students’ mathematical knowledge. In previous studies, we developed origami and technology activities for high-school mathematics, but we wanted to explore if such approach would work in primary school as well. For this reason, we chose a flat origami model оf the crane and we used this model to introduce students to basic geometrical notions and definitions, such as points, lines, intersections o…

Developing and Evaluating Educational Innovations for STEAM Education in Rapidly Changing Digital Technology Environments

In this paper, we offer three examples from our research projects on both technological and pedagogical innovations to illustrate the impact of rapid technology changes on research. Members of our research team both developed and used technology applications in their research projects, utilizing design-based research (DBR). During the experiments, we encountered new challenges by the end of the research cycle due to updates in technologies. Although we had an idea of how to redesign the project for the next cycle based on the analyses of data, we noticed that we needed to not only redesign our approaches based on the research results but the changes in technologies were so rapid that materi…

Kids Inspire Kids for STEAM

Abstract The goal of the Kids Inspiring Kids in STEAM (KIKS) project was to raise students' awareness towards the multi- and transdisciplinary connections between the STEAM subjects (Science, Technology, Engineering, Arts & Mathematics), and make the learning about topics and phenomena from these fields more enjoyable. In order to achieve these goals, KIKS project has popularized the STEAM-concept by projects based on the students inspiring other students-approach and by utilizing new technologies, tools, open educational resources, and everyday items and materials. Through the students-inspiring-other-students-approach, we have aimed to get participating students developing STEAM activitie…

STEAM Practices to Explore Ancient Architectures Using Augmented Reality and 3D Printing with GeoGebra

Abstract In this study, we develop mathematical educational practices for students to explore ancient buildings using GeoGebra, Augmented Reality and 3D printing. It is an interdisciplinary approach, intertwining history, culture, mathematics, and engineering. For example, the 3D modelling of Cheomseongdae in Korea and the Temple of Dendera in Egypt can enable students to practice a multimodal set of traditional and innovative learning approaches. Students might use their mathematical knowledge to reflect on architectural and cultural history in a modeling task.

Developing a Method for Measuring Science and Technology Oriented Creativity (STOC)

Abstract The article contains the results of a research within the STIMEY (Science, Technology, Innovation, Mathematics, Engineering for the Young) project funded by the European Union’s Horizon-2020 research and innovation program (2016-2021). In the project, a hybrid learning environment (LE) was developed for both on-site and online learning suitable for the learning conditions in the COVID-19 era and beyond. The purpose of the research segment presented in this paper was to develop an instrument for assessment of the learner’s progress in creativity as one of the key targets of STIMEY. COVID-19 has shown that creativity is also needed to allow education systems the flexibility for unexp…

STEAMTEACH Austria: Towards a STEAM Professional Development Program

The STEAMTEACH (STEAM Education for Teaching Professionalism) project works with teacher trainers to develop a program of Transcultural STEAM Professional Development for in- and pre-service teachers. Following a literature review, a semi-structured questionnaire then interviews approach was used to elicit current practice, challenges for teachers and recommendations from Austrian teacher trainers. These recommendations were then compared with and supported by STEAM academic literature. It was found that none of the institutions offered a STEAM approach and it does not appear in the curriculum. Indeed, this fact is the primary challenge to overcome. Recommendations were that teachers should…

A Mission Impossible? Learning the Logic of Space with Impossible Figures in Experience-Based Mathematics Education

Most visual effects based on mathematically and physically describable phenomena and formalizable processes. Creating visual illusions, paradox structures and ‘impossible’ figures through playful and artistic procedures, holds an exciting pedagogical opportunity for raising students’ interest towards mathematics and natural sciences and technical aspects of visual arts. The Experience Workshop Math-Art Movement has a number of pedagogical methods, which are connected to visual paradoxes and perspective illusions. In the first part of our article, we introduce classroom exercises connected to the Hungarian artist Tamás F. Farkas’s paradox structures and impossible figures. There are certain …

Bridges Baltimore 2015: Charmed by Mathematics in Charm City

In 2015, the Bridges World Conference, the most significant annual international gathering to be held for exploring connections between mathematics and the arts, met in Baltimore, USA. The conference program included lectures by recognized scholars and artists, the world largest exhibition of mathematical art, thematic theatre performances, a poetry afternoon demonstrating how mathematics can interrelate with literature, and a short film festival as well as workshops organized by researchers, educators and artists. nonPeerReviewed

Integrating STEM-related Technologies into Mathematics Education at Large Scale

This paper outlines the growing phenomenon and need to integrate technologies into mathematics and science teaching and learning. There are a number of successful projects for valuable integration of technologies around the world, however, these successes are often limited reaching a relatively small number of teachers and students. In this paper, we aim to offer examples of large-scale technology projects that could create a critical mass of users that could further drive innovation and sustainability for educational technology integration. We outline how GeoGebra became one of the most widely used dynamic mathematics software with a user base of more than 100 million; highlight directions…

Two Solutions to an Unsolvable Problem: Connecting Origami and GeoGebra in a Serbian High School

Our “Visuality & Mathematics — Experiential Education of Mathematics Through the Use of Visual Art, Science, and Playful Activities” Tempus Project started in 2012 with the cooperation of eight European universities and scientific institutions, in order to develop Serbian mathematics education with technological equipment and interactive, experience-centered, and art-related content. The general objectives of this two-year-long project are justified by the findings of the PISA 2012 survey as well, which show that 15-year old Serbian students' mathematics performance is significantly below the OECD average. For the improvement of the Serbian students' mathematical literacy and abilities, wha…

Modelling Environmental Problem-Solving Through STEAM Activities : 4Dframe's Warka Water Workshop

In this paper the Korean 4Dframe educational modelling kit’s rich capacities are presented within a STEAM (Science, Technology, Engineering, Arts and Mathematics) education workshop. The workshop is an adaptation of the Warka Water social design project, launched by the architect Arturo Vittori in response to Ethiopia’s diminished sources of drinking water. Participants of the workshop will study the geometry of the Warka Water tower and understand its water harvesting technique, which is based on collecting water from the air. peerReviewed

Hands-On Math and Art Exhibition Promoting Science Attitudes and Educational Plans

The current science, technology, engineering, art, math education (STEAM) approach emphasizes integration of abstract science and mathematical ideas for concrete solutions by art. The main aim was to find out how experience of learning mathematics differed between the contexts of school and an informal Math and Art Exhibition. The study participants (N=256) were 12-13 years old from Finland. Several valid questionnaires and tests were applied (e.g., SRQ-A, RAVEN) in pre- and postdesign showing a good reliability. The results based on General Linear Modeling and Structural Equation Path Modeling underline the motivational effects. The experience of the effectiveness of hands-on learning at s…

Mathematics and Art Connections Expressed in Artworks by South African Students

In this chapter, we examine a collection of drawings, and paintings from South African students between the ages of 10 to 17, that provide fresh and original perceptions to some already known topics, but also several unexpected connections between mathematics and art. These works reference classic math-art connections such as: golden ratio, spirals, infinity, and geometric figures; they also contain several personal reflections, unique discoveries and references to ethnomathematical connections within the African cultural heritage. To introduce their pieces and themselves, students shared their own interpretations of their artworks. These commentaries make possible the identification of cog…

Bridging Art and Mathematics: Introduction

There is a long history of interdisciplinary discussions on the relations between science, mathematics, geometry, art, aesthetics, and artistic praxes. These discussions remain active and pertinent today: the aforementioned relations are explored in various scientific communities, journals, and at conferences. Globally, numerous scholars and artists share a common interest in combining creative thinking, intellectual curiosity, and aesthetic sensibility in their work. Various experts working in different scientific and technological fields are inspired by phenomena that combine mathematical and artistic qualities. Respectively, several contemporary artists, graphic designers, craftsmen, and…

Computational Thinking Development: Benefiting from Educational Robotics in STEM Teaching

<p style="text-align: justify;">The delivery of science, technology, engineering and mathematics (STEM) learning to improve an individual’s competence and future career interests has become a critical scientific undertaking for teachers and researchers alike. A plethora of research has proposed various hands-on robotics activities built on constructivist theories, thereby facilitating the development of knowledge based on reality for scientific and non-scientific stakeholders. Robotics may become an essential focus point within technology provision, which is an essential underlying characteristic for the seminal development of computational thinking (CT). However, despite the potentia…

KIKS Creativity and Technology for All

Abstract To help meet an educational and societal requirement for all students to enjoy, have confidence and ability in creativity and technology, the “Kids Inspiring Kids in STEAM” (KIKS) EU project adopted an intensive Hothousing process challenging students in Finland, Spain, Hungary and the United Kingdom to engage in collaborative problem solving to develop solutions to: “How would you get your schoolmates to LOVE STEAM?” The project provided a process and technology toolkit for students, including those with special educational needs, to achieve their solutions. A completion rate of 90% suggested that all schools and students could cope with and enjoy the process and associated techno…

Multiple Creativities Put to Work for Creative Ecologies in Teacher Professional Learning: A Vision and Practice of Everyday Creativity

AbstractIn this chapter, we argue for a new vision for teacher professional learning based on the diverse creativities as practice which catalyzes educational change in whole-school contexts. We argue that it is possible (and preferable) to expand improvements to teacher education and professional development beyond neoliberal notions of “workplace readiness” and toward an environmental, ecological, sustainable education for lives worth living. This creative ecological approach considers the entire context and community of various stakeholders.Applying a case study approach, we analyze teachers’ published assignments in a blended in-service teacher education course entitled “Everyday Creati…