Handbook of Mathematical Science Communication

The following sections are included:

• Contents
• Foreword
• Acknowledgment

The mathematics exhibition in Munich 1893 on the occasion of the Annual Meeting of the German Mathematical Society (founded in 1891), curated by Walther von Dyck, is one of the visible starting points of Mathematical Science Communication: it drew a large crowd to the Technische Hochschule München, where objects and results of mathematical research were displayed in four rooms for an interested public. One of the rooms presented a “Wunderkammer” of geometric models — they attracted the interest of the audience due to their aesthetically pleasing nature and the unusual, novel shapes they represented [1]…

For over two decades, the NRICH team has been developing rich mathematical teaching and learning activities for students, families, and teachers. This trailblazing, research-informed project welcomed over 30 million pageviews to its online activities over the last 12 months (Source: Google Analytics). NRICH also works face-to-face with thousands of students and their teachers each year. This chapter explores the evolution of the NRICH project, from its early days as an online mathematics club for students to becoming an award-winning leader in mathematics education today.

At a time when developing effective problem-solving skills is becoming an increasingly crucial focus for jurisdictions across the globe, NRICH’s rich mathematical activities are helping to ensure that future generations of students develop and embed the types of transferable skills that will enable them to adapt and thrive in their rapidly changing world.

The Experience Workshop — International STEAM Network started in 2008 in Hungary and 2010 in Finland as a collaborative effort of mathematicians, artists, teachers, parents, and children. Experience Workshop has not formalized its’ membership. Members are loosely connected through various mailing lists and social media groups, and they are involved in a variety of events, conferences, and workshops in the role of contributors or participants. Experience Workshop organizes various math-art-education events and interactive exhibitions, workshops, seminars, and trainings all over Europe, along with educational and research collaborations in Africa, America, Asia, and Australia. Over the years, more than 40,000 people participated in our projects. Connections between mathematics and arts education provide Experience Workshop’s pedagogical basis. As mathematics and arts connections always involve a wide cultural background, we are increasingly focused on the need for Science, Technology, Engineering, Arts, and Mathematics (STEAM) integration in learning. The development of collaborative and inter-, multi-, and transdisciplinary problem-solving capabilities, which enable students to discover unexpected connections between different aspects of various complex phenomena, is not only a useful tool but is recognized as one of the most important goals of today’s learning societies. STEAM in today’s European schools represents a dynamically developing, but mostly unexplored field. In this chapter, we introduce our methods and various tools from Experience Workshop’s collection. By introducing one of our projects in detail, we would like to highlight especially those components focused on “mathematical arts and creativities”, uniting these diverse educational cultures with a more global perspective.

The following sections are included:

• Introduction
• What Can Teachers Learn from Mathematical Science Communication?
• University Courses on Mathematical Science Communication for Teachers
• Conclusions
• References

This chapter describes the development of a math trail for high school students. In 2016, we developed this trail through Leiden (The Netherlands) during a student project for the Science Communication and Society specialization, a track for master students at the Faculty of Science at Leiden University. Our aim was to provide a guided trail through the city that links everyday sights to mathematical concepts within the curriculum of high school students between 13 and 15 years old. The entire project was carried out in 3 weeks. We did background research, consisting of literature reviews, target audience surveys with school children, and focus groups with teachers. Based on the conclusions from this background research, we developed questions that suited both the goal to make the math trail a fun experience that makes math less abstract and the goal to include questions from across the curriculum. In this chapter, we would like to share our insights from the background research and our experiences in developing a math trail. We moreover aim to provide those who are interested in designing a math trail in their city with a practical step-by-step plan and checklist.

On the appropriately symmetric date of 12/12/12, over three hundred people gathered at the north end of Manhattan’s Madison Square Park to celebrate the flipping of a giant switch from 0 to 1. That switch simultaneously turned on the power to a new museum and updated the count of North American museums devoted specifically to the public communication of mathematical sciences. How did this day come to pass?

The following sections are included:

• Context
• The Permanent Exhibition
• Outreach Activities
• Assets
• Challenges
• Conclusion
• References
• Links

Mathematics Adventure Land, a well-attended permanent exhibition in a municipal museum in Dresden, Germany, was established in September 2008 as the result of a co-operation between the city’s technology museum and the mathematics department of TUD, Dresden’s renowned university of technology. We sketch the concept of the exhibition and explain its contribution to science communication.

As of now, Mathematics Adventure Land has existed for over a decade. An exhibition living for so long cannot be static, it must evolve. The organizing team is constantly developing a variety of additional offers to complement the current exhibits. The three authors of this article represent different aspects of this development: Bernhard Ganter, a now retired professor of mathematics, was one of the two founding directors and initiated many of the exhibits himself. In section “Origin, Motivation and Guiding Principles”, he will report how the project came about and which ideas were implemented in the process. Rahel Brugger holds a Ph.D. in mathematics and presently undergoes a traineeship in the museum (Volontariat). She reports in section “Education Formats in and Around Mathematics Adventure Land” on the many additional activities that have been initiated and realized. Section “Mathematics Adventure Land and Teacher Training”, written by Andrea Hoffkamp, who is a professor of didactics of mathematics and also a scientific director of the exhibition, shows how the exhibition contributes to the teacher training in co-operation with TU Dresden.

In this chapter, we will take you on a journey through mathematics exhibitions and other mathematics public engagement activities our nonprofit organization IMAGINARY has brought to life. This journey started in 2007 and was made possible through many collaborations and partnerships to get us to where we are in 2021, with more than 100 countries having seen our exhibitions, workshops, or other activities. The idea behind this article is to highlight key decisions we took on our journey, some personal insights, and to introduce our open and participative way to engage the general public with mathematical sciences.

In the first part, we will describe how the IMAGINARY project evolved over the last 14 years and how we have focused on refining our didactical approaches we deem appropriate for public engagement. This makes us a strong advocate for non-formal mathematical education. We have gathered our experience in creating material for outside-of-school workshops and help teachers prepare modern mathematical topics for the classroom, as well as other science educators. Another aspect that we took seriously and, as the project grew, had to dynamically adjust, was our approaches to customizing material for different demographics. The focus was both on the cultural context of different regions in the world, as well as the inclusion of groups that typically would not be exposed to mathematics exhibitions or workshops. This would include empowering girls and women as well as families from poorer socioeconomic backgrounds. In the process we revised our policies, balancing a strong commitment to free and open licenses, with our paid services covering our work. Our network has grown beyond the academic world of mathematicians and now includes different companies, artists, museums, and cultural mediators.

In the second part we will walk through a few of our latest projects that expose what is IMAGINARY nowadays. The highlights are the two exhibitions: La La Lab — the Mathematics of Music (2019) and I AM A.I. — explaining artificial intelligence (2020). We invite the reader to follow IMAGINARY on the next steps of its mathematics journey by providing a glimpse into a couple of currently ongoing projects we are involved in: the International Day of Mathematics (2020), our new 10 Minute Museum on the mathematics of the Climate Crisis (2021), and our exploration into interactive children story books through Mathina (2021).

Good illustrations of mathematical content enhance the science communication of mathematics as well as the scientific process itself. However, the creation of these illustrations, the rendering of videos, the process of mathematical making, is still underdeveloped and undervalued by many professional mathematicians. The semester program Illustrating Mathematics aimed at closing some of the gaps between the richness of mathematical content and the availability of corresponding illustrations by creating new and novel ways to show and present mathematics.

This article reports on the program’s related science communication and public outreach activities. To present the frame in which the activities took place, the first two sections briefly introduce the institutional setup and the scientific aspects of the semester program. The following sections each present one outreach activity in detail.

The following sections are included:

• Introduction
• Objectives
• Message
• Communicator and Audience
• Motivation
• Methods
• Time Frame
• Location and Adaptability
• Impact
• Concluding Remarks

There are many shifting ideas of how we learn and understand, and these inhabit current views supporting transdisciplinary education. Such diverse perceptions suggest a greater need now for discussions on how science, technology, engineering, and mathematics (STEM) integrate with the arts (A) across a range of learning settings, thus acknowledging STEAM. Still, experiencing STEAM is more than the acronym suggests. It is more than integration, as Keane and Keane, McAullife, and Burnard and Collucci-Gray attest [1–3]. A key aspect of STEAM learning points to the importance of considering personal and individual transformation through connected experiences [4,5], in which the dynamic contribution of dialectical emotions is appreciated and valued…

In this chapter, I would like to share my experience in making films about mathematics, about the tasks I set myself, about the difficulties I encountered, and about the reactions of ordinary spectators, and professional mathematicians.

In this article, I want to put the study of purely educational films beyond the scope of this paper. I am interested in representations of mathematics in popular films aimed at a wide audience, whose viewers are not only going to gain specific mathematical knowledge but enjoy the film as well.

The following sections are included:

• Prologue
• The Idea of the Film Project
• The Math and Culture Project
• The Fantastic World of M.C. Escher, the Movie
• Minimal Surfaces: Soap Bubbles
• The Möbius Band
• Other Few Examples
• Cinema and Mathematics
• The Audience
• Conclusions
• The Art and Mathematics Film Project
• References

Graphical representations can facilitate people’s understanding of mathematical content. This is crucial, for example, when health statistics are communicated to patients. In this chapter, we describe different graphical means and will, in particular, focus on icon arrays and natural frequency trees. Icon arrays are already understood by children and made their way into school curricula. They can be used to explain the pros and cons of different medical interventions as well as their risks and are increasingly used in the media — albeit not often enough. Natural frequency trees allow for transparent representations of the effectiveness of medical tests and interventions…

Societal and economic processes between organizations and individuals are increasingly designed with algorithms. Examples are digital consumer scorings, digital nudges, and dark patterns in marketing. These algorithm-based information architectures, more precisely their design, their interaction with individuals and the resulting dynamics, can empower but also manipulate. Therefore, political as well as civil society and consumer-specific debates are necessary. However, to take part in these debates and in novel societal and economic processes, individual prerequisites are required. Various approaches to algorithm literacy and data literacy (besides media literacy, digital literacy, competencies in the digital world, information literacy, etc.) attempt to define these prerequisites, but ignore the overlap with existing research too often. Taking into account the concepts that seek to formalize algorithm-specific preconditions, a roadmap is presented in order to inform developers of literacy concepts for the smart world.

The roadmap: From an existing general competence framework (e.g., concept of data literacy), competence fields (e.g., planning) can be isolated for the area of algorithms by analyzing the fields’ characteristics (including different competencies, for example, information search). On the one hand, it must be examined which existing concepts address these fields of competence at least in part. Overlaps between different concepts have to be identified and demarcations need to be made to the general competence framework. On the other hand, it has to be determined whether the current real-world state of the challenge is addressed. To this end, a test scheme has to be formulated to assess whether one’s competence framework of existing (and possibly added) competence fields can be ecologically valid. If the selection is justified, the premises — the motivational selection — need to be made explicit. One example is the premise that consumers can obtain quality-assured results when facing algorithms. Such premises are needed to determine literacy objectives (example: consumer has the competence to act with regard to receiving quality information by his scoring provider). Only with these objectives, the literacy levels can be formalized. The levels can range from awareness of systems to a commitment to algorithm regulation. It is then important to specify the competence contents implied by the chosen competence fields and the subject matter of algorithms (e.g., fairness of a classification) and to sharpen them to such an extent that quantitative investigations are possible. The level assignment has to be reproduced reliably with the selected contents in empirical tests. Standardization studies would then be necessary. In addition to such efficacy proofs in assessment, randomized controlled (experimental) studies should prove the effectiveness of competence differences. Qualitative work is also needed here to explore the scope of competence differences, for example with regard to trust. The roadmap presented is purpose-oriented to substantiate smart-world literacy concepts with regard to education and regulation needs but also innovation potentials.

As a consequence of digital transformation, mathematical forms of knowledge production and political processes are increasingly intertwined. On the one hand, mathematical and databased representations of the world play a greater role in policy design and implementation — a phenomenon that can be described as algorithmic governance. On the other hand, it is becoming increasingly clear that values and political implications are often embedded in mathematical systems. This interrelation can lead to a gap between the implicit political decisions made in mathematical models and the need for their democratic legitimation, raising the question how the societal relation between mathematics and politics is to be configured in response to the resulting problems. The chapter argues that mathematical science communication can play an important role in this arrangement. However, it needs to go beyond the still common “deficit model” and explore more dialogic and participatory forms. Only if political actors and citizens are part of a broader setting of two-way communication with mathematical experts can one hope to achieve adequate democratic legitimation for practices of algorithmic governance. Some conditions and strategies for shaping such a setting are laid out and concluded with a brief illustration of the case of fairness and transparency in machine learning as well as an outlook.

Mathematics (more generally: mathematical sciences) and publishers of journalistic content in general coexist in a complex alliance. We will focus here on two aspects of this relationship: on the one hand, journalists are deriving news stories from actual scientific results or events in the mathematical community; they are producing articles about mathematics. On the other hand, journalists can benefit from mathematical research by applying maths itself in the process of producing the news stories; they are producing news by the means of mathematics.

A lively scene of STEM activities and initiatives has arisen in Germany beyond the public school system during the last two decades. In this article, we make an inquiry on existing activities and initiatives in STEM subjects in Germany with a focus on the youth, Germany’s “Science Years” (“Wissenschaftsjahre”), the “Year of Mathematics” (2008), and its aftermath. We try to give an exhaustive outline on the existing activities but will not evaluate what’s being offered. We aim to show if or how the offer completes public education and ask for reasons for this extensive offer beyond the public school system that reaches from education to edutainment. Additionally, we outline trends in science communication in Germany with an emphasis on mathematics during the past 20 years. That’s why some of the sources below date back to the year 2000 and before. Links to online material for the various activities and initiatives can be found in the footnote section, the most recent entry being from March 2022. Printed sources may be found in the reference section. Some sources appear in both sections when the access via internet is free of charge.

The following sections are included:

• Epilogue: National Museum of Mathematics (MoMath): A Place for All People
• Index