Science Communication

Mathematical science communication has, as a field of science communication in general, gained momentum over the last decades. It aims at informing the public about contemporary research, enhancing the factual and methodological knowledge, fostering a greater interest and support for the science of mathematics, and enabling the citizens to apply it to their practical life, as well as decision-making on a bigger level. These objectives are met by the various formats and media in which mathematical science communication is brought to the public. There is classical journalism, which tells enticing stories about the subjects and protagonists of mathematics, science museums and events focused on engaging the participants in mathematical activities, and the internet hosts another variety of entertaining and interactive mathematics projects such as YouTube channels and interactive platforms. In the first part of the book, we want to build a body of comparable project descriptions to illustrate the variety of motivations, methods and goals.

Yet while the community of active practitioners is exchanging experiences, not much conceptualization has happened. Hence, the second parts focusses on the theorization of the many endeavors. The discourse of the field of science communication, has shifted (at least theoretically) from the deficit to the dialogue-model. How far has mathematical science communication come in this transformation? Mathematics is the provenance of making sharp definitions and thus, its science communication should follow its heritage and start the process of conceptualization. How can we terminologically differentiate between factual and methodological knowledge about mathematics and an affective response like interest, support and appreciation which are often demanded as a response. Is this adequately reflected in the use of terms such as understanding and awareness of mathematics? What are the dimensions of mathematical literacy? The definition given by the OECD in the PISA study1, may be a starting point to weigh in the aspects of being able to apply mathematics in the role of a democratic citizen. These and other questions will be considered in Part B.

The first part of the book consists of reflections of best-practice examples. Various actors in the field of mathematical science communication introduce their projects and give insight into the motivation behind their endeavors and describe their objectives. Where do they locate themselves between science communication and informal science education and which methods and instruments do they use, to bring their message across and to whom? How did they define the success of their project and in what ways was it measured? Were there any other forms of feedback implemented?

**What? (What is communicated?)**What are mathematical contents that are transported? How scientifically precise is their representation? Are they educationally reduced? Are any other ideas, concepts and beliefs part of the communication?**Goals? (What is the main objective of the project?)**Here, the narrative of the project is described. What is the message that should be brought across? Where can the project be located in terms of raising the public awareness, understanding or mathematical literacy? How much emphasis is put on (in)formal education?**Who? (Who is the communicator and audience?)**Who is the primary target group of the project? Are there secondary target groups? (i.e., reaching out to teachers in order to get through to pupils, or enhancing the visibility in the community by having a project that aims at the public.) Who are the actors behind the project? What institutions are involved, what is their profile and how does it relate to mathematical outreach activities?**Why? (What is the motivation?)**What is the motivation to realize the project? Where does the funding come from? How does the project relate to the political goal of enhancing the STEM subjects? Is there a general need for the objective of the project? Is there a scientific gain from the project, like for example in citizen science projects?**How? (What methods are used?)**What is the format of the project? What media and methods are used? How are the participants addressed? How much active participation from the public is possible? Is there a dialog between the participants and the scientists, or is it more an active sender and passive receiver scenario? If there is a dialog, how did the input from the participants shape the design of the project?**When? (What is the time frame?)**What is the time frame of the project? Does it have a history and have the objectives, methods and actors changed over time? How did the change of the media landscape (social media, etc.) affect the methods of the project?**Where? (Location)**Is the project locally linked? Where are the actors and participants located? What is the setting of the project? (local, international, internet, etc.)**Success? (What does success look like? Is it measured?)**What measures were undertaken to quantify or qualify the impact of the project? What conclusions can be derived from these numbers or impressions? What does success mean for the specific project?

The second part discusses the structural aspects of mathematical science communication and lays down the basics for its theoretical framework. Here we want to discuss the following questions:

**What?**- What are the objectives of mathematical science communication?
- What is mathematical literacy, public understanding, and public awareness of mathematics?
- What is risk literacy?
- How does it relate to general mathematical literacy?
- What are the beliefs and world-views of mathematics in the general public?
**Why?**- Why do we need mathematical science communication?
- Why is (scientific) mathematics of interest for the public?
- What is the narrative of mathematics in the 21st century?
- Why is raising the public awareness and understanding of mathematics and mathematical literacy a political goal?
**How?**- How can the public be actively engaged in a dialog about mathematics? (From deficit model to dialogical model of science communication.)
- What measures proved to be successful in order to alter the beliefs about mathematics?
- What synergies and differences are there between mathematical science communication and formal or informal education?
- Which role does Citizen Science play in mathematical science communication?
- How can Citizen Science be applied to mathematics?
**Who?**- What is the motivation of the mathematical and scientific community to engage in outreach activities?
- What target groups of mathematical science communication can be classified?
- How can we address diversity?
**When?**- History of mathematical science communication
**Where?**- What is the local component of mathematical science communication

For classification, comparability and transparency of the many projects in mathematical science communication, it is necessary to clearly define what public awareness, public understanding and scientific literacy means for mathematics.

In many everyday life decisions being able to understand risk and statistics is an important factor and has an effect on the health of the individual and the economy. Research on risk literacy studies whether individuals are sufficiently equipped to substantiate their decisions according to the statistical results, e.g., if they understand them “well enough”.

In the field of math education, the concept of beliefs and world-views is defined and studied. Can these concepts be broadened to the public awareness of mathematics and how do these beliefs and world-views correlate with public understanding and literacy?

Many mathematicians engage in popularizing their work in order to make it accessible to the general public. Since science is mostly funded by public means, there is a certain pressure to report about the achievements. Another reason can be to attract the next generation of successful mathematicians. A profound discussion of the motivations behind the endeavors to popularize the work of mathematicians seems insightful.

Abbot’s novel Flatland that coincides with the discovery of the fourth dimension has become very popular in the end of the 19th century. In the 70th, a homemaker stumbled across a mathematical problem in a magazine and significantly contributed to its solution. There are more stories to tell about the history of mathematical science communication and its repercussions to scientific mathematics.

What are the differences in mathematics education? What collaborations and synergies emerge from international networks and conferences? What role does the location in the global north vs. south play?