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Mathematical Communication

The Why and The Who

About the Lesson

Purpose

Discuss the importance of points and goals for all communications, the communication needs of distinct audiences, and the many different communication formats and styles.

Goals and Outcomes:

  1. Participants will be able to tell the difference between the points and goals for communications.
  2. Participants will provide an example point and goal for a draft communication of their own.
  3. Participants will be able to describe the needs of different audience types
  4. Participants will discuss how different methods of communications work for different audiences
  5. Participants will critically appraise multiple methods of communicating

Tools Used

  • For sharing ideas and best practices we use Scrubmlr

Lesson Notes

The Big Questions for all Communications

  • What is your Point?

    • What do you want people to take away?

  • What is your Goal?

    • What do you want out of the presentation?

  • What does success look like?

    • How can you tell if you succeed?
  • Always keep these in mind!

Examples of Points

  • This is how I proved my Theorem about the Null Sets of Integer Magic Edge Labelings
  • Here are applications of my work on Energy Market Optimization
  • I think this research program can move Green Energy Systems Modeling forward
  • We should focus more on Pushing Solar than Building New Nuclear Power Plants
  • We have been thinking about Uncertainty and Decarbonization all wrong

Common Goals

  • Inform/Educate
  • Entertain
  • Increase Engagement
  • Trust Building
  • Change Minds/Behavior
  • Starting a conversation
  • Impact Policy/Decisions
  • Get/keep a job
  • Have fun

Things to Think About When it Comes to Points and Goals

  • Your Point

    • Is your point clear and well defined?
    • Are you identifying a solution or a path forward?
    • What are the common misconceptions and arguments about your point?
    • What could get in the way of you getting your point across?
    • Are these things you can control?

  • Your Goal

    • How completely do you need to meet your goal?
    • Does your audience need to know your goal to achieve it?
    • Will your audience be in the right mind space for your goal?
    • What could stop you from achieving your goal?
    • Are these things you can control?

Points and Goals Activity

  • Choose (or imagine) and upcoming communication you will be engaging in. Outline what the point and goal of the communication will be, as well as what success will look like.
    • Discuss with a neighbor potential impediments in getting your point across and obstacles toward reaching your goal.

Audiences

  • Assets, Not Deficits

    • Consider the strengths, skills, knowledge, and culture of the audience and design your communication to connect with those those
      • Audiences are not blank slates to be filled with knowledge
      • Understand your audience’s curiosity, interests, and concerns; this is your communication sweet spot
        • Audiences are more likely to react positively to communication if it has relevance to their lives
      • It is a “What can we build upon?” instead of “What is missing?” perspective
    • Recognize that your perspective is not the SINGULARLY CORRECT perspective for contextualizing your results and their potential impacts; no matter how correct your results happen to be
      • The lived experiences and cultural knowledge of your audience deserve to be respected and acknowledged
    • (Holland et al., Nisbet and Scheufele, Simis et al.)

  • Not a Monolith

    • Understand that no audience will be homogenous
      • Everyone will bring in their own identities and positionalities to your communication
      • These identities/positionalities are not independent and their intersections need to be considered
      • Reactions to your communication will also not be monolithic
    • When creating your communication consider:
      • What assumptions you are making about your audience?
      • How will these assumptions impact your audience members? Especially those whose intersectional identities and positionalities are not a part of the dominant culture
        • Note: The dominant culture in this case has to do with what culture/group holds the power in the communication. It could be the group in the majority (mathematicians for a talk presented Joint Mathematics Conference), in the minority (economists for a public panel on inflation) or it could be an individual (teacher for a class) (Bussmann et al.)
      • In what ways can you design your communication to include those with non-dominant identities/positionalities and welcome their engagement?
    • (Canfield et al., Longnecker, Shimmin et al.)

  • The Audience is NOT an OTHER

    • The communicator is not separate from the audience
      • Creating a Scholar/Public or Teacher/Students dichotomy can lead to deficit approaches, harmful power dynamics, and marginalization of “non-expert” voices
    • Communicators are a part of the collective
      • Class instead of Teacher/Student
      • Community instead of Scholar/Public
    • (Simis et al.)

Audience Identification Activity

  • Using the example communication from earlier imagine who your audience will be and describe them in as much detail as possible, from age to disciplinary knowledge to culture and more.
    • Discuss with a neighbor how you would use this understanding of your audience to help them connect with your communication.

  • Technical Audiences

    • Fellow Experts in sub-discipline
      • Go Deep Deep Depp
      • All the theorems
      • Definitions can be less explicit
        • Jargon is not just expected but useful
      • You can assume they understand the significance
    • Fellow Disciplinary Researchers
      • Go Deep, but with context
      • Explicit definitions
      • More Citations
      • Explicit possible connections
      • If you make the impact clear, they will understand the significance
    • STEM Professionals
      • Creating a shared understanding across disciplines
        • Clear definitions, and definitions for the definitions
        • All the context
        • All the connections
        • All the citations
      • Do not assume they know why it is interesting
        • Focus on significance and impact
    • (Hutchins, Karvonen, Wettstadt)

  • Students 

    • Primary School
      • Questions
        • This goes both ways, ask them and welcome them!
        • Follow their curiosity if possible
      • Tangents are ok, but try to stay on course
      • Children are smart, trust them enough to explain
      • (Letters to a Pre-Scientist)
    • Secondary school
      • Connect concepts to the students’ lives
      • Discuss your research process, and provide an example of what it means to be a mathematician or scientist
      • (Inria, Lesperance-Goss)
    • Ask the Teachers!
      • They are with their students every day
      • They know what works
      • They know what does not
    • Higher Education
      • STEM Focused Students
        • Delve deep
        • Connect to other areas of STEM
        • Focus on how and why it was developed
          • Help to socialize student into the community and culture
      • Non-STEM Focused Students
        • Why is it interesting?
          • In general
          • To a student specifically
        • Connect to the world outside of STEM
          • Focus on Applications
        • How does this move them forward in their studies? In their careers? Etc.
        • (Cotner et al., Dawson et al.)
      • Graduate vs Undergraduate
        • Undergraduates may or may not be going on into research
        • Never assume either group understand the motivation
        • How much do they NEED to know?
          • Do not assume either will understand the connections between different fields within math or other STEM disciplines
            • Undergraduates may not NEED to, but they may find it interesting
        • Undergraduate education is about developing the thought process
        • Graduate education is about developing the explicit knowledge and skills
      • (Hutchins, Karvonen)

  • General Audiences

    • Children/Youth
      • Hands-on if possible
      • Rely on their curiosity
      • Make it relevant to their lives
      • Share more of yourself than just STEM
      • (Molinari, NASA, Yale)
    • Adults
      • General Public
        • Be very careful about any assumptions about knowledge
          • Lack of knowledge does not mean lack of intelligence
        • Trust your audience to dig deeper if they want to know more
          • Many of them have long term interest in STEM
        • Be clear and honest about what is known and unknown, and why
          • If there are other perspectives be willing to discuss them, even if they are not factual
        • (Deng, Dries et al., Karvonen, Meredith)
      • Governmental/Policy Level
        • Dual audiences
          • Staff
          • Lawmakers
          • Both need the main point/conclusion, especially how it will impact voters
          • If a full report is read it will be by the staff
        • Understand their political frame and how it will influence their perception of your work
        • The Deficit Model works here
        • (Meredith, Simis et al.)
      • Industry
        • Consider the possible business cases/objectives your communication may raise or meet
        • Clearly summarize the results for the decision makers
        • (inChemistry)

Different Audience Activity

  • Choose a different audience for your communication example. Describe what you would change about your communication to meet the needs of the new audience
    • Discuss the new audience and your changes with your neighbor.

  • Other Audience Considerations

    • Education Level

      • Really easy or really hard to determine
        • Lean toward assuming less education

    • How Many

      • 1-10
        • Communication as Conversation
      • 11-50
        • Communication as Talk/Lecture
      • 51-500
        • Communication as Performance
      • A whole lot
        • Communication as Show
      • Smaller than expected
        • Shift toward letting the audience guide you
      • Larger than expected
        • Shift toward guiding the audience
      • (Anderson, Morgan)

    • Location

      • Think about WHERE your audience will take in your communication
        • Are they in the room with you?
        • Are they sitting at their desk?
        • Are they doing other things at the same time?
      • How will this impact your communication?

    • Directionality

      • Are the audience seeking you out?
        • Why are they seeking you out?
        • How can you keep them from disengaging?
      • Are you seeking them out?
        • How can you make your communication more attractive to your potential audience?
      • Are they being brought to you?
        • Why are you being provided with this audience?
        • What is their likely engagement level?

Summary Activity

  • Write a summary of your most recent research for two audiences with different amounts of technical knowledge
    • These will be used in the next session

References

Anderson, J. (2009, September 22). _Size Matters – Shaping Your Speech To Match Your Audience – The Accidental Communicator_. Link to Resource
Anonymous. (n.d.). _Perry’s Model of Cognitive Development during the College Years • Article_. BYU-Idaho Learning and Teaching. Link to Resource
Bussmann, J., Altamirano, I., Hansen, S., Johnson, N., & Keer, G. (2020). Science Librarianship and Social Justice: Part One Foundational Concepts. _Issues in Science and Technology Librarianship_, _94_, Article 94. Link to Resource
Cotner, S., Thompson, S., & Wright, R. (2017). Do Biology Majors _Really_ Differ from Non–STEM Majors? _CBE—Life Sciences Education_, _16_(3), ar48. Link to Resource
Dawson, J. Q., Allen, M., Campbell, A., & Valair, A. (2018). Designing an Introductory Programming Course to Improve Non-Majors’ Experiences. _Proceedings of the 49th ACM Technical Symposium on Computer Science Education_, 26–31. Link to Resource
Deng, Q. (2024). Who Are the Science Audiences? A Typology Study on Digital Scientific Audiences: Persona, Performance, and Public. _Science Communication_, 10755470241252160. Link to Resource
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Holland, K., Moultrie, S., Smith, K., Carr, C., Barker, J., & Weaver, C. (n.d.). _Comparison Between Asset and Deficit Based Approaches_. Engaged Scholarship Curriculum. Link to Resource
Hutchins, J. A. (2020). Tailoring Scientific Communications for Audience and Research Narrative. _Current Protocols Essential Laboratory Techniques_, _20_(1), e40. Link to Resource
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Longnecker, N. (2023). Good Science Communication Considers the Audience. In S. Rowland & L. Kuchel (Eds.), _Teaching Science Students to Communicate: A Practical Guide_ (pp. 21–30). Springer International Publishing. Link to Resource
Meredith, D. (2010). _Explaining Research: How to Reach Key Audiences to Advance Your Work_. Oxford University Press. Link to Resource
Molinari, M. (2023, November 14). _Our 10 top tips for engaging young people_. Science Museum Group. Link to Resource
Morgan, N. (2011, January 12). Does size matter? How audience size changes speeches. _Public Words_. Link to Resource
NASA Science Editorial Team. (n.d.). _Enhancing Engagement: Strategies for STEM Professionals to Encourage Youth to Consider STEM Careers - NASA Science_. Link to Resource
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Shimmin, C., Wittmeier, K. D. M., Lavoie, J. G., Wicklund, E. D., & Sibley, K. M. (2017). Moving towards a more inclusive patient and public involvement in health research paradigm: The incorporation of a trauma-informed intersectional analysis. _BMC Health Services Research_, _17_(1), 539. Link to Resource
Simis, M. J., Madden, H., Cacciatore, M. A., & Yeo, S. K. (2016). The lure of rationality: Why does the deficit model persist in science communication? _Public Understanding of Science_, _25_(4), 400–414. Link to Resource
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Yale Wave Editorial Staff. (n.d.). _6 Fun and Engaging Ways to Encourage a Love of Science in Younger Students_. The Yale Wave. Link to Resource