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A Word Problem:�The How’s and Why's of �Mathematics Communication

#MathComm

https://tinyurl.com/naswMathComms

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A Word Problem:�The How’s and Why's of �Mathematics Communication

With

Sam Hansen, They/Them

Noelle Sawyer, She/Her

Kenna Hughes-Castleberry, She/Her

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Welcome!

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The Why

Mathematics has a Big Problem!

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The Why

Many people do not see themselves within mathematics
Most people are never given the chance

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Sam does this slide ��All of those problems can really boil down to 2 big issues.

When people first set foot in a mathematics class it is rather understandable. Mathematics is a rather abstract and often otherworldly (tell me where else in the multiverse people comfortably go off on the features of the 137^th dimension) and it is often seen as being somehow beyond the human sphere. So of course they do not see themselves within mathematics.

But then there should be a moment, a chance to let them see themselves within mathematics except for most people they do not even get that chance.

The way mathematics is discussed in classrooms, in culture, in the media, etc it is very rarely mentioned that mathematics is done by anyone who is not a white guy, or potentially a South or East Asian Guys who immigrated to the US or Europe if they are going for diversity.

Even if they are ranging past just white guys this still leaves the vast majority of people in the world out of the narrative, out of the story of mathematics.

It also erases a huge amount of mathematical history. You know like the introduction of zero, the creation of Algebra, or the first solutions for systems of multiple equations

And if a person can not see themselves within mathematics, how can they ever feel as though they belong.

Add personal story about how being in math made me not think about my queerness or my gender because I did not have any stories other than Turing and that is not a happy one

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The Why

Mathematical Belonging is THE predictor of mathematics learning
Studies have shown that being mathematically confident at a young age is linked to higher self-esteem

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Barbieri CA, Miller-Cotto D. 2021. The importance of adolescents’ sense of belonging to mathematics for algebra learning. Learning and Individual Differences. doi/10.1016/j.lindif.2021.101993

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The Why

Mathematics communication, especially stories and narratives, can help create mathematical belonging through:

Increasing a sense of group membership
Normalizing struggle
Battling stereotypes
Creating a growth mindset

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The How

What does it mean to communicate mathematics?

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The Who

Math is for everyone, but who is your writing for specifically?
Keep your audience’s knowledge and their curiosity in mind.

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Language of Mathematics

Mathematics relies heavily on very specific, formal definitions - aka JARGON

Definitions that are often different from what almost everyone in the world things those words mean
For example: Real, Normal, Magic, Kernel

So please make sure to define your terms!
Be careful of jargon in your definitions!

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Language of Mathematics

Do not be afraid to use a Black Box

Your audience doesn’t have to understand everything, especially in math.

The Black Box can use analogies as the vehicle to get the more technical concepts across (we’ll talk about this in a second)

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Language of Mathematics

A curve 𝛼 that is parametrized by arclength is a geodesic if and only if for any two points P=𝛼(t₁) and Q=𝛼(t₂) on 𝛼 that are sufficiently close, all other arcs joining P and Q are at least as long as t₂-t₂.��
A geodesic is the shortest path between two points._��

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VS

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Language of Mathematics

Let g₁and g₂be two negatively curved Riemannian metrics on a compact surface S. If MLS(S, g₁)=MLS(S, g₂) then g₁ is isometric to g_2��
The collection of lengths of the shortest closed curve in each homotopy class is enough to determine the geometry of a negatively curved compact surface.

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Language of Mathematics

The collection of lengths of the shortest closed curve in each homotopy class is enough to determine the geometry of a negatively curved compact surface._��
If we agree that we’re looking at the same shaped object, and you tell me how long it takes to walk around all the holes in it, I can tell you the exact dimensions of the object.

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VS

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Analogize This

Dances between sine/cosine waves
“Jumps” in discrete quanta
Asymptotes - Cliff’s Edge
Fair Division - Cutting a Cake

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So, Let’s Talk Examples

Carefully defined or artfully black boxed the mathematical concept you are trying to communicate is only the start of your work
It is now time to bring in The Example!

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So, Let’s Talk Examples

Ways to use examples for communicating mathematics

The Running Example
One Example for Many Approaches
The Multi-Level Example

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A 1000 Words

If you have an image use it!
If you do not have an image make one!
If you do not know how to make one, ask a mathematician to make one.
If they say it is not possible to make the image you are asking for, ask them if they can make a simplified one.
If they still say no, that is ok. You did your best, and there is no more that anyone can ask for.

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An example:�Area of a triangle on a sphere

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The triangle on the bottom is the intersection of the three wedges above�
Adding up the areas of all three wedges is the area of the sphere + counting the triangle 4 extra times�
Area (triangle)�=(area of wedges -area of sphere)/4

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Application

Motivation

Applications can help with:

Your audience understand the mathematical theory
Your audience developing an intuitive sense of the mathematics
Your audience become engaged with the mathematics
Placing your story, both for the impact and/or the subject

The type of help you are looking for will tell you where to put and how to use the application

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Applications of Math

Math is literally everywhere!

A lot of stories involve more math that you might think

AI stories, art stories, even animal behavior stories

-That’s why understanding a few simple mathematical communication tips can be beneficial in making the research and writing easier

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Applications of Math

Some applications of math are more complicated than others

Examples: AI or quantum computing
This doesn’t mean that you have to get too into the weeds to tell your story.
Instead, ask yourself how much math is necessary to tell this story?

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Inaccurate

Accuracy

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Final

Tips

Passion Comes Through
Excitement is Engagement
Leave them with One Good Memory

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Sam take this one��

When we tell stories we are expressing our passion for the subject as well as our excitement. Those things will help people connect with mathematics.

I was talking with the mathematician and mathematical mime Tim Chartier once about his ideas with regard to teaching mathematics for liberal arts students and he said all he wants is to leave them with one good memory of mathematics so that the next time someone brings it up they don’t think about how they can’t do math or how they hate it, instead they think about that one cool math trick they learned or that one fun math story they know. That one good memory give them the foundation to build upon until they not only do not immediately think about how they hate it and instead like it and are the ones telling the stories themselves.

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Contacts

Sam Hansen�samuel@acmescience.com�https://samuelhansen.com�https://relprime.com

Kenna Hughes-Castleberry: kenna.castleberry@gmail.com www.kennacastleberry.com

Noelle Sawyer�noellesawyer@gmail.com�www.noellesawyer.com

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