1 of 35

Modeling a Pandemic

Math Teachers’ Circle 4 Justice

Dates: 7/9/20 and 7/14/20

The MTC4SJ Team

2 of 35

Zoom Logistics

Click on your name

More

Type Name and Grade you Teach

Leave the meeting

3 of 35

WELCOME!

The Team!

Kyle Evans

Scott Kapralos

Georgina Rivera

Megan Staples

Today! Agenda

Intros/Welcomes
Modeling a Pandemic

Background
Problem solving

Connections to SJ

The Future!

Year-long MTC4SJ

4 of 35

Meeting Norms

Begin and end on time

Be screen ready

Be present both physically and mentally

Assume positive intentions

Step out of my comfort zone

Commit to learning and supporting others’ learning

Be mindful of airtime

Ask clarifying questions

Search for Social Justice Mathematics connections

5 of 35

Opening Circle:

CHAT

Share one silver lining from the past 3 months.

6 of 35

Our Group Goals

Capacity - problem-solving experiences with social justice mathematics

Community - shared experiences, resources, supporting pedagogical conversations

7 of 35

What do we mean by social justice math?

Using math to make the world more just

Analytic tool to MAKE SENSE OF the world
Tool to ADVANCE CHANGE in the world

Link - Read the world and Write the world

We lead with the mathematics and content drawn from the world around us. What content, problems, issues demand that we use math?

As soon as you’re talking about equity - you have to be talking about mathematics. (similarly for systematic bias)

But beyond fairness for groups. Also about using math to see how we are taking care of our climate, food supply, etc.

What this is not about - not about pedagogy, tracking, student identity. All related, but we do not lead with those.

[Capacity building. Not intended to be Make-and-Take]

Other notes:

Not sure how much we want to say here. Page 18 of Berry's book has nice description of what they mean by SJ. Page 23 has helpful set of goals of teaching M4SJ, which includes "help students learn to value mathematics as a tool for social change" and "empower students to confront and solve real-world challenges they face".

8 of 35

Features of Social Justice Math

Investigation

Awareness / Problem-solving

Reflection

Identity

Viewing yourself

Diversity

Viewing others

Justice

Viewing fairness

Action

Combat Injustices

9 of 35

Teacher Considerations

Strong mathematical CONTENT
Authentic and relevant CONTEXT
(When?) Sequencing and scaffolding (both math and SJ)
(How?) Pedagogy and assessment (both math and SJ)

10 of 35

Modeling a

Pandemic

CT Coronavirus Case Count

NYTimes 7/7/2020

11 of 35

Guiding Questions

How can mathematics help us understand the phenomenon of a pandemic?�
What factors impact the spread of a disease like Covid-19?
Which of these factors can we influence? (society, in schools)

How can mathematics help us act during a pandemic toward better outcomes?

12 of 35

What Factors Impact the Spread of Disease?

Post one or more factors in the chat

CHAT

13 of 35

D.O.T.S.

D = Duration (how long infected)

O =Opportunity (dependent on social interactions)

T = Transmissibility (likelihood of “effective transmission” of the virus, based on how it travels and travel conditions)

S = Susceptibility (likelihood of catching if exposed - varies with population, immunity, etc. )

Four Factors (Quantities) that Impact the Spread

Megan

Megan - connect what they have posted in the chat (with Slide 12) to D, O, T, S

Note = What can we impact]

(DOTS from The Rules of Contagion: Why things spread and why they stop. by Adam Kucharski - https://www.nytimes.com/2020/03/05/health/coronavirus-deaths-rates.html)

Duration - can’t really change - how long are you infectious for - (can change quarantine if exposed)

Link to chat: quarantining; contact tracing

Opportunity – any contact where it could spread (opportunity changes with density -- e.g., prisons, meat packing plants)

Link to chat: change - social distancing, stay at home can’t change -- density of cities

?? masks go here instead??

Transmissibility – likelihood it can move around!

Link to chat: masks, washing hands, outdoors over indoors - can’t change how infectious.

Susceptibility – likelihood of catching if exposed

Link to chat: vaccine, herd immunity can’t change our biology

14 of 35

Example

DOTS

Duration - 5 days

Opportunity - 15 contacts per day

Transmissibility - 4% chance of transmission

Susceptibility - 95% likelihood of catching if exposed

15 of 35

Example

DOTS

D * O

5 * 15 = 75 total contacts

T * S

4% * 95% = 3.8% chance of contracting virus per contact

D * O * T * S

75 * 3.8% = 2.85

What does this quantity represent?

Duration - 5 days

Opportunity - 15 contacts per day

Transmissibility - 4% chance of transmission

Susceptibility - 95% likelihood of catching if exposed

CHAT

16 of 35

Reproductive Value (R)

R = D * O * T * S

R₀ = The Reproductive Value of the virus (unmitigated/potential)

R_e = The Reproductive Value in context = R effective

Reproductive value can change
Varies with community (immunity; density; norms of social interaction)

On average, how many other people does one person infect?

17 of 35

PUBLIC HEALTH POLICY aims to impact the R value.

What R-value (R_e) are they aiming for?

Get R_e below 1!

CHAT

R0

18 of 35

What is R_e in each state?

Look at “rt.live”

R_e = D * O * T * S

Megan

Moderator: Kyle

This is a math problem in and of itself -- extrapolating from data to determine the R values

[[consider showing other states- same slide]]

[[doesn’t tell you how many people are sick -- just how changing over time]] [[might be surprising NV is higher than TX]] [[MES - find out current #s from NV and TX, and CT]] CT 47000, new cases less than 100 per day TX - over 9000 new per day NV - 700 per day

[[our model will work with both]]

[[this shows one policy -- the stay at home orders]]

[[parallel to work we’ll be doing]]

Now we’re going to use these ideas -- of DOTS, which produce this reproductive value -- to try to better understand the spread of disease during a pandemic like we have, and ultimately we’ll look at some school policies and how they can impact the spread of disease.

19 of 35

Modeling a

Pandemic

20 of 35

Group Work … Learn learn about the App

21 of 35

Introducing a general model…

SIR model

From Dan Teague- Flattening the Curve: Understanding R₀.

22 of 35

Let’s Model Using the Applet

Duration

Days contagious = 5 days

Opportunity

Number of Contacts per Day = 10 Contacts

Transmissibility and Susceptibility

Chance of contracting virus per contagious contact = 5%

Gives us R_O = 2.5

D.O.T.S.

S

I

R

Tonight we are going to use the NCTM pandemic app the url is being pasted in the chat or you can google “NCTM pandemic app”

This app allows you to change the size of the population

And the DOTS values

Duration… Days contagious

Opportunity… # of contacts per day

T and S (transmissibility and susceptibility) are combined as the Chance of Contracting per contagious contact

I am going to do one right now to show you how to navigate the app:

Population is set for 400 (reasonable school size)

5 days,.. 5%...10 contacts… Ro = 2.5

After you calculate or recalculate the results, you can “hit the replay button to see each variable separately or together. For example, If i “cross out” no longer contagious and just infected to see contagious, we will see this...

So what we are going to do in a moment is start to manipulate the DOTS values and see how the data are affected.

23 of 35

Task #1: Breakout Rooms...

In your Breakout Rooms (7 Minutes)

Introduce yourself to your group members

On your own: Get to know the app by manipulating the variables and running simulations.

How do the different DOTS values impact the outcomes?
Are some variables “more influential” than others? For which outcomes?
Can we model a “flattened” curve?

As a group: Ask each other questions as you explore

24 of 35

Group Work Samples

25 of 35

Task #2: Breakout Rooms...

Group time! (15 mins)

How do policies implemented by the state and school districts influence the spread of Covid 19 in the schools?

Select an App Driver
All contribute (use annotation option)
Explore different policies and how these affect the variables

Write Up One Policy to Share (will be on web)! (10 Minutes)

Use the template provided
compare a “control” situation and an “experimental” situation under a policy.

Merge Groups (6 minutes, 3 minutes per group)

One person (not app driver) will share your policy and outcome with another group by sharing your product.

If you need help, please add a comment in the slide deck!

26 of 35

[POLICY DESCRIPTION]

Caption (if needed)

Initial Conditions:

Population: 400

Days contagious: 10

Chance of contracting virus per contact: 5%

Number of contacts per day: 5

Assumptions:

Observations:

Limitations:

IMAGES

I am going to model how I may want to complete this template… Megan, Kyle, Gina, and Myself will be modeling how the group will work.

I will be the app driver. I am going to share my screen so that the rest of the group can see the screen.

You already mentioned some policies that the state is using, I am going to pick one that they are NOT doing just to give you an indication on what the work flow looks like.

The best way to do this is have the app driver split their screen.

I set the parameters to

Population: 400

Days contagious: 5

Chance of contracting virus per contact: 5%

Number of contacts per day: 10

Then I run the simulation. I only want to see the number newly infected and contagious.

So what if we chose the “test student temperatures” policy

I will ask “what variable do you think would be affected by checking temperature
Megan will say “number of days contagious because we will send them home and get them out of the population”
I will ask “what number should we change this to?
Kyle will say “how about decreasing it by one day?”
Gina will say “that sounds like too few… maybe two days”

As you can see figuring out what variable to adjust and by how much is the challenge. Remember that all models have limitations so your models will not be perfect.

27 of 35

Social Justice Math

Reflection

How do we take the next steps to incorporate SJ features?

Using math to make the world more just

Analytic tool to MAKE SENSE OF the world
Tool to ADVANCE CHANGE in the world

28 of 35

Features of Social Justice Math

Investigation

Awareness / Problem-solving

Reflection

Identity

Viewing yourself

Diversity

Viewing others

Justice

Viewing fairness

Action

Combat Injustices

29 of 35

Visit our website for updates and resources

bit.ly/mtc4sj

30 of 35

QR code

Please Take our Survey

bit.ly/mtc4sjSurvey

31 of 35

Coming Next!

Analyzing Racial Injustices

Tuesday, August 11th at 7pm

32 of 35

Resources

News reporting

New York Times - Daily update on states and countries. Shows trends. https://www.nytimes.com/interactive/2020/us/coronavirus-us-cases.html

NYT - July 5, 2020 - The Fullest Look Yet at the Racial Inequities of the Corona Virus

Podcasts

BBC -More or Less - many episodes about counting covid cases, understanding spread, etc.

Visuals/demonstrations to show elements of spread

Washington Post 03.14.20 Why outbreaks like coronavirus spared exponentially, and how to “flatten the curve”

Dynamic Graphic - showing spread, and how stay-at-home helps https://thespinoff.co.nz/wp-content/uploads/2020/03/Covid-19-Transmission-graphic-01.gif?fbclid=IwAR1TfOz6c7vk7aN4-JH9CixA8CFpBA_PLILiDzTHNaxITXRW40h_ydfHxQE

Watch how Exponential Growth Really Works

https://www.pbs.org/video/watch-how-exponential-growth-really-works-37154/

33 of 35

What is R₀ for Covid19?

34 of 35

35 of 35

Equitable Mathematics Teaching Practices

Draw on students’ fund of knowledge	Monitor how students position each other	Press for academic success
Establish classroom norms for participation	Attend explicitly to race and culture	Attend to students’ mathematical thinking
Position students as capable	Recognize multiple forms of discourse and language as a resource	Support position of sociopolitical disposition

Bartell, Battey, Edwards, Foote, Spencer, Wager

2017

CHAT