I posted that image on Twitter last week, asking:
Which of these bushfire relief donors was the most generous? What’s your ranking? What information matters here? What would your students say?
Some teachers quickly identified a connection to ratios.
@math6falcon here’s a ratio activity for you!— Matt Murray (@Mr__Murray) February 6, 2020
Meanwhile, Lee Melvin Peralta critiqued ratios as too limited to fully model generosity.
I think it goes beyond a ratio problem when one considered the absolutely messed up things BP and Bezos has done in the areas of labor, the environment, and local economies and culture (negative externalities are just the start) /n— Lee Melvin Peralta (@melvinmperalta) February 7, 2020
I tend to side with George Box here, who wrote:
All models are wrong, but some are useful.
Anyone who thinks that proportional functions fully describe runners in a race, or that linear functions fully describe the height of a stack of cups, or that quadratic functions fully describe the height of objects under gravity, or that ratios fully describe generosity is, of course, kidding themselves.
But those models are all useful. Ratios are a useful way to think about generosity.
Emily Atkin originally stirred this question up for me in her fantastic climate change newsletter:
Chevron’s donation is paltry, however, given its earnings and relative contribution to the climate crisis. Not only is Chevron the second-largest historical emitter of all the 90 companies, it also earned about $15 billion in 2018. So a $1 million donation amounts to about .00667 of its yearly earnings. To the average American, that donation would amount to about $3.96.
So Atkin is evaluating generosity as ratio of net worth/earnings to donation size. But then she also considers the donor’s contribution to climate change.
The model is complex and grows more complex!
One teacher wanted to add fame and notoriety to our model, something Chris Hemsworth donates that Mariam might not. (Maybe she’s a TikTok teen, though. We can only speculate.) I talked with someone who lives in Australia about this question, and she said Hemsworth is less generous than someone from another country donating the same amount because of his identity as an Australian citizen. Robyn V wondered how to evaluate time donations, and even the donation of one’s life.
So ratios aren’t a perfect model for generosity, but they do offer us an important insight that, under some circumstances, someone who donates $75 is more generous than someone who donates one million dollars, which one teacher noted is a quantity that is really hard for students to fathom!
One teacher preparation program asked the question:
What do we think of this Maths problem ... interestingly fuzzy or annoyingly vague 😁 https://t.co/aqeYmcz4X9— Hull PGCE (@hullpgce) February 7, 2020
If the ambiguity of the original question strikes you as anything other than a feature, then please don’t risk the conversation.
If you go into the conversation presupposing a model for generosity rather than admitting to yourself in advance that all the models are broken, you’re likely to diminish students who suggest variables you had already excluded.
Okay, yes, um, ‘whether or not someone lives in Australia.’ Okay, that’s one idea, but can I get some other ideas, please? Perhaps ones more related to the math we’ve been studying?
All of these models are complex. All of them are certainly broken. And all of them offer you the opportunity to celebrate and build on your students’ curiosity and contextual knowledge, an experience that is all too rare for students in math class.
BTW: Shout out to Christelle Rocha for her observation that individual generosity is no way to solve the climate crisis.
Also, given that 3 out of the 4 pictured are people, are we implicitly positioning the entity as a person, or the people as entities? Another wondering: when individual generosity is compared, how might this distract from the responsibilities of agencies to preserve communities?— Christelle Rocha (@Maestra_Rocha) February 8, 2020