Can We Model Generosity With Mathematics?

four celebrities and their donations – hemsworth $1000000, mariam (hs student) - 75, British Petroleum - $700000, Jeff Bezos – $700000

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.

Meanwhile, Lee Melvin Peralta critiqued ratios as too limited to fully model generosity.

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:

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.

Desmos Is Also a Curriculum Company Now

If you knew me as a classroom teacher, you knew I was very, very cranky about the ways many math textbooks treated students and mathematics, how they failed to celebrate and build on student intuition about mathematical ideas, how their problems were posed in ways that hid their most interesting elements, how they were way too helpful.

So it’s been a joy to get to do something more active about that problem than write cranky blog posts, to get to team up with some fantastic teachers, designers, engineers, and funders all continuously interrogating their assumptions about education, design, technology, math, and society, all to create what I think is …

the very best middle school math curriculum.

This is it.

Call off the search.

You found it.

Read more about the curriculum at the Des-blog, including details about our upcoming pilot.

[extremely Oprah voice] You get a debt of gratitude! You get a debt of gratitude! You get a debt of gratitude!

Aside from my enormous gratitude to the fantastic team I work with daily, I’m especially grateful to two groups:

  • The authoring / publishing team at Illustrative Mathematics / Open Up Resources who created and openly licensed a fantastic math curriculum, one which is the foundation of our own work. They dropped a massive gift on the math education community (or a hydrogen bomb from the perspective of the K-12 math publishing industry) and we were extremely happy to pick it up and build on it.
  • You. I’m talking about the folks who have been reading this blog, commenting on my posts, critiquing my ideas from day one. Your thoughts and mine are all tied together and run all the way through this curriculum.

This blog has been quieter over the last few years for reasons that are predictable – family, Twitter, the death of blogs, etc. – but also because, for the only time in my career, I haven’t been able to write about my work.

That changes today and I’m very excited to collaborate with you folks once again on the work that matters to me most. It won’t be at its best without you.

2020 Resolutions

Meanwhile, Nepantla Teachers, a group of math educators focused on social justice in their work, asked several educators to contribute a resolution for the new year. Here’s mine:

I'm resolving to spend as much time next year thinking about student lives outside of school as I do their lives inside of school. Teaching and curriculum have enormous influence on student learning but the influence of those in-school factors is dwarfed by out-of-school factors like housing and food security. So I'm resolving to practice humanizing pedagogies and to protest school closures in my city, to create interesting mathematical activities and to urge my representatives to protect and expand social programs. I'm resolving to ignore the distinction between educator and citizen. 

Click through to read resolutions from thoughtful people like Carl Oliver, Hema Khodai, Idil Abdulkadir, Marian Dingle, Makeda Brome, and Tyrone Martinez-Black.

The 2010s of Math Edtech in Review

EdSurge invited me to review the last decade in math edtech.

Entrepreneurs had a mixed decade in K-16 math education. They accurately read the landscape in at least two ways: a) learning math is enormously challenging for most students, and b) computers are great at a lot of tasks. But they misunderstood why math is challenging to learn and put computers to work on the wrong task.

In a similar retrospective essay, Sal Khan wrote about the three assumptions he and his team got right at Khan Academy in the last decade. The first one was extremely surprising to me.

Teachers are the unwavering center of schooling and we should continue to learn from them every day.

Someone needs to hold my hand and help me understand how teachers are anywhere near the center of Khan Academy, a website that seems especially useful for people who do not have teachers.

Khan Academy tries to take from teachers the jobs of instruction (watch our videos) and assessment (complete our autograded items). It presumably leaves for teachers the job of monitoring and responding to assessment results but their dashboards run on a ten-minute delay, making that task really hard!

Teachers are very obviously peripheral, not central, to the work of Khan Academy and the same is true for much of math education technology in the 2010s. If entrepreneurs and founders are now alert to the unique value of teachers in a student’s math education, let’s hear them articulate that value and let’s see them re-design their tools to support it.

Fave Five

Five of my favorite articles from the last month.