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Mathematical Modeling 3 Act Presentation

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Mathematical Modeling 3 Act Presentation

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email laura.rulsion-lange@savvas.com

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DM on Real World Math

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NCTM- Promoting Growth Mindset with 3 Act Math

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NCTM- Promoting Growth Mindset with 3 Act Math

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Folks, if you teach stats in middle school or high school, 2019 is your time to shine.

Here are a couple of items where the world needs your help and one way where the world (a/k/a Desmos, the New York Times Learning Network, and the American Statistical Association) is here to support you.

Marginal Tax Rates

Here is a clip from 60 Minutes in which Congresswoman Alexandria Ocasio-Cortez proposes a 70% top marginal tax rate.

And here is a ranking of the last five words of that sentence for "concreteness of meaning to average Americans":

1. 70%
2. tax
3 [tie]. rate, top, marginal

A 2013 YouGov poll convincingly illustrates how little Americans understand our marginal tax rate system. YouGov posed the following scenario:

Suppose that your income put you at the very top of the 28% tax bracket and you earned one more dollar such that you were now in the 33% tax bracket.

They asked 818 respondents to choose between two options:

1. My tax bill would go up a very small amount.

2. My tax bill would go up substantially.

Only 52% of respondents correctly answered that their tax bill would go up a very small amount. Democrats answered that question correctly nearly twice as often as Republicans, a difference which is amply explained by all the Republican leaders who are smart enough to know how marginal tax rates work lying to people about how marginal tax rates work.

Explaining tax rates before Reagan to 5th graders: "Imagine if you did chores for your grandma and she gave you $10. When you got home, your parents took $7 from you." The students said: "That's not fair!" Even 5th graders get it.

- Scott Walker (@ScottWalker) January 15, 2019

We need to help our students - whatever their political inclinations - believe fewer lies.

There are lots of interesting questions our students (and their teachers!) should ask about taxes and the kind of society they want to live in, questions like " What are the upsides and downsides of making Dwayne 'The Rock' Johnson pay 70% of the money he makes above 10 million dollars in taxes?" But we cannot answer those interesting questions if we don't have a basic command of the facts of our tax system, if we allow our leaders to deceive us about how marginal tax rates work.

Stats teachers: you have the power to make your students smarter about taxes in a day than fully half of Americans have been in their entire lives.

1. Take a few representative individuals from the world - real or imagined, but definitely including The Rock.

2. Hypothesize their income. Just make up numbers across an income distribution.

3. Use our tax brackets to calculate their tax bill.

4. Create a new set of brackets that are more just.

What's Going on in This Graph?

At Desmos, we've been enormously enthusiastic about the partnership between the New York Times Learning Network and the American Statistical Association they call What's Going on in this Graph?

In that partnership, the NYT team selects a newsworthy and timely graph from their award-winning output. The ASA team hosts a conversation on the NYT website about what students notice and wonder about those graphs.

For the rest of the school year, my team at Desmos will be helping teachers host those conversations in their classrooms from our Activity Builder platform. A new graph and activity every week. Give them a try.

There's no time like 2019 to start all of this.

Featured Comments & Emails

Ben Orlin offers a useful lesson plan here:

One of my favorite parts of teaching Precalculus was a "Design Your Own Income Tax System" project, which went something like:

-Make up your own system (minimum: 5 brackets);
-Write a paragraph justifying your decisions;
-Make up 5 individuals (+ their professions) and compute how much tax each would pay;
-Express MTR as a function of pre-tax income (and graph it);
-Express tax owed as a function of pre-tax income (and graph it). (By far the hardest step.)

An unhappy email:

While the information about Americans misunderstanding taxes did not surprise me, your choice to bring politics into the situation did. How do you propose we use your information about the tax knowledge of Democrats vs. Republicans with our students? Should we poll the students on their political affiliation and spend twice as much teaching taxes to our Republican students as we do our Democrat students?

The difference in tax knowledge between Democrats and Republicans along with the propensity of Republican leaders to lie to their constituents about marginal tax rates is meant to heighten the importance of good instruction here. Whether students grow into Republicans or Democrats is irrelevant to me (in this particular moment). If they or their parents pay attention to Republican leaders or media, they are getting lied to about this particular issue and we can do something about that.

Another unhappy email:

You've made this particular mail also about politics. Roughly: "Dem/good Repub/bad" Does that serve your core goal (statistics pedagogy)? Thanks for this free service. I hope to read the next one.

FWIW I'm more inclined to believe "people/bad" than "Democrats/good" "Republicans/bad." But it certainly seems true that Republican leaders are willing to lie about this issue and that Republican voters are believing those lies. Teachers can and should subvert that relationship. Not necessarily converting Republicans to Democrats but making sure Republicans disbelieve their leaders when they lie.

Another:

This sort of proselytizing does nothing but polarize. You're taking advantage of those who follow you for your insights with math education to preach your opinion about complex, controversial political topics that require nuanced thought and discussion to resolve. Have you ever changed your mind due to other people smuggling in their unsolicited opinions about politics like this? If you're looking to change people's minds about politics, do it through an open, honest platform where that is your sole purpose. I hope you stick to math without trying to fit in other agendas that distract from this purpose in the future.

I get that it's a drag to see a) Republican leaders lying to their constituents, and b) their constituents believing those lies, but those aren't "opinions" of mine. They're the facts of the situation, and teachers need to work an overtime shift countering that deception. I hope that directly before or after you emailed me you emailed a complaint to the Republican leaders who are making your job harder.

Another:

When I was at university, we would have been required to present various viewpoints on an issue. Our professors would have required us to present pros and cons for each side. For examples, [dopey climate denier webpage] would give an alternative for our students to consider.

Thanks for the comment. Some issues are controversial enough that they deserve a hearing of multiple sides. Many other issues deserve no such hearing. The fact that " global climate change caused by human activities is occurring now, and it is a growing threat to society " is a settled issue by climatologists, our government, the military, and even for=profit insurance agencies. Now we need to decide what to do about it. By contrast, whenever I write my post declaring The West Wing the most overrated show of the 20th century, I will be sure to allude to opposing points of view.

Reader Bill Rider sent in his account of a lesson from his class:

I stated that this prompt came from a political discussion that revealed a lack of understanding about marginal tax rates among fellow politicians and pundits. Our learning about this idea would make us better informed that many adults. ( This enhanced their attention.)

In true Dan style, I didn't want to script this too much. Together, we wrote the seven marginal tax rates on the board.

I asked them how much tax one would pay (Individual) on a salary of $9,525. (Upper end of the lowest bracket.)

I then asked how much extra tax one would pay if they received a $10,000 raise. This allowed the kids to learn that some of the money is taxed at one rate and the rest at another.

We then considered someone who earns $520,000 a year. How much of that salary would be taxed at 37%?

In their groups, they collaborated to determine the total tax bill on $520,000.

Collecting each of the seven tax bracket computations allowed us to see things like: .32| 157,501 - 200,000| = tax for that portion of income

We determined that effective tax rate. Each class had at least one student who asked "why can't we just make life easy and use that effective rate for everyone?" Rich discussions ensued.

We discussed the many who fear moving into the next tax bracket and why such a fear was unfounded.

We discussed a representative's proposal to move towards a higher upper bracket of 70% , historical higher rates, the number of folks that might be affected and whether one would pay 70% on all income as a high earner.

I started to type up a worksheet but it seemed to scripted/guided... and it didn't come from their questions and their desire to be better informed than an adult.

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Folks, if you teach stats in middle school or high school, 2019 is your time to shine. Here are a couple of items where the world needs your help and one way where the world (a/k/a Desmos, the New York Times Learning Network, and the American Statistical Association) is here to support you.

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Real World Problem Soving

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I train mathematics educators who want their students to be better problem solvers.

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3 Act Task