Stats Teachers: 2019 Is Your Year

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.

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.


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.


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.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. +1 to all that.

    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.)

    The math goal was to give kids deeper experience of piecewise-defined functions (and the function concept in general); the civic goal was to help them understand the primary mechanism by which our government is funded.

    Students came up with wild, awesome stuff. Some gave negative MTRs (basically recreating the earned income tax credit); some gave MTRs above 100%; one precocious kid (who already knew calculus) gave MTRs that varied continuously with income, thereby requiring integration to compute your tax owed.

    • I am stealing, erm, I mean “borrowing”, this for my Precalculus class. Thanks for the awesome idea Ben!

    • It is probably interesting to note that the current MTR does vary continuously with income level. If we figure out total federal income tax owed (based of the MTR tax table) and divide by gross income, then the percent of income paid towards federal income tax does continuously change even within a given marginal rate.

  2. It’s funny – I didn’t think any of this was controversial until I read your follow-up message about the controversies.

    It seems to me that your scope was too limited. IMO, all teachers are responsible for teaching critical reading and critical thinking about validating or debunking claims that cannot be backed up by evidence and sensible reasoning.

    I don’t know why this would be limited to Statistics teachers.

    PS – I love Ben Orlin’s invent your own tax system assignment. Must.. find… a… way… to… build… this… into… Algebra 1…

    • I was just thinking, the next topic when we come back from exam week is piecewise functions, so I should definitely be able to work this into my Algebra 1 class. So I also hace to think on these details.

  3. The marginal tax rate issue seems more like a math type of thing as others have pointed out. What is the statistics angle?

    Interpreting the YouGov poll and commentary analytically (and skeptically) seems more appropriate for a statistics class.

    Q: Is there really a difference in understanding between the parties? The YouGov article itself points out that the participants may be “following implicit partisan cues” and possibly “aren’t responding to reality of what a policy is, but simply interpreting statements about how the world works as mere partisan chanting.”

    Q: Is there non-anecdotal evidence on the accuracy of tax policy statements from party leaders?

    Q: If there really is a difference in understanding of marginal tax rates between parties, are there other possible explanations for this difference? Association vs Causation and all that. The YouGov article talks about this a little bit.

    Somewhat related is this article detailing the actual vs estimated vs preferred wealth distribution. The differences between subgroups is far smaller than the difference between perception and reality.

  4. Kim Morrow-Leong

    January 20, 2019 - 11:41 am -

    I love the additional resources popping up in the comments that explore the idea in depth. Here’s a really great, simplified one, that made me think of @gfletchy’s progressions videos.
    Interestingly enough, the mathematics of these brackets is maybe a weighted average kind of task, but it’s also middle school appropriate. How much time do we spend getting ready to do other things in high school but run out of time in all of secondary school to do important things like this?

  5. Only two problems with your title: It’s not just statistics teachers and it’s not just this year. But, this is a good place to start. Thanks for saying it. I will admit that when I do lessons like this, I worry about being too political. But, I have many social science friends and they have discussions about these topics all the time. They have given me good ways to frame questions to make all students feel that they can contribute and lead to a robust discussion. The MPS ask us to have students “communicate and critique the reasoning of others.” It does not just have to be about how to add a fraction or the trend free throw points in a basketball game. For example, we can look at climate change data and we have to conclude that it is changing. We can have opinions about what to do about that: decrease carbon use, or just build dams, etc, but the numbers tell us the climate is changing. Our colleagues in other disciplines can help us feel comfortable about approaching these lessons.

  6. Crowd sourcing is frequently used in economics when forecasts are conflicting or disputed.

    There must be some reason why virtually all developed nations reduced their tax cuts on the wealthy over three decades following the early 1970s.

    Were all nations, including all of Scandinavia, badly mistaken in choosing to hugely reduce tax rates on the wealthy?

    For example, lot’s of bad things happened in Sweden in the 1960s and 1970s when the Swedes were trying to confiscate almost everything from it’s highest income earners.

    Especially look at
    For more details see

    • There must be some reason why virtually all developed nations reduced their tax cuts on the wealthy over three decades following the early 1970s.

      Thanks for the comment. The US had a 90% top tax rate during the Eisenhower administration, which corresponded to a period of high growth and low income inequality. Since the tax cuts in the Reagan years, income inequality has expanded at an alarming rate.

      Personally, I would take the budgetary policies of any Scandinavian nations over ours right now and I’m happy to chat more about it. However this post is meant to illustrate how hard it is to have even this particular conversation when lies about how taxes work go unchallenged. I’m hopeful math teachers will do more here.

    • Hi Dan,

      The Nordic Tax marginal tax rates are not all that much higher than the USA tax rates if you factor medical insurance costs, transportation, and other benefits the Nordics get for their taxes and we pay for on top of tax rates.

      What you’re saying is that you’re right and virtually all the other developed nations of the world were wrong in reducing the rates for highest income people 1970-2005.

      I don’t think so. The Swedes are Exhibit A on what goes wrong with high marginal tax rates.

    • One thing to note about Scandinavian tax rates: they are much flatter. Their top tier starts at about 1.5 times the average income. Here in US the top tier doesn’t apply until you make 8 times the average income. That is a big reason why the top tier rates appear “lower.” The similar tier for U.S. under the new 2019 rates would be 24% for income over $84,200 which is bout half what Nordic countries. Now THERE’s an interesting problem, accurately compare rates for countries with different brackets–both with and without healthcare/higher-ed/parental leave/tattoo removal (Simpson’s reference).

    • I’m not arguing they’re the best, I’m arguing that your argument is a lousy argument.
      (Pointing out really, but I sooo wanted to use the “argue” THAT many times!!)

  7. What you’re saying is that you’re right and virtually all the other developed nations of the world were wrong in reducing the rates for highest income people 1970-2005.

    I mean … I’m not saying I’m right. There are plenty of economists who identify the neoliberal turn of the 1980s as responsible for the extraordinary inequality around the world and poor quality of life in the US. Just because the whole world ( probably debatable IMO) has done a thing, doesn’t mean it was the right thing to do, particularly given the results.

  8. Find the flaw in the following argument…
    Given: All countries with tax rates that are too high will lower them.
    Prove: The US should not raise their top tier tax rates.

    Statement 1:
    Nordic countries had a top marginal rate that was too high.
    Based on the premise and the observable fact that Nordic countries reduced their highest marginal tax rates (citation needed)

    Statement 2:
    If the US raised their top tier marginal tax rate, the rate would be too high.
    The US rate would be higher than the rate of the Nordic countries, which are too high.

    US should not raise their top tier marginal rate.

    P.S. I’m in the middle of a unit on proof writing, so I’m hypersensitive to the formulation of arguments. My wife told me she loved me this morning and I didn’t believe it because there was a flaw in her argument. So don’t take this as a personal attack, just some recreational fun that caries a high price when held up against our social constructs.

    P.P.S. This “proof” might be misrepresenting your reasoning, feel free to revise.

  9. This conversation has run its course and is probably chasing off folks interested in other conversations.

    I hope you two can find each other somewhere else on social media and I look forward to hearing one day about what you both resolved.

  10. I would like to learn so much more about this! I find it very interesting! I’m also enjoying reading some the emotional comments! I’m more or less a republican, but I don’t get offended very easy…and I’m technically considered a millennial. Can anyone direct me to a TED talk or reliable source that can teach me more about tax rates? I would really like to teach this, but I feel like I know so little!

  11. The math is great. I always love the math. The politics, not so much. If we bring politics into the class we need to challenge existing paradigms, many of them – not just one of them. If we believe we are in a bifurcated political world – we need to challenge both “forks”. There are great opportunists to challenge many beliefs and paradigms through this type of problem – read on.

    Another fair question to ask is, “Why would someone want to turn a $10,000,000 company employing 50 people into a $50,000,000 employing 250 people (creating 200 more jobs) if they will automatically lose 70% of their profit? We could go on to ask the kids to calculate how the additional tax would / could be added to the price of the product / service. Ask the kids about the costs of doing business (e.g., labor, rent, equipment, tax bill…). There are arguments that math can tell that says taxes are just another cost of doing business. There are other math stories that show taxes as being completely different and NOT a true cost of doing business since it is only applied AFTER the profit has been determined. It just depends on how the tax is implemented.

    We could go on to ask the kids to calculate the taxes generated by the employees and their wages. This would involve students having to make some reasonable and varying assumptions, an important enduring skill in itself. What tax revenue could be generated if the employer increased his payroll and staff and compare that to the tax paid by business owner…

    As you can see, lots of good math here but if paint this with one dimensional brush strokes we will turn a lot of people off and lose influence.

    • Mike, if it were possible to like comments on this blog, I would like yours. In fact, I would create multiple accounts so that I could like it multiple times. I think the politics should be brought in. Math is a tool to talk about the issues, and important issues are by definition a part of politics. Teachers (and politicians) should lay both sides on the table. When only one side of the story is cast, most arguments are convincing. …But nothing is ever that simple. Thank you.

  12. My reaction in clicking on various student comments was: there is so much misunderstanding, where does the teacher start?

    For example, in a graph about market caps of companies compared to Apple, the kids were mostly way off target (understandably so). Common: no idea what market cap was….the most common comments implied that Bank of America actually had its $321 billion of cash, for example (“how do they spend it?”).

    I think of your other blog – try to deal with student mistakes differently, try to start with the question they are correctly answering. But often you can use that technique in a few seconds, productively.

    So I wonder how to start a conversation being swept up in the needed background knowledge which might take several minutes, expanding constantly with relevant student questions, whereby the lesson never really gets back to the graph at hand….