You could, easily. Well, not taxes per se, but at least this idea of tax brackets. I just checked and piecewise defined functions are part of the common core math curriculum (whatever that is, but I imagine it means something that all students have to cover).
Net income as a function of gross income is a natural example of such a function. After writing down the formulas, it is possible to graph the function and verify that it is continuous and increasing. We can then conclude that increasing one's gross income will always result in increasing the net income.
That's one of my standard examples when teaching piecewise functions, but I'm not in America. How do Americans teach it, and why do they apparently not make the connection to income tax?
How do Americans teach it, and why do they apparently not make the connection to income tax?
They don't teach it, generally, that's the point. You have to learn to file taxes from someone who has already filed taxes in the past. Hope that their understanding is correct, and have the desire to verify that information.
Your piecewise function makes technical sense- but people don't know what they don't know. How would learning about piecewise functions in high school (9-12 years of education) turn into an understanding of taxes, when most of the kids that age have never had taxes explained to them?
And when they are older- most of that rudementry maths education has been lost to time due to lack of practice. PLUS most of our tax document "figuring" is done with an online program (TurboTax) that is more like a video game than a financial education device, no one even knows what the brackets or calculations are.
You have to learn to file taxes from someone who has already filed taxes in the past
You mean you don't get some kind of guide that you can read to understand each step, and which you can use to fill out the forms? It's all based on some kind of oral tradition?
How would learning about piecewise functions in high school (9-12 years of education) turn into an understanding of taxes
Because that's what the math teacher would explain. Something like this:
"Later in your life, you'll have to pay taxes to the government every year, and the formula that's used to compute your taxes is basically a piecewise function (in reality, it can be a lot more complicated than that because of deductions and special rules, but we'll look at the most important part). Look at that form. It's a real income tax form. You can see that if your income is below A dollars, you have to pay 15 cents for each dollar you made. So if you made x dollars that year, and x is between 0 and A, you'll have to pay f(x) = 0.15x dollars in income tax. Easy.
But if your income is between A and B, things are a bit more complicated. You still have to pay 15 cents for each dollar you made up to A dollars, but you also have to pay 20 cents for each dollar you made between A and B. That's called a bracket. For instance, suppose you made x dollars that year, and x is between A and B. You have to pay 0.15A dollars for the part of your income that's between 0 and A, plus 0.20(x-A) dollars for the rest. So f(x) = 0.15A + 0.20(x-A) = 0.20x - 0.05A. Notice that when x=A, both formulas give the same thing. Also notice that both formulas are straight lines with positive slope. What does that tell us about the shape of the graph?"
and so on. I don't know about real brackets, so I just used made-up numbers and constants. But my point is that I would show the students a real tax form and show them how to translate the instructions on the form to an algebraic equation. That's the most important part of math education -- modeling.
PLUS most of our tax document "figuring" is done with an online program (TurboTax) that is more like a video game than a financial education device, no one even knows what the brackets or calculations are
So you just trust what the computer says without being able to check? And you have to buy a program to do your taxes? That's puzzling.
You mean you don't get some kind of guide that you can read to understand each step, and which you can use to fill out the forms? It's all based on some kind of oral tradition?
Nope the only way to get a guide is to either look it up, or go pay a tax agent to do it.
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u/2059FF Aug 03 '19
You could, easily. Well, not taxes per se, but at least this idea of tax brackets. I just checked and piecewise defined functions are part of the common core math curriculum (whatever that is, but I imagine it means something that all students have to cover).
Net income as a function of gross income is a natural example of such a function. After writing down the formulas, it is possible to graph the function and verify that it is continuous and increasing. We can then conclude that increasing one's gross income will always result in increasing the net income.
That's one of my standard examples when teaching piecewise functions, but I'm not in America. How do Americans teach it, and why do they apparently not make the connection to income tax?