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Why No Elementary or Geometry?
Why No Elementary or Geometry?

An extended explanation of why Citizen Math doesn't write lessons for Elementary or High School Geometry

Karim Ani avatar
Written by Karim Ani
Updated over a week ago

Citizen Math develops lessons for Grades 6, 7, 8, Algebra 1, and Algebra 2. However, we do not currently develop lessons for elementary school or high school Geometry. What gives??

To understand why we don't write lessons for these courses, it's helpful to understand how we write lessons. In particular, it's helpful to understand the role that real-world issues play in Citizen Math lessons versus in traditional instructional resources.

In a traditional resource like a textbook, a task author will often use a familiar situation from the so-called "real world" to illustrate some underlying mathematical concept or skill. For instance, consider a word problem that asks students to calculate how long it will take for a train traveling at 60 miles per hour to reach a station 150 miles away. If you asked someone, "What is this activity about?", they might reply, "The task is about trains." In fact, it's not about trains at all. (When students emerge from the activity, they haven't learned anything about trains that they didn't already know.) Instead, the author merely uses trains as a convenient frame for solving the equation 60x = 150. Even though the activity involves the world, it's fundamentally about the math.

Citizen Math is completely different. When our team sits down to write a lesson, we don't begin with a particular mathematical objective in mind and search for a context to fit it. Instead, we begin with an actual question about the world...and then determine the math from there. For instance, someone might read a newspaper article about how cities add late fees to unpaid parking tickets and wonder, "What impact does this have on people with different incomes?" Or they might play the latest XBOX game and think, "How much more powerful have gaming consoles gotten over time?" It's only when we sit down to explore the issues in depth that we discover the mathematics involved: in these cases, linear functions and exponential growth.

Traditional Resources

Citizen Math

use the world to look at math

use math to look at the world

Task Author:
"I need a situation that involves linear functions. I've got it: trains!"

Lesson Team:
"How long will it take to pay off a ticket. I've got it: linear functions!"

Teachers and students who use Citizen Math lessons often say, "The lessons feel totally different than traditional ones do." This is why. Unlike traditional resources that use the world as a setup for contextualizing math, we use math as a lens for analyzing the world.

So what does this have to do with elementary school and high school geometry? Everything. Because all of our lessons begin with an authentic real-world question, they'll always help students think differently about the world around them. That's the upside. The downside, though, is that the only mathematical standards our lessons can address are those that actually come up in real life. And unfortunately, at least in our experience, very few real-world issues boil down to elementary or geometry standards.

Take elementary school. In grades 1-5, students are focused primarily on number sense and operations, e.g. subtracting integers and adding decimals. While these are important real-life skills to have -- when shopping at the grocery store, for instance, you need to be able to add $1.37 and $4.28 -- they're still primarily about the math. In other words: math for math's sake. The same is true of high school geometry, which consists primarily of theorems and proofs. Intellectually, it's interesting to prove that "all circles are similar." Practically, though, it's not something that comes up. Of course, a textbook author could invent a scenario that situates circle theorems in an ostensibly real-world context, perhaps by having students prove that all car tires are similar. But as is often the case, their motivation for doing so would be more mathematical than automotive. (One exception to the geometry-isn't-applied rule are trigonometric ratios, which are incredibly useful for analyzing everything from trajectories in golf to blue in photography. But they're also the exception that -- wait for it -- proves the rule.)

We're flattered when people ask when we'll write lessons for elementary and geometry. And we'd love to be able to oblige. But before we do, we have to be sure that we're putting teachers and students in a position to legitimately use mathematics to analyze the world around them, and not just coming up with cooler versions of longstanding word problems. Because that's not the role that Citizen Math plays. Our mission is to provide educators with the absolute best real-world lessons around. In order to do that well, there are some other things that we might not be able to do at all. Including elementary and geometry.

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