A question we often hear at AoPS is:
"What does problem solving look like in language arts?"
The best way to answer this question, I think, is to look at a language arts problem.
An Example Language Arts Problem
Here's one of my favorites — it comes from the first lesson of our Language Arts Triathlon summer camp for fifth and sixth graders:
How would you make a case that the word "well" is a noun?
It's not really helpful to use a dictionary—the dictionary will tell you that "well" is a noun, but your challenge is to make a case that it is a noun. A recursive argument like, "It's a noun because the dictionary says it's a noun," is not very persuasive. Instead, think about what you know about how nouns work. How can you show that "well" works like a noun?
Think through this a moment before you continue reading.
Got an idea? Great!
You're welcome to take a look at my solution at the end of this article, but I'm actually way more interested in how you thought about the problem than whether you came up with the right answer. Plus, we're about to get to the fun part.
(For extra credit, you can also try making a case that "well" is an adjective, a verb, and an adverb. Our students do this in class, but, in the interest of keeping this post short, I won't explain it all here.)
Okay, ready for the next part of the problem? Here's where it gets juicy:
Don't worry about finding the adjective, verb, and adverb (unless you want to)—just look for the noun. How can you use what you know about nouns to decide which word in this sentence is the noun?
Take another moment to think about this before you read on.
Got an idea? Excellent! Again, you can take a look at my solution at the end of this article, but that's not really the focus here. Instead, I want you to focus on your brain: what did it feel like while you were thinking through that problem?
Maybe you felt curiosity, or desire to figure out the answer, just to see if you could. If you did, that's awesome. That's what problem solving feels like.
Now, let's shift gears. What happens when you approach a grammar exercise that doesn't spark the same kind of curiosity?
How AoPS Language Arts Problems Compare to Standard Exercises
Try thinking through a more typical grammar exercise:
A noun is a person, place, thing, or idea. Label the nouns in each of the following sentences:
- The dog chased the ball across the yard.
- Emily read a book in the library.
- The sun shines brightly in the sky.
Does this exercise strike you as… less interesting? Does it fail to pull you in like the "well wells" problem did?
That's because this isn't a problem, it's a prompt. A prompt is an assignment: it assumes that you have no choice but to complete it, so it doesn't try to hook you. A problem, on the other hand, is interesting. It's meaningful; it's a puzzle that begs you to solve it.
That's what we aim for in our language arts curriculum: to create problems that will make students want to solve them. Because when you give students problems they want to solve — when you challenge them with interesting scenarios and meaningful questions — they become naturally motivated to keep practicing their language skills.
Myth Quest Case Study: How Problem Solving is Built into a Full Course
A problem like the "well wells" sentence is a bite-sized example of what problem-solving can look like in language arts. But, what happens when you build problem-solving into an entire language arts course? To answer that question, let's take a look at one of our summer camps for fifth and sixth grade: Myth Quest.
Myth Quest is built around a meaningful question that has real-world relevance: How do archaeologists figure out the stories people told in ancient societies?
To answer this question, students become archaeologists exploring the ruins of a fictional ancient society called Kaloneira. Other archaeologists have pieced together a partial picture of Kaloneiran culture, but they haven't been able to deduce a central aspect of Kaloneiran life: their creation myth. The challenge for students is to reconstruct this myth using fragmentary artifacts and their new understanding of how myths functioned in real ancient societies.
For example, in the fourth lesson, students must interpret a piece of pottery that has been discovered on Kaloneira:
The images on the pottery seem to tell a story, but what story? And how does it relate to the creation myth students are trying to reconstruct?
To unravel this puzzle, students first learn the Hero's Journey story pattern. You are almost certainly familiar with this pattern, even if you haven't come across the term before. It's the plot of dozens of popular movies, like Star Wars, Lord of the Rings, or Moana (my favorite). In this type of story, a character (the hero) is compelled to take on a dangerous journey through an unfamiliar world. With the help of friends they meet in this world, they conquer a series of challenges that lead them to a big, final "boss battle." Once they defeat the big boss, they return to their old, familiar world, but they are forever changed by their experience.
The Hero's Journey has appeared again and again in stories throughout history and around the world. Because it is so prevalent, scholars have been able to use it as a key to unlock the meaning of ancient myths that otherwise might be difficult to interpret. In class, students read and analyze a Maori myth about how the hero Maui brought fire to the world. Then, they return to the image of the pottery and apply their new knowledge of the Hero's Journey to infer details about the story the pottery seems to tell.
Try it yourself: take another look at the image of the pottery with the Hero's Journey in mind. As you think about the hallmarks of the Hero's Journey — the Hero, the unfamiliar world, the friends and helpers, the "boss battle" — can you begin to imagine a story that the images may be telling?
The story you are imagining is your solution to the problem the pottery poses. And this story is just one piece in a larger puzzle that students will solve throughout the entire summer camp. As students gain more interpretive tools like the Hero's Journey and examine more artifacts, they develop their own, complete idea of the creation myth the artifacts refer to. On the last day of the class, they take part in a simulated mythological conference where each student archaeologist shares and defends their version of the reconstructed myth.
Why Language Arts is Problem Solving
So, what does problem solving look like in language arts?
The answer to this question is that problem solving can look many different ways in language arts. It can be a small, contained grammar problem, or a multi-layered project that encompasses a range of interpretive and creative skills.
But at the heart of all of these problems is a key idea: with problem solving, students aren’t just memorizing definitions or filling in blanks—they’re engaging with complex, meaningful questions that require critical thinking. In both the "well wells" problem and Myth Quest, students must draw on their knowledge, recognize patterns, and make logical connections to uncover answers. This approach mirrors the way real scholars, linguists, and archaeologists work, making learning feel purposeful and immersive.
When students wrestle with ideas, defend their reasoning, and discover solutions for themselves, they develop a deeper understanding of language arts—not just as a subject, but as a way of thinking. That’s why problem solving isn’t just for math and science; it’s at the heart of how we learn to read, write, and interpret the world around us.
Now, since this is AoPS, I'll leave you with some more language arts problems to puzzle over. Can you find the nouns in each of these classic sentences?
- Rose rose.
- Police police police police.
- Buffalo buffalo buffalo buffalo.
- Can cans can cans?
- That that that that person used was confusing.
(You can find the solutions below.)
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Grammar Solutions
First Grammar Problem
For fun, here's how I'd explain it: we know from the problem statement that a noun names a person, place, thing, or idea. So, we can think about "well" in this sense: a well is a thing --- it's a deep hole that's used for storing water. That last sentence also shows us a couple interesting things about how nouns work in general: they can come after a word like a or the, as in "a well," and they can be the subject of a verb, as in "a well is a thing." So, we have three points that help make the case that "well" is a noun: it names a thing, it can come after the word "a", and it can be the subject of a verb.
Second Grammar Problem
It's the second one --- "wells". We can explain this using the qualities of nouns that we just learned:
- We know that a noun can come after a word like "a" or "the." So, let's try re-writing the sentence so that "wells" comes after "the": The wells well well. (Notice that the sentence becomes nonsense if we try this with a different "well": "Well the wells well well.")
- We also know that a noun can be the subject of a verb. Let's try swapping out the verb in this sentence to show more clearly that "wells" is the subject: "Well wells work well." (Again, this would not work with another "well" in this sentence: "Well wells well work.")
- Finally, we know that a noun names a person, place, thing, or idea. We can replace "wells" with a synonym like "water hole" to see that "wells" is a noun: "Well water holes well well." In other words, water holes that aren't ill work properly. (We really can't replace other "wells" in the sentence with "water hole": "Well wells well water hole," or "Well wells water hole well.")
Final Grammar Problems
The nouns are bold:
- Rose rose.
- Police police police police.
- Buffalo buffalo buffalo buffalo.
- Can cans can cans?
- That that that that person used was confusing.
