Pi is both perfectly orderly and wildly unpredictable. It follows precise mathematical principles, yet its decimal expansion stretches infinitely without ever settling into a repeating pattern. If we tried to force Pi into a neat formula, we’d lose the very essence of what makes it fascinating.

I can’t help but see the parallel to how we teach writing.

We want our students’ writing to be structured and clear, but also original and thoughtful. Yet so often, we end up emphasizing formulas that provide structure at the expense of authentic thinking. Five-paragraph essays. Prescribed sentence starters. Mandated quote counts per paragraph.

The goal isn’t eliminating structure—some scaffolding is necessary for developing writers. But I’ve discovered something critical: there’s a tipping point where our helpful formulas become rigid constraints that actually prevent students from developing as thinkers.

Why Formulas Dominate Our Teaching

Throughout our Frankenstein unit, I asked my students to analyze how certain words evolve throughout Frankenstein. When we got to putting this into more of an essay format, one immediately raised her hand: “How many quotes should I use in each paragraph?”

This wasn’t her first analytical essay. She’s written dozens. Yet she still wanted a formula—a guaranteed path to success.

And who can blame her? Formulas provide safety in a process that can feel overwhelming. When faced with a blank page, it’s comforting to have a clear template to follow.

As teachers, we reinforce this because formulas make our lives easier too. They streamline assessment. They provide clear expectations. They’re efficient ways to teach basic organizational principles.

But here’s what I’ve realized after years of trying to balance structure with freedom: Our educational systems aren’t just encouraging formulaic writing—they’re practically demanding it. Standardized assessments require standardized preparation. District mandates provide cookie-cutter solutions that rarely account for the messy reality of our individual classrooms.

And this creates a fundamental problem most of us don’t talk about: Students who can produce “correct” writing without engaging in authentic thinking. They follow the recipe without understanding the principles of good cooking. They pass our assessments without developing the creative thinking skills they’ll actually need.

The Formula Paradox

Here’s the tension I struggle with daily: formulas are both necessary and potentially harmful.

When formulas help:

• They give novice writers clear organizational principles
• They provide security for students who struggle with structure
• They build confidence through mastering basic patterns
• They create a foundation of skills that students can later adapt

I’ve seen this firsthand with my ninth graders. Many come to me unable to write a coherent paragraph. Teaching them the basic “topic sentence + evidence + analysis” structure gives them a foothold, a way to organize their thoughts when everything feels chaotic.

But when formulas hurt:

• Students become dependent, unable to write without them
• Writing becomes mechanical rather than thoughtful
• Students believe there’s only one “right way” to communicate
• Original thinking gets sacrificed for predictable structure

This became clear with my students analyzing Frankenstein. If I’d limited them to a standard analytical essay formula, they would never have discovered the fascinating patterns that emerged from tracking a single word throughout the novel.

One student followed the word “beauty” and uncovered how Frankenstein’s definition transforms from external appearance to internal character—a shift that perfectly mirrors his moral journey. This insight came not from following a formula, but from following the text where it led her.

What makes this problem even more complex is that students are constantly negotiating two different processes. There’s what happens in the text—the author’s deliberate construction, the patterns they create, the development they craft. And then there’s what happens in the reader’s mind—the actual process of discovery, the moments of surprise, the connections that form in unexpected sequences.

I was trying to explain this to my students recently. “You might notice something that catches you off guard as a reader,” I told them, “but when you go back and look more carefully, you realize the author was setting up that moment all along.” This journey of discovery—being surprised, then tracing back to see the deliberate craft—is a crucial part of interpretation.

Yet our traditional essay structures don’t account for this intellectual process at all. They assume a clean, linear analysis that never existed in the first place. They ask students to present their thinking as if they saw the pattern immediately and analyzed it methodically, erasing all the messy, recursive steps of actual discovery.

The quality of analysis my students produced when freed from formulas was dramatically better than what I typically see in their formulaic essays. And this is what finally made me confront an uncomfortable truth: Sometimes our scaffolding isn’t supporting thinking—it’s replacing it.

Breaking Free: The Process Approach

I spent years searching for the right balance—enough structure to support students without constricting their thinking. The breakthrough came when I shifted from product formulas to process frameworks.

One of the most transformative has been the Madman, Architect, Carpenter, Judge approach:

Madman: This is the creative, exploratory phase where ideas flow without constraint. Students brainstorm, free-write, question, and make connections without worrying about structure or correctness. They follow curiosity rather than formulas.

Architect: Once ideas emerge, students step back to design an appropriate structure. Note that the structure follows the thinking, not the other way around. Different ideas require different organizational approaches.

Carpenter: Now students build sentences and paragraphs, crafting language to communicate their ideas effectively. They focus on clarity and precision.

Judge: Finally, students evaluate their work with critical distance, revising for both ideas and execution.

Personally, I used to use this metaphor a lot, especially when I was trying to get students to brainstorm or during exploratory thinking. But never for drafting analytical essays. A colleague mentioned it while I was on the brink of essay writing with my students

This framework gave me what I’d been missing: a way to provide structure without imposing rigid product templates. It acknowledges that different writing tasks might emphasize different phases, and that the thinking should determine the structure.

I saw this work beautifully with the Frankenstein assignment. Instead of prescribing a five-paragraph formula, I had students:

1. Track their chosen word throughout the novel (Madman phase)
2. Look for patterns and turning points (still Madman)
3. Organize evidence to show this evolution (Architect and Carpenter)
4. Craft an analysis that revealed their insights (Carpenter)
5. Develop a thesis about how the word’s meaning evolves (Architect)

Notice how the thesis—what traditional essays put first—actually emerged last in their authentic thinking process. Their understanding developed through exploration, not from following a predetermined path.

The results? They were honestly surprising. One student tracked “creature” and showed how the word initially appears neutral, becomes increasingly dehumanizing, then shifts meaning entirely when the creature begins narrating. This sophisticated analysis emerged not because she was following a formula, but because she was following the text.

Another student examined “darkness” and uncovered how it transforms from literal to metaphorical, revealing Frankenstein’s psychological descent. Could this essay fit in the 5-paragraph essay formula? Yes, probably. Would my student have gotten there if I asked them to use that model? Experience says probably not.

The Uncomfortable Truth

What’s been hardest for me to admit is how much I’ve relied on these formulas for my own comfort. The standardized five-paragraph essay isn’t just easier for students—it’s easier for me to teach, to scaffold, to assess.

But here’s the more disturbing reality I’ve had to confront: Many students spend their entire secondary education trying to “master” these formulas—and during those critical years, they’re thinking and writing at a shallow level.

Think about that. Six years of English classes. Six years of essays. Six years of “topic sentence, evidence, analysis.” And for what? By the time they finally master the formula, they’ve developed habits of shallow thinking that are incredibly difficult to break.

I’ve watched seniors who can produce technically “correct” essays that say absolutely nothing original or insightful. They’ve learned to arrange words in acceptable patterns without engaging deeply with ideas. They follow the rules perfectly while missing the entire point of writing—to develop and communicate thought.

This tension between structure and creative thinking isn’t just a teaching dilemma. It’s the central challenge of education itself: How do we teach foundational skills without limiting where those foundations might lead? How do we avoid spending six years teaching students to think inside a box that we then expect them to break out of?

I don’t have a neat formula for resolving this tension. That would be missing the point entirely.

What I do have is a growing conviction that our students deserve better than years of shallow thinking disguised as mastering structure. They deserve both: the security of knowing the rules and the freedom to break them when their thinking demands it.

Because ultimately, isn’t that what we’re really after? Not students who can write perfect five-paragraph essays, but students who can think deeply and communicate effectively—no matter what form that communication needs to take.

I’ve created a Pi Day writing exercise that explores this balance if you’d like to try it. 

After all, like Pi itself, authentic thinking resists tidy resolution. Its value comes from how far it can take us—not how neatly it fits into a box.

Next month, inside my membership, we’re exploring exactly how to balance structured thinking and creative flexibility—experimenting with frameworks that give students a secure foundation without trapping them inside formulas. If you’re wrestling with these same tensions, join us before April 1 and let’s see what happens when we let authentic thinking drive our teaching, not rigid templates.