“The Sense of Incongruity of PDCA in Education”—What is the true nature of “PDCA fatigue,” and what thinking models actually fit education? [Column] The Science of Thought (No. 89)

🧠 Three things you will learn in this column

• The structural reasons why the PDCA model creates a “sense of incongruity” in educational settings
  　→ The mismatch between linear function assumptions and the non-linearity of education.

• Understanding alternative thinking models like Spiral, Chaos, and OODA
  　→ You will learn perspectives that are better suited to the essence of education.

• The importance of the “intelligence to use different thinking models appropriately”
  　→ You will gain a perspective to grasp education as a “structure” and act adaptively.

🚪 Introduction: A journey to explore the true nature of “incongruity”

🎯 Catchphrase:
The wheel won't turn; the path itself is different after all.

📚 “Is PDCA really working?” I sometimes wonder

I often hear this in school staff meetings.
“Let’s make sure to run the PDCA cycle properly” and “Let’s connect this to improvement.” 🌀

But... isn't education something that doesn't go according to plan?
Children are completely different from day to day.
In the field, it feels more appropriate to “be there for them” than to “run a cycle.”

💤 “Reflection again?” “Improvement for the sake of improvement?”

Surveys at the end of class 📋
Weekly action plans 🗓️
I try hard to write them, but I wonder somewhere along the way.

That might not be because you lack motivation, but because the
structure is misaligned.

📐 “f(x) = ax + b” is probably not enough

PDCA is a model like a linear function.
For an input $${(x)}$$, the output $${(f(x))}$$ is proportional.
But learning isn't like that. It's much more tangled.

Even in the same class, there are children who resonate with it and those who don't.
A method that worked well yesterday might not work at all today.

This feels like a non-linear function. For example, $${f(x₁, x₂, ..., t)}$$.
There are many variables, and they fluctuate over time.

✨ So, I want to give this sense of incongruity a name

In this column, I don't intend to deny PDCA.
I just want to think about “why it doesn't work” using mathematical expressions.

Spirals, chaos, OODA, and more—
While taking a peek at some slightly unusual thinking models,
let's explore together: 'What is the fundamental structure of education anyway?'🔍

It's a bit theoretical, but quite interesting.
Why not start that journey right here?

📐Chapter 1: Why was PDCA introduced into education?

🎯Catchphrase:
Before you start spinning, take a look at the shape of the wheel

🏭 The origins of PDCA are inside the factory

'PDCA didn't originally come from education.'
In fact, it is a 'quality management method' popularized by American statistician W. Edwards Deming🛠️

We want to reduce product variation.
We want to create good things consistently.
That is how these four cycles were born:

• Plan: Think about how to do it

• Do: Try doing it

• Check: Look at the results

• Act: Fix it and do it again

Spinning this cycle around and around to make things better little by little—
This is the concept of continuous improvement.

🎓 Why in the world of education, too?

'The results of a class are hard to see.'
'The evaluation is vague.'
PDCA answers those kinds of voices📊

For example:

• PDCA for class improvement📚

• PDCA for in-school training🧑‍🏫

• PDCA using guidance records📄

• PDCA based on survey results🗳️

'Make a plan → Do it → Reflect → Change it'
This clarity is the reason why it is valued even in educational settings where management and accountability are required.

➗ But is education really that simple?

Here, let's talk a little about mathematical formulas 🧠

PDCA is actually a linear function-based way of thinking after all.

$${f(x) = ax + b}$$

In other words—

• $${x}$$ is the "teaching method" or "instructional adjustments"

• $${a}$$ is the "degree of success"

• $${b}$$ is the "initial state"

• $${f(x)}$$ is the "learning outcomes or improvement results" ✨

The image is that results $${(f(x))}$$ grow in proportion to the input $${(x)}$$.
That is precisely why it is structured to make you feel the "tangible results of improvement."

🤔 But that can also create discrepancies

PDCA is a model where "improvement progresses linearly."
However, education is—much more convoluted 🌀

A joke that worked in yesterday's class might not land at all today.
Concentration levels differ on days when you've slept well, and a single word from a friend can change your motivation.

In other words, isn't education more like $${f(x₁, x₂, ..., t)}$$ ?

There are many variables, it fluctuates over time, and causal relationships aren't immediately visible.
Therefore, isn't "if you keep cycling it, it will get better" half true and half false?

🔗 A topic that leads to the next part

PDCA is a very orderly and well-crafted model.
But that is a story about a world where the environment is stable and causality is easy to see.

Now then.
Is a classroom really such an orderly place?
With children who are each different, and in an atmosphere that changes daily.
Does it really work just by "cycling it"?

In the next chapter, I would like to delve a little deeper into the nature of that discrepancy from a mathematical perspective 🔍

🔀 Chapter 2: Learning is not a linear function

🎯 Catchphrase:
Round and round, sometimes leaping, and getting deeper

🌀 Is the shape of learning not a straight line?

“I taught it, so why don’t they understand?”
“They were no good last year, but they suddenly improved this year!”
The field of education is full of mysteries like these.

This may be proof that learning progresses in a spiral 🌀
In other words, while going around and around, at some point, it suddenly “clicks.”

Unlike a linear growth curve, it branches, goes back, stops, and leaps...
It is, so to speak, “a wild, unruly function.”

🧮 In mathematical terms, it looks like this

PDCA is this kind of thinking:

$${f(x) = ax + b}$$

A fixed input $${(x)}$$ produces a fixed result $${(f(x))}$$.
But education is like this:

$${y = f(x_1, x_2, ..., x_n, t)}$$

For example—

• $${x_1}$$: The teacher's teaching method

• $${x_2}$$: The individual's motivation

• $${x_3}$$: Relationships with friends

• $${x_4}$$: Home environment

• $${x_5}$$: Yesterday's sleep duration

• $${t}$$: The timing

There are too many variables, it's practically chaos 🌪
Moreover, as time $${t}$$ changes, the function itself changes.
It's a world where yesterday's “I don't get it” becomes today's “I see.”

⏳ Results don't happen immediately

“That was a good lesson today.”
But the test scores don't go up...
Even so,sometimes things are slowly growing🌱

This is because oftime delays (lags).
Even though some learning ferments slowly, PDCA tends totry to produce results and make improvements immediately.

For example—
Why were the test scores good?
The teacher's teaching style? Studying at home? Coincidence?
—The causes are all tangled up,making clear “C (Check)” or “A (Action)” difficult.

🧩 If the model is different, the view changes too

Education has a structure like this:

• It's not a straight line, butit's curved

• There are many variables, andthey are tangled

• Results don't appear immediately, butthey take effect later

• The reasons aren't clear, it's ahazy type

When you apply PDCA, which says “Check & Improve in a straight line!” to this reality,

it's only natural that it doesn't feel right.

That “vague sense of discomfort”is not just a feeling.
It might be a structural mismatch🔍

🔗 Topics leading to the next section

So—
How should we look at this unruly learning process?

In the next chapter, I want to introduce more flexible models
like the “spiral structure” and the “OODA loop”🧭

“Even if it's not organized, it's growing.”
I will guide you on a journey to rethink learning from that perspective🚀

🔄 Chapter 3: What are adaptive models in education?

🎯 Catchphrase:
The path of learning, winding and responsive

🔁 A spiral that deepens as it goes around

“I finally understood after encountering it many times.”
Have you ever had an experience like that?

Learning isn't completed in one go.
It goes around and around, deepening little by little🌀
This is the concept of a “spiral curriculum.”

👨‍🏫 Bruner (a psychologist) once said:

Take, for example, the concept of “area.”
The depth of understanding is completely different between elementary school and high school, even with the same content.

In mathematical terms, it’s not “repetition” but a “growth loop”:

$${Learning = \text{Revisit} + \text{Reframe} + \text{Deepen}}$$

PDCA is a straight line. But learning is climbing while spiraling.

🌀 The learning jump caused by chaos

One day, you suddenly become able to do something.
A child who had no motivation suddenly gets motivated 🔥
I’m sure you’ve seen something like this, haven’t you?

This is chaotic leaping.
It’s unpredictable, but it definitely has meaning 🌪

Theoretically, it’s the “butterfly effect”—
small changes produce big results.
For example:

• Becoming friends with the person next to you after a seat change

• A book you happened to see at a bookstore

• A word from a teacher

Those “little things” completely transform learning.

Chaos is a symbol of “leaping learning” and “shifting changes.”

🧭 What is OODA? How is it different from PDCA?

Have you ever heard of OODA?
It originated as a military term. But it’s a model that also fits education very well 👀

OODA proceeds like this:

🔍 O (Observe)
🧠 O (Orient)
✅ D (Decide)
🏃‍♂️ A (Act) → Loop back to observation!

First observe, interpret the meaning, and act.
The starting point is the exact opposite of PDCA, which begins with Plan.

🆚 OODA vs PDCA Let's Compare

🔹 Difference in Starting Points

• PDCA: Starts with Plan. You decide "let's do this" before you start moving.

• OODA: Starts with Observe. It begins by first looking at "what is happening right now?"

🔹 Rhythm of Thinking

• PDCA: A stable cycle that repeats the same framework.

• OODA: A dynamic loop that is adjusted each time. You can change rules and priorities.

🔹 Speed of Response to Change

• PDCA: Improvements are put on hold until the next cycle. The Plan-Do-Check-Act flow is mandatory.

• OODA: If you notice a change, you can make immediate decisions and take action on the spot.

🔹 Assumed World

• PDCA: Assumes a stable and predictable situation.

• OODA: Assumes a situation that is rapidly changing and unpredictable.

🔹 Compatibility with Education

• PDCA: Perfect for routine tasks (lesson planning, school evaluation, etc.).

• OODA: Perfect for learning environments and situations requiring impromptu decisions.

PDCA is about deciding firmly, verifying, and correcting.
OODA is about observing, thinking, and changing immediately.

👀 A "Learning Stance" that begins with observation

What is important in OODA is 'to observe first'. Observe well, feel well, and decide on your actions.

For example:

• Observing the students' state and changing the flow of the lesson

• Receiving feedback from parents not as 'data' but as 'meaning'

• Valuing learning through on-the-spot judgment rather than a uniform approach

OODA is not a model for 'acting immediately.'
It is a way of thinking for 'observing deeply and responding flexibly'.

I recommend this book ▼

🔗 Changing sites require changing structures

Educational settings are full of variables.
'Going according to plan' is actually rare.

What is needed at such times is—
📌 Spiral (deepening)
📌 Chaos (rebounding)
📌 OODA (adaptation)

All of these are structures that adapt to 'things that change.'

In the next chapter, I would like to summarize these complex structures of learning and rethink, 'So, what is education?'

🪞 Summary

'Learning' is,

not a function, but a trajectory of relationships

🧩 Let's notice the gap in models

PDCA is neat and easy to understand.
It offers a sense of security like, 'Do this → Measure this → Fix it, and you're good!'

But education isn't that simple.
There are days when you teach but it doesn't get through, and
there are days when they grow even if you leave them alone.

It's not a straight line, but a spiral.
It bounces lightly or deepens gradually.
If you apply a 'straight rule' to such 'squishy' things,
it's bound to become painful.

🔢 'Fluctuations in learning' seen through mathematics

PDCA is a world of linear functions, like "$${f(x) = ax + b}$$".
But learning is a non-linear function where both $${x}$$ and $${y}$$ fluctuate and sway over $${t (time)}$$.

For example:

• You couldn't do it yesterday, but for some reason, you can today

• Test results might be due to "just physical condition" rather than the person's actual ability

In other words, education is not about “optimization” but “fluctuation of distribution”.
There isn't just one goal, and “change” is more important than “the correct answer”.

🧠 It is fine to use models selectively

PDCA, OODA, and spirals are all just tools.
Depending on the purpose and situation, some fit and some do not.

• Use PDCA for lesson planning

• Use OODA for the movement of students' hearts

• Use spirals for the rhythm of growth

When you change the tool, the world you see changes too.
In education, it is not the “correct tool” that matters, but the “intelligence to use them selectively” 🧰

🌀 Because learning is a journey of change

Learning is not something measured by someone else, but something you can realize for yourself: “I have changed.”

Efficiency, numerical values, and the like—
I want to cherish the sensations that cannot be separated by such things.

🗺 A final question for you

What kind of shape is your learning tracing?
Is it straight? Is it curved? Is it stopped?

If you felt even a slight “vague sense of incongruity,”
I would be happy if this column could be a hint for noticing that “structural gap.” 🌱

✏️ This column was written utilizing ChatGPT.
It is an attempt to connect the potential of generative AI with the warmth of human language.

🧡 Likes, follows, and comments are a great encouragement!
Please, tell me about “the trajectory of your learning.” 🗣

Profile | Kazuomi Matsunaga

🧭Thinking Navigator

Biography:Graduated from Kyushu University, Faculty of Engineering (Materials Engineering) ⇒ Engineer at a metal materials manufacturer in the Chukyo region (Production Engineering) ⇒ Advertising sales for a local free paper in Nagasaki Prefecture ⇒ School corporation staff (← Currently here). Living in Nagasaki Prefecture, in my 50s. Both of my children are now university students who have left the nest, and I live with my wife. I am a writer who lets my thoughts play daily at the intersection of 'questions' and 'curiosity.' Recently, I have been writing about my own unique perspectives on themes such as education, stories, psychology, AI, and design, centered on the serial column 'The Science of Thought.' I am exploring 'free knowledge design' that goes beyond existing frameworks. My motto is 'Imagination opens up the world.'
In my professional life, while working in university and education-related fields, I value carefully observing 'the moment when someone starts to like something' and 'the scenes where questions sprout.'
🧭 I would be happy if I could deliver articles that leave you with a 'new perspective' after reading them.
📮 Impressions and messages of support are always welcome!