Facts Don’t Matter

Why your brain doesn’t care about correct answers (and what it cares about instead)

The Second Draft: #0085

I write weekly articles for educators who are ready to get unstuck from outdated curriculum, resistant institutions, and a career that was built for a world that no longer exists.

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The Learning Formula

In this series we’re exploring how cognition and learning actually work.

We started by undercutting an objection to AI in education using the idea that we don’t teach kids to ride a bike until they learn on training wheels.

We dismantled that idea and saw that training wheels actively teach the wrong things about bike riding!

Training wheels are actually the cause of epic fails when kids transition from training wheels!

And then we simplified the idea to say this core idea that characterizes much of teaching practice: students need to learn X before they Y.

We explored how this idea is based on probably the most widespread and indeed damaging understanding of human cognition, which sees the human brain as a file cabinet and education as the system that fills that cabinet with facts in an organized and specific order. Each course or discipline is a folder, arranged neatly from Fact A (Week 1) to Fact Z (Week 15).

We then introduced the idea that cognition is more like a web, or a rhizome, using our exploration of the word “snow” to show that our brains “store” facts as hubs of connections, which we then surface subconsciously based on the intensity of the connections we have developed.

Then, we introduce a formula that simplifies all of this to show, basically, how learning actually works:

WM_i = WM_{i-1} × (1 + GC × EA × TC_i × DP)

One crucial insight from this formula is that it runs on multiplication, not addition.

Which means, adding facts to the file cabinet is at best a suboptimal process for initiating learning.

Today we’re going one level deeper, breaking down each component.

(For the sharp readers who are thinking, wait this feels backwards! Yes, when I do this series as a workshop, we start with the bot and build with it immediately. Participants engage in the process, and develop useful outputs, but they don’t have enough context to understand how to refine those outputs to better align with the formula. So, throughout, I layer the concepts at the right times so the participant-teachers are better equipped to refine the outputs. Good catch—thanks for keeping me honest!)

After this article I’ll be sharing the template you can use for any assignment and finish us up with how to build a bot that automatically turns any assignment using this entire formula!

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WM: World Model

Your world model is your current way of understanding how the world works.

Not “the facts you know.” Not “the information you’ve memorized.”

Your operative framework for making sense of reality.

When you see “snow,” your world model activates:

• Personal history (that time I . . .)

• Physical properties (cold, wet, white)

• Aesthetic judgments (beautiful? ugly?)

• Social implications (no school, vacation)

• Causal relationships (temperature → precipitation)

All of that is your world model of snow.

It’s not in a file.
It’s how your network organizes itself to process “snow.”

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The Rule of Operative Plausibility

Your brain keeps world models that work, not world models that are “correct.”

The rule of operative plausibility is perhaps the most foundational concept in this whole series.

Here’s the key thing about how we engage with the world and the world models we have about it:

Your brain doesn’t “care” if what it knows is factually “correct.” Your brain primarily cares if what it knows “works.”

If your world model lets you navigate reality successfully, you go with it!

Our world models basically run on rules which are essentially just simplified heuristics, inferences to the best explanation of how the world works.

Consider the child learning to speak.

At some point the child develops more advanced speech and says something such as, “runned.”

This is genuinely amazing!

The child, in all likelihood, has never heard anyone say “runned” before. In fact, they have probably heard people say “ran” often.

But, they have developed—mind you without anyone “teaching” them grammar—a rule about how our language works, such that if you are referring to something that happened in the past, you add an “ed” sound to it.

Thus, “run” becomes “runned.”

While “runned” is technically wrong, their model about the world of language is basically correct.

More importantly: their model is generative.

They can now produce past tense for ANY verb they encounter, even ones they’ve never heard before.

That’s not memorization.
That’s understanding!

And, again, most importantly, no one “taught” them any of that.

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What This Means for Education

Traditional teaching assumes:

Students need the correct rule before they can use language.
They need X before they Y.

Reality:

Students build working models through use, then refine them.

We spend weeks drilling irregular verbs.

But the kid who says “runned” already has a more sophisticated understanding of language than the kid who’s memorized a list.

Because “runned” proves they have a generative system.

Memorizing “ran, went, ate, saw” proves they have a list.

So here’s what this means:

If brains keep models that work rather than models that are correct
And if traditional education optimizes for correct answers over working models
Then traditional education is fighting against how brains actually work and how we actually learn!

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Learning = World Model Transformation

Most of education treats learning as accumulation:

• You didn’t know X, now you know X

• Add it to the file cabinet

• Stack up knowledge

But here’s what the formula means:

WM_i = WM_{i-1} × (transformation factor)

Learning isn’t adding.
Learning is transforming.

Now, quick truth.

Of course the child’s world model about grammar does get updated when someone says, “it’s not “runned, it’s ran.” And in a very real sense that is addition.

However, as we will see shortly as we explore challenges, human beings as we are, learning to speak “well” is a latent challenge that children are naturally interested in. Quite a different situation for a 7th-grader learning the difference between a gerund and a present participle!

So, those examples actually show the reality of world models.

When you add disparate facts that have no obvious impact on how someone makes sense of the world, a person’s world model doesn’t update in any meaningful way.

Another quick truth.

Actually, a person’s world model does change when, year after year, they are forced to become interested in, memorize, and get tested on facts about which they see no relevance. Those experiences do change the world model of learning, such that research has found that creativity declines by as much as 87% from ages 5 to 15!

The big idea here is that world models don’t operate on facts. They include facts, connected to other facts and experiences and emotions and relationships and . . . and . . . and . . . but they are not transformed by facts.

Facts by themselves only ever fill the file cabinet (and do so poorly).

For real learning to happen, for cognitive change to occur, something needs to test, challenge, and refine the world model.

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GC: Genuine Challenge

I am defining a genuine challenge as a real problem where the path forward is uncertain and feedback comes from the world.

Remember our training wheels.

The balance bike is a genuine challenge for new riders as they don’t know yet how to balance and as they lift their feet up the world/physics, their emotional and physical reactions, gives them feedback on what works and what doesn’t.

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Five Features of a GC

A genuine challenge has:

1. Immediate entry — you can start right now with what you have

2. Undeniable feedback — the world tells you, not just the teacher

3. Embodied struggle — learning happens through doing, not applying pre-learned content

4. Emergent threshold concepts — insights arise from attempts, or when they become necessary (from the instructor)

5. Cheap failure — you can iterate rapidly

If any of these are missing, the GC gets closer to 0.

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Read & Respond

“Read Chapter 5 and answer the questions at the end.”

1. Immediate entry? You have to read first. Not immediate.

2. Undeniable feedback? Teacher grades it later. Not from the world.

3. Embodied struggle? You’re reading and writing answers. Passive → active at best.

4. Emergent TCs? The chapter already explained everything. Nothing emergent.

5. Cheap failure? One submission, points deducted if wrong. Expensive.

GC = 0.

And this alone explains why students don’t care about our assignments!
Honestly, we wouldn’t either if we had to do them!

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Latent vs. Activated

Challenges can be sourced two ways:

Latent: Problems learners already have but may not recognize.
Example: “I don’t know how to complete my college application”

Activated: Problems created by the learning experience itself.
Example: “This boat keeps sinking and I need it to float”

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Meta vs. Micro GC

Challenges can also come in two flavors:

Meta GC: The overarching challenge
Example: “Design a policy that balances free speech and safety”

Micro GC: The immediate challenge within an iteration
Example: “Defend this specific provision against the objection that . . .”

Good assignments have both:

• Meta GC gives direction and meaning

• Micro GC gives immediate traction

Students know where they’re going (meta) and what to do right now (micro).

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EA: Embodied Agency

Embodied agency means you actually DO something, observe what happens, and adapt.

You don’t think about doing it.
You don’t create a plan for doing it.
You definitely don’t just read about how others did it.

Your body engages with the problem and gets feedback.

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Why “Embodied”

Embodied is not just physical activity, but it is definitely more than just mental activity.

“Embodied” means:

• Your entire cognitive system is engaged (not just the verbal/symbolic parts)

• You’re processing feedback in real-time (not reflecting on it later)

• Your actions and observations are coupled (you act → you see → you adjust)

When you’re balancing on a bike:

• Your inner ear sends signals

• Your muscles adjust

• Your eyes track movement

• Your emotional state affects risk-taking

• All of this happens in the moment of doing

That’s embodied.

When you’re debugging code:

• You write a line

• You run it

• It breaks (or works)

• You immediately see where

• You adjust

• You run it again

That’s embodied.

When you’re reading about debugging code in a textbook:
Not embodied!

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Why “Agency”

Agency means you have control over your choices and their consequences.

Without agency, learning becomes passive reception.

You watch someone else solve the problem. You follow a procedure someone designed. You implement a solution that was handed to you.

None of that transforms your world model.

Agency is what makes the feedback loop yours.

When you have agency:

You decide what to try next. You own the consequences of that decision. You feel the stakes of success and failure. You develop intuition about what works.

However, agency doesn’t mean chaos or anything goes. Agency means meaningful choice within constraints (and this comes back to the GC you create).

The balance bike has constraints:

Two wheels Gravity exists Must propel forward

But within those constraints:

You choose how fast to go You choose when to lift your feet You choose how to shift your weight

Those choices are what make the learning yours, which is also what makes learning happen.

Training wheels remove agency. The mechanism handles balance.

No choice = no agency = no learning about balance.

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TC: Threshold Concept

A threshold concept is the smallest idea that changes what you can do next.

That is gold right there, btw. 👆

The TC is the idea that reorganizes how you see the domain.

Before the TC: You’re stuck or flailing. After the TC: You have the framework that makes the next move possible.

If direct instruction has a role, it is this (but more on that below).

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A TC Can Be

• A heuristic (”check edge cases first”)

• A framework (”beginning/middle/end”)

• A mental model (”displacement, not weight”)

• A rule of thumb (”wide base = stable”)

• A structural insight (”the conclusion is just the introduction inverted”)

• A mnemonic (”PEMDAS”)

• Something else

The key: It’s generative.

It doesn’t just answer one question.

It unlocks a class of problems.

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Emergent vs. Seeded

TCs can also come from the experience itself our outside.

Emergent TC: These insight surfaces from attempts. This is the student learning the rules of balance on the balance bike or ideas around structural integrity in the marshmallow tower. These TCs are perhaps unstated, but they are learned.

Seeded TC: These insights are introduced outside the attempt. Developing and introducing seeded TCs is the primary role of the instructor in this arrangement. This entire series, the formula, and the unpacking of each aspect of it, was purposefully designed around essentially a fractal of TCs.

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The 3-part TC Unlock

A good TC does three things simultaneously:

1. Reveals the hidden rule (the move experts use without naming)

2. Explains the structure (why the parts of the domain fit together)

3. Gives a reusable method (a system you can apply in the next attempt)

If you’re hoping for an example of a good TC, there it is 👆. Very meta, for sure.

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Why It Has a Subscript (TC_i)

Because you might get a different threshold concept at each iteration.

Attempt 1: “Wide base makes it stable”

Attempt 2: “But too wide and materials run out—there’s an optimal ratio”

Attempt 3: “And it depends on weight distribution—concentration matters”

Each iteration can unlock a new TC.

Each TC makes the next iteration more productive.

That’s why DP matters.

More iterations = more TCs.

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DP: Deliberate Practice

Deliberate practice is targeted repetition on the parts that break.

Not just “do it again.” And definitely not just “practice more.”

Identify where the system fails, isolate it, work on it specifically.

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The 7 Elements

Deliberate practice has these elements:

1. Help of a teacher (or expert model, or structure)

2. Protected environment (where failure is cheap)

3. Opportunities for reflection (noticing what worked/didn’t)

4. Ongoing and meaningful repetition (not one-and-done)

5. Structured problem-solving practice (not random attempts)

6. Exploration of alternative approaches (not just repeating the same thing)

7. Informative feedback (based on performance, from the world when possible)

Also, if you ever need to define what good teaching looks like, that is it 👆.

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The Zero Diagnostic

Now let’s bring this all together and see how you can diagnose any assignment.

Here’s our guiding question: Where is it zero?

“Read Chapter 5, answer questions at the end”

• GC: Challenge is artificial (getting right answers), feedback delayed → GC ≈ 0

• EA: Reading and writing, not embodied in actual challenge → EA ≈ 0

• TC: Chapter explained everything, nothing emergent → TC = inert

• DP: One attempt, submit and done → DP = 0

Learning = Old × (1 + 0 × 0 × 0 × 0)
Learning = Old × (1 + 0)
Learning = Old

No transformation. You end up adding to file cabinet, not expanding the rhizome.

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Stop Adding. Start Multiplying.

You now have the complete formula:

WM_i = WM_{i-1} × (1 + GC × EA × TC_i × DP)

And you know what each component means:

WM: World model transformation (not fact accumulation)
GC: Genuine challenge (real, undeniable, cheap to fail)
EA: Embodied agency (doing, not just thinking)
TC: Threshold concept (insights that unlock new moves)
DP: Deliberate practice (targeted iteration on failure points)

You know why it’s multiplication.
If any component is zero, the entire equation is zero.

You can look at “Read Chapter 5” and see: zero, zero, zero, zero.

⚠️ Quick diagnostic: Take one assignment. Give each component a score from 0-10. Multiply them. That’s your learning coefficient.

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What’s Next

In the next article, I’m giving you the template.

The actual structure you can use to redesign any assignment so that all components are greater than zero.

Then we’ll build a bot that does this automatically.

See you in the next one. 🔥