February 4


Notice, Wonder, Discover

The Power of Noticing

I was asked in my Facebook Group where to start with a three-year-old using Caleb Gattegno's philosophy. This question comes up in a host of different forms. Where do I start with a teenager? Where do I start with a child with autism? Where do I start with a child who is behind? Where do I start with a child who has dyscalculia?

As promised, I'm writing a blog post series on the answer to that question. But my short answer will always be the same: Notice, Wonder, Discover (NWD). 

You can find a series of workshops I did on NWD here. The information in these posts is more about the big picture of the why behind my answer. 

Before you get to math, or language, or anything else, we need to back up. What is education? What is it that is being educated?

It is my belief that Gattegno was correct. The thing we ought to be educating with intention, because it is the only thing that can be educated, is awareness.   

What Is Awareness?

Awareness is having knowledge of or the ability to perceive a situation or fact. Awareness encompasses the entire process of:

  • gathering information; 
  • recognizing relationships between bits of information and organizing it as well as adjusting oneself in relationship to that information (making sense of it); 
  • and then having the ability to articulate the information in a way that is useful to you or someone else.

We call this whole process Notice, Wonder, Discover. Scientists call it cognition.

Let's Take a Look At Notice

Noticing is the process of gathering information. Sounds easy, but it isn't.
If you think it is a simple thing, you probably aren't a good noticer. Noticing is fraught with all kinds of difficulties. I have space here to barely skim the surface of this topic - but my point should be clear. 

Problems with Noticing

You Don't Choose What You Notice

This is one of the biggest problems with noticing. You don't pick what sticks out to you. Much of what you notice depends entirely on what your normal is.

We tend to notice things that are unusual. If I'm driving down a road I've traveled 100 times, I might drive to my destination and not even remember the trip, unless I was nearly hit by an ambulance rushing to a car wreck. That I'll notice.

Too Much to Notice

We are bombarded with billions of bits of information all the time. Just get up in the morning and you could notice: temperature, sounds, air flow, light, carpet, cobwebs in the corner, dirt on the floor, the pain in your side, how tired you still are, where your body aches, smells on the sheets, smells in the house, lack of smells, how dusty the ceiling fan is and so much more. Are you tired yet?

We need a mechanism to shut out information or we'd go crazy. The trick is to shut out the unnecessary information. Sometimes it's obvious. If I'm changing the oil in a car, the color of the shutters on the house is meaningless. But knowing what is and isn't important becomes increasingly difficult as information and situations become more complicated.

 Sometimes we get it wrong, and the results are catastrophic. 

Inability to Direct Attention

Attention is a skill that requires a tremendous expenditure of mental effort. When people are attending to something and lose their focus, it can take anywhere from 5 minutes to an hour to get them back into the groove again. 

Even if you can attend, it doesn't mean you have the ability to zoom your attention in and out. Can you zoom in to the details and out to the big picture and all the way along the path? Most people see themselves as either big picture or detail-oriented people.

Let's say you have control of your attention which you can zoom in and out to become aware of the facts or situation. You can see what is there. Can you also see what isn't there that ought to be there? Can you see what is missing? 

Noticing With Intention

Given the difficulty that noticing presents, we have two options:

  1. We can approach life in a way that we are casual noticers, missing what doesn't jump out at us.
  2. We can learn to notice with intention and purpose as well as direct and control our attention. 

If we remain casual noticers, how much content do you think your student will absorb? How much of their childhood will be remembered? How many learning opportunities will be left behind, simply because they went unnoticed?

When we consider the building blocks of thinking, the very first ones have to do with the noticing and gathering information phase. This phase is also where we make close to half of our mistakes. Most of us are sloppy noticers.

Intentional noticing requires that we:

  • Recognize there is something to notice or perceive.
  • Gather information without impulse - act with a purpose.
  • Gather with precision and accuracy.
Noticing is a cognitive skill. Cognitive skills are not a possession. It's not a have vs don't have deal. Rather, cognitive skills are a spectrum. We all fall somewhere along the line from immature to mature. Scientists are currently unsure of what the upper limit of cognitive development looks like.

To some degree, we all have what Feuerstein calls "blurred and sweeping perception." This refers to noticing without regard for detail or precision. This isn't just an attitude problem.

I've noticed that when there are too many novel details, my brain becomes overwhelmed. My immediate solution is to notice the big picture only and let the rest be a haze. Noticing with intention requires a mental investment. I usually only do it if I have a reason (meaning), time, and a reasonable hope of understanding structure and categories of the topic at hand.

Blurred and sweeping perception happens when we approach anything new. But it's also a way of orienting oneself to the world. Some people go through life perceiving very little of it. This is part of what Gattegno says needs educating. How does one learn to notice? 

Charlotte MAson


“We all have need to be trained to see,

and to have our eyes opened before we can take in the joy that is meant for

us in this beautiful life.”

How do we train ourselves and our children to see? We don't have to leave it to chance and hope. We do it by providing the categories in which information belongs. After it is categorized, we can move on to the wonder phase of awareness and make sense of it. 

Categories of Noticing

You may not realize that you are already familiar with the categories we use for efficient noticing. If you want a more in-depth look at the categories, please check out the Notice, Wonder, Discover bootcamp video on noticing. The following are the basic categories of noticing. Each of these categories can be broken down even further. 


  • What do I see?
  • What is the question?
  • What is the point?
  • Who is involved?
  • What are we counting?
  • What is being measured?
  • What are we measuring with?


  • What should I do first? Next? Last?
  • Last year? Next year?
  • What happened before this?
  • What happened after?
  • Questions about morning, afternoon, night.
  • Sequencing
  • On, at, and in prepositions: on my birthday, at sundown, in a week.


  • Above/below
  • Around
  • Near/far
  • Top/bottom
  • On/In
  • Up/down
  • Side by side
  • End to end

Which Kind?

  • Color
  • Shape
  • Size
  • Odd/even
  • Prime

How Many?

  • What can be counted?
  • How many of each?
  • How many altogether?
  • What are we counting?
  • Differences between numbers?
  • Multiples of numbers?


  • How are things the same/different?
  • Relationship of distance: near/far, longer/shorter.
  • Relationships of quantity; more/less, bigger/smaller/equal.
  • Mathematical relationships; additive, multiplicative, fractional, exponential, difference, equality. 
  • Symmetry
  • Reflection

Action: Is There Movement?

  • What kind of movement?
  • What direction/intensity do you find?

What I Wonder

If it is true that half of our thinking mistakes happen in the gathering of information phase, I would spend at least half my school time developing the ability to gather and record accurate and precise information. This begins early.

Gathering information does not have to be a math activity. This can be done with any subject. There is a big difference between: "Today, I saw a red bird," and "Today, I saw a medium-sized red bird sitting in the Ginko Tree. It had a red pointed beak, with a black mask around its eyes. It also had black wings and a crested head." 

If you were able to notice well, what would be the upper end of what you could accomplish? How much more joy could you find in living? What if you noticed well, had control of your attention, and could direct it to observe both details and the entire picture? How could that change your life? What if you could teach in a way that helped your children develop these skills? What would their futures look like?

If you want some help learning to teach Notice, Wonder, Discover, you can join my email list here. If you want some help with math, you can learn more about our academy courses here


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    Caleb Gattegno

    Educator, Mathematician 

    Only awareness is educable. . ."