Learning Well at Home

Category: Foundations

This is your core philosophy. The articles that explain why everything else exists.

  • Review of Charlotte Mason a Living Math

    Review of Charlotte Mason a Living Math

    Eight years ago, a conversation about Charlotte Mason, Gattegno, and mathematics landed in my Facebook group, Learning Math with Base Ten Blocks. My friend and my sidekick, Lacy, was engaging the Charlotte Mason community and introduced many families to Cuisenaire rods. The conversation quickly turned to whether Cuisenaire rods fit within a Charlotte Mason education. I thought we were discussing beans and rods. I wrote my response to that conversation. Looking back, we were asking a much larger question. Denise Gaskins participated in those discussions and wrote several essays exploring the relationship between Charlotte Mason’s philosophy and mathematics. Eight years later, she has written Charlotte Mason’s Living Math. I’ve been waiting for this book for eight years. I just didn’t know it until she wrote it.

    Denise Gaskins is the founder of Tabletop Academy Press and the author of Let’s Play Math, the Math You Can Play series, and now Charlotte Mason’s Living Math. Through her website, Let’s Play Math, she has spent years writing about mathematical play, games, puzzles, investigations, and

    learning. She also runs the Math Teachers at Play (later Playful Math) Blog Carnival, a monthly collection of articles from classroom teachers, homeschool educators, mathematicians, and recreational math enthusiasts. I hosted several editions of the carnival over the years, and its archives remain one of my favorite collections of mathematics resources.

    Denise and I have known each other for nearly a decade. She has always been generous with her time and careful with her words. Because she remains my fairy math mother, I’m not pretending to be neutral. 

    Underlying Assumptions About Math and Charlotte Mason

    Before I can review Denise’s book, I need to answer an underlying question.

    Denise is asking what it means to teach mathematics in a way that is faithful to Charlotte Mason’s educational philosophy. Charlotte Mason described education as the science of relations. 

    Calling something “Charlotte Mason friendly” isn’t enough. Many educational methods are compatible with Charlotte Mason. That doesn’t mean they arise naturally from her philosophy. I want to answer this question: If we truly taught mathematics as a science of relations, what would it look like? That is the measure by which I read Denise’s book. Not can you use it if you are a careful reader of Charlotte Mason, but if you are a careful reader of Charlotte Mason, how does her philosophy intersect with math. 

    I come to that question with my own assumptions. You should know what they are. I know many of my readers are highly inclined toward Charlotte Mason. It helps to know where my potential biases are.

    One of them is that numbers are not objects. You can’t point to something and say, “This is a ten.” The orange Cuisenaire rod isn’t ten. It is a colored rod made of plastic or wood. In our lessons, we don’t mark the rods, and we don’t encourage children to call them by number. Only after establishing that the white rod represents one do we name the rod ten. We use “white = 1” as the unit by which other rods are measured. The same orange rod can represent one, and then white would be 1/10. One hundred and white would be ten. The relationship provides context and meaning. The rod is the object. 

    You cannot know ten on its own. We know it through the infinite relationships that point to ten and give it its meaning. Ten is two fives and five twos. Ten is half of twenty. Ten is one more than nine, but one less than eleven. It is the same length as two light green rods and a purple when white is the unit. None of these relationships is ten. Each one enriches the child’s understanding of what ten refers to.

    If education, including math, is truly a science of relations, then I would expect children to come to know numbers through richer networks of relationships rather than through isolated facts or procedures. New ideas would grow naturally from earlier relationships. Learners would develop fluency because each new relationship gives the child another way of knowing the same referent. Most of all, I would expect mathematics to become more coherent as children learn, not more fragmented.

    That is the lens I bring to Denise’s book. It isn’t the only possible lens, but it is the one I find most faithful to Charlotte Mason’s phrase, the science of relations. 

    Part One: The Philosophical Foundation

    Before Denise tells us how to teach mathematics, she asks a more important question: What is mathematics for?

    That choice sets the tone for the entire book. Rather than beginning with curriculum, manipulatives, or lesson plans, Denise begins with Charlotte Mason herself. She argues that if we want a genuinely Charlotte Mason mathematics education, we must first understand Charlotte Mason’s educational philosophy. Only then can we ask how mathematics fits within it.

    Denise takes Mason’s insistence on relations seriously. Instead of asking which manipulatives or textbooks Charlotte Mason might have approved of, she asks how Mason’s principles should shape the way we think about mathematics itself. Throughout these opening chapters, she returns to familiar Mason themes: children are born persons, education is an atmosphere, a discipline, and a life, the cultivation of good habits, living ideas, narration, and the training of reason. Her point is that mathematics should not stand outside this philosophy. We should teach mathematics according to the same principles that govern every other subject.

    Part Two: From Philosophy to Practice

    Once Denise has established the philosophical foundation, she shows readers what those principles look like in practice. Rather than presenting a prescribed curriculum, she offers a way of thinking about mathematics lessons. The emphasis remains on reasoning, conversation, investigation, and the habits of mind that Charlotte Mason believed education should cultivate. Mathematics is treated as something children actively engage with rather than passively receive. Gattegno said somewhere, “We give children things to do and stuff to talk about.” Mason was doing the same thing. Denise shows you how to do it with math. 

    One strength of this section is that Denise draws from a wide range of mathematicians and mathematics educators. She does not recreate a nineteenth-century classroom. Instead, she asks which modern practices embody Charlotte Mason’s philosophy. The result is a book that is both historically grounded and educationally current. Readers will encounter mathematical games, investigations, conversations, puzzles, and rich problems, all chosen because they encourage children to reason and make connections rather than simply produce correct answers.

    I was pleased to see the Substitution Game included among the mathematical conversations. Substitution is one of the most important mathematical ideas children encounter. It teaches them that different expressions can refer to the same mathematical reality. That habit of recognizing equivalence reaches far beyond arithmetic and becomes foundational for algebra, functions, and higher mathematics. Its inclusion here illustrates Denise’s larger point: mathematics grows through relationships between ideas, not through the accumulation of isolated facts.

    Is Denise Faithful to Charlotte Mason’s Philosophy?

    I believe the answer is yes.

    One of the strengths of Charlotte Mason’s Living Math is that Denise refuses to reduce Charlotte Mason to a collection of educational techniques. She does not ask whether Charlotte Mason would have approved of Cuisenaire rods, games, or a particular curriculum. Instead, she begins where Charlotte Mason herself began: with a philosophy of education.

    The opening chapters establish that philosophy before discussing mathematics. Denise returns repeatedly to Charlotte Mason’s central ideas about children and education. Rather than treating mathematics as an exception, Denise shows you how to enter the arena of mathematical relationships instead of learning about them. She does this by showing you how to apply Mason’s ideas to math. That was the premise of the response I wrote eight years ago.

    That argument isn’t window dressing. It changes the conversation from “Which math curriculum would Charlotte Mason have used?” to the much more interesting question, “What would mathematics look like if it were taught according to Charlotte Mason’s philosophy?”  Those are not the same questions. There is no equal sign between them. The first looks for historical approval. The second asks whether a way of teaching grows naturally from Charlotte Mason’s understanding of education.

    By beginning with philosophy rather than methods, Denise gives readers a coherent framework for evaluating mathematics instruction. Whether or not one agrees with every application, the argument grows naturally from Charlotte Mason’s educational principles rather than from a collection of isolated quotations. For me, that is the book’s greatest strength. It also is the approach that has shaped my own work for the past eight years.

    Finally, Is the Book Helpful?

    That depends.

    Helpful for what? Here we encounter those referents again. Like the number 10, helpful needs to refer to something. 

    If you’re looking for a guide to navigating a national park, probably not.

    If you’re looking for a complete mathematics curriculum, again, no.

    If you’re looking for a scripted lesson to teach tomorrow morning, only in the broadest sense.

    But those aren’t the questions this book is trying to answer. If you’re looking for help rethinking your relationship to mathematics, then I believe the answer is yes.

    If you’re a Charlotte Mason parent trying to understand what it means to teach mathematics according to Charlotte Mason’s educational philosophy, then I believe the answer is absolutely yes.

    Denise is not trying to hand parents another curriculum. She is offering a vision. Like Let’s Play Math, this book gives parents permission to believe that mathematics is something children can reason about, wonder about, discuss, investigate, and enjoy. It invites parents to treat children as people who have mathematical ideas worth listening to.

    For many parents, that shift in orientation will be far more valuable than another collection of lesson plans.

  • Hunting the Snark

    Hunting the Snark

    On Missing Referents, Blank Maps, and Why Carroll Was Telling the Truth Exactly

    Children are amazing. They teach you an astonishing amount if you learn to teach well and listen.

    This summer, while I have been migrating our courses to a new community platform, my students and I have been sailing in search of a Snark. Lewis Carroll’s The Hunting of the Snark is one of the funniest poems ever written. Funny the way Flannery O’Connor is funny. Funny the way Fargo and the wood chipper are funny. Fargo is devastating, hilarious, and the cinematography is exceptional. If you’ve been tracking what the story has shown you, Carl meeting the wood chipper is the joke arriving on schedule. If you haven’t, it’s just horror — sudden, from nowhere, exactly the same horror as a Boojum taking the Baker and the Misfit taking Grandma.

    Still of Jerry, played by William H Macy, above the parking lot. Fargo, produced and directed by the Coen brothers. 1996

    One of my young sailors noticed that our expedition was hunting with forks.

    “Forks,” he said. “Why?”

    A reasonable observation and a wonderful place to begin.

    “What kind of forks are these? Dinner forks? Meat forks? Or maybe a fork in the road?”

    I nearly died. Not from a Boojum. From laughter.

    Then another sailor asked an even better question.

    “Why does this bring anyone hope?” Excellent question.

    “Why should hunting with thimbles, railway shares, and forks inspire confidence?” I asked. I have never looked at a drawer full of silverware and thought, “Today feels promising.”

    Another member of the crew noticed that the expedition possessed a map; the map was blank.

    By this point, I was laughing hard enough that I was becoming an unfit captain.

    “What good is a blank map?” someone asked.

    “Indeed,” I replied. “What good is a blank map?”

    Another sailor chimed in.

    “And why are they sailing in circles? Why not just sail from one place to another?”

    One of my students, who actually knows something about sailing, observed that the Bellman’s commands would never get a ship anywhere at all. The Bellman gave orders with complete confidence and considerable solemnity. Unfortunately, his navigation appeared to bear only a passing acquaintance with boats, wind, or the sea.

    Naturally, the Bellman’s crew adored the map. Who wouldn’t? It was wonderfully easy to read. No troublesome coastlines. No distracting islands. No currents. No reefs. No ports.

    No inconvenient reminders that the world has a shape.

    Everything a sailor normally uses to find his bearings had been thoughtfully omitted. The result was a map anyone could understand at a glance. Carroll describes it perfectly:

    What’s the good of Mercator’s North Poles and Equators,
    Tropics, Zones, and Meridian Lines?’
    So the Bellman would cry: and the crew would reply,
    They are merely conventional signs!’

    ‘Other maps are such shapes,
    with their islands and capes!
    But we’ve got our brave Captain to thank —
    A perfect and absolute blank!’

    – The Crew

    My crew announced the map was useless. Who can argue with that? I voted yes.

    I asked about wisdom. The crew in the poem had decided the Bellman was wise because he had good posture, moved gracefully, spoke with confidence, and carried himself with great solemnity.

    “Does saying something three times make it true?” That one came quickly. Everyone agreed it did not. Then I asked, “What about being solemn? Does that make someone wise?”  The Zoom room became much quieter. It was the sound of thought. That was a harder question to answer. 

    One of the remarkable things about children is that they have not yet learned to confuse appearances with reality, but they also recognize that appearances often point toward reality. Solemnity has the right shape. A thoughtful, serious person is often wise. A calm physician inspires confidence. A patient teacher usually knows something worth learning. The shape is not arbitrary. It points somewhere. The question is whether it always points to wisdom.

    Identifying a Snark

    We couldn’t decide whether a solemn man was wise, so we set it aside and kept reading. The poem continued to reward us. The Bellman declared the Snark tasted “meager and hollow, but crisp,” which struck my crew as an unusual way to describe flavor. A Snark gets up late, which may tell you something about its sleeping habits but remarkably little about how to recognize one. Some Snarks have feathers and bite. Others have whiskers and scratch. Fortunately, they do no harm. Except for the Boojum. The Bellman assures everyone that they will know a Boojum when they find one. This is perfectly true. They disappear.

    Carroll has just given us five unmistakable marks by which genuine Snarks may be known. He has classified them, organized them, and distinguished them carefully. He has all the machinery of a proper naturalist. Then, at the very end, he gives us the one characteristic that actually matters. Unfortunately, it arrives at precisely the same moment as the consequence. Identification and disappearance occur together. The taxonomy is beautifully organized, wonderfully detailed, and perfectly incapable of helping the crew find the thing they have set out to hunt.

    My young sailors noticed this immediately. Without ever studying philosophy of science, they began asking one of its oldest questions. What makes a description useful? What belongs in a category? When does a classification help us recognize the thing we are looking for? A description is useful because it helps us find the thing it describes.

    At this point, I should probably stop and say something about Lewis Carroll, because it matters.

    Charles Dodgson and Lewis Carroll

    Lewis Carroll was the pen name of Charles Lutwidge Dodgson, a mathematics lecturer at Christ Church, Oxford. Under his real name, he spent his career writing about logic, geometry, voting theory, and symbolic reasoning. Under his pen name, he wrote some of the most perfectly constructed nonsense in the English language. That combination is not an accident. It is the reason The Hunting of the Snark works as well as it does.

    Carroll insisted the poem was nonsense. Readers have spent nearly a century and a half refusing to believe him. The Snark is death, they say. Or ambition. Or the Victorian examination system. Or the search for God. Or existential dread. Every generation confidently announces that it has finally discovered what the Snark “really” means.

    They are hunting with forks.

    Carroll was telling the truth. The poem is about nonsense. But nonsense, to a logician, is not randomness. It is not simply saying silly things. It is something much more precise. Nonsense happens when the machinery of meaning continues to run perfectly while the things it is supposed to connect have disappeared. The grammar still works. The logic still works. The categories still work. The authority remains intact. The connection between the sign and the thing it claims to signify has been lost.

    Linguists call that connection a referent. A referent is simply the thing a word, a symbol, a map, or a number points to. A map is useful because it points to rivers, roads, mountains, and landmarks. A word is useful because it points beyond itself to something in the world. Mathematics works because its symbols reliably point to relationships that remain true no matter who writes them down. The sign is not the thing. It exists to lead us to the thing.

    That is exactly what keeps failing in The Hunting of the Snark.

    The Bellman’s map has all the dignity of a proper nautical chart, but it points nowhere. His famous instruction to “steer to starboard, but keep her head larboard” sounds wonderfully nautical until one notices that it issues two incompatible commands at once. “What I tell you three times is true” offers proof that refers only to itself. The statement does not point beyond itself to reality. It simply circles back and declares itself sufficient.

    The crew is assembled in exactly the same way. There is a Boots who makes bonnets. A Barrister retained to settle disputes on a voyage with almost nothing to litigate. A Banker hired at enormous expense. A Baker who can bake only wedding cake, for which there are neither ingredients nor customers. A Butcher whose only professional qualification is killing Beavers, only to become the Beaver’s closest companion. Every member of the expedition possesses a recognizable identity. Every title sounds appropriate. Every profession has the right shape. Yet each has been disconnected from the work the voyage requires.

    The Baker forgot his name. He forgot his boxes. He forgot his clothes. He delivered his warning in Hebrew and Dutch and German and Greek, then forgot to say it in English, which is the language everyone aboard the ship speaks. He possessed an abundance of what did not matter and lacked the one thing that did. The excess obscured the absence.

    And the Snark itself. What if the Snark is not merely a creature to be hunted, but the one thing in the poem that genuinely lies outside the crew’s own system of references? The one thing that is real enough to be found. The entire expedition is organized around finding it, yet every tool they possess has lost its ability to orient them toward reality. The map is blank. The directions are circular. The captain’s authority points only to itself. His plan is to cross the ocean by ringing his bell. The descriptions identify nothing. They are not unable to find the Snark because Snarks are rare or obscure. They cannot find Snarks because you cannot hunt something real with instruments that no longer point beyond themselves. You will sail in circles and call it navigation.

    Which makes the Boojum the most terrifying possibility in the poem. If the Snark is that which genuinely exists outside the self, then the Boojum is its perfect counterfeit. It wears the face of the real thing while pointing nowhere but back to itself. You cannot distinguish the two until the moment of contact. And when you finally reach for something that has no reality beyond itself, there is nothing to meet you. Nothing to resist you. Nothing to correct you. Nothing to orient you. You reach for the thing and there is no thing. Only the reflection of the reaching.

    Disappearing is what happens when you have navigated by self-referents for so long that there is nothing outside yourself left to locate you.

    The Baker knew enough to be afraid. His uncle had warned him. He knew there was a difference between a Snark and a Boojum. He carried the warning across six languages and forgot the only one that could have helped him. The referent was present. The connection was not.

    Navigation with Blank Maps:
    The Education Problem

    Blank maps are shockingly common. We hand them to children every day. I know. I once was a Bellman myself. A few years ago, I was in a homeschooling group, and a mom sincerely asked, “How do I explain to my child that three-quarters of an apple divided by three-quarters of an apple is one whole apple?”

    Her question told me several things. She either did not understand what division is, she did not understand the difference between number and kind, or both. She had performed the procedure correctly. The answer was right. She began with three-quarters-of-an-apple as the kind, and somewhere in the middle she changed the kind to one whole apple, and hadn’t felt it move. She was holding one of something, and that something was no longer what she thought it was. The machinery kept running after the referent had shifted.

    When she couldn’t explain how the answer worked, she asked: “How do I explain this to my child?”

    Every parent in the room knew how to divide fractions. The procedure was familiar. The answers came out correctly. What no one could explain was what the procedure was doing or why it worked. I understood immediately what the problem was. I had felt this same thing as a kid. Math seemed like some strange magic, a bit like voodoo. How do you divide a part of an apple into pieces and get a whole apple?

    When we count, we always count number and kind. We ask, “How many of what?” Three apples and four oranges are not seven until we decide to count fruit. Our place-value system preserves the same pattern. One hundred thirty-four is one of the hundreds kind, three of the tens kind, and four of the ones kind. Number never appears by itself. It always belongs to something.

    This is why isolated math facts create so many confident but disoriented students. A child may know that seven times eight is fifty-six and still have no idea what multiplication asks, what kind of thing fifty-six names, or how that fact connects to every other fact in mathematics. The answer is correct. The web is missing. It is a blank map.

    Some children eventually construct the web for themselves. They discover the relationships despite the instruction. They find the referents on their own. Others do not. That difference is often mistaken for intelligence. I suspect it is something else. One child eventually notices that the map does not match the territory and begins looking for landmarks. The other trusts the map, which is the perfectly reasonable thing to do when it has been handed to him with great solemnity. Some children shout the emperor has no clothes. And they are right.

    The Misfit, The Boojum and The Wood Chipper

    Missing clothes are shockingly common. In Flannery O’Connor’s short story, Grandma’s manners stopped referring to actual love decades before the Misfit arrived. The Baker’s warning stopped referring to actual danger somewhere in its sixth translation. Carl’s confidence and hubris stopped referring to actual competence long before the wood chipper did what wood chippers do. The Bellman’s map stopped referring to any coastline the moment “no conventional signs” got cheered as a virtue. The fraction mom’s answer stopped referring to the actual kind of thing she was counting. Every case is the same failure in a different costume: the sign kept running, doing its job smoothly, entirely uncoupled from the thing.

    That is the point. Whether you see these things as comedy, not the slapstick funny, but the incongruity funny, is whether you can pick out the incongruity. If you can, then you know, the patterns always come knocking. 

    Flannery O’Connor said that for readers who are almost blind, you draw large and startling figures. That is what the wood chipper is doing. That is what the Misfit is doing. That is what the Boojum is doing. The referent is large and hard to ignore. It’s knocking. 

    The Structure of Nonsense

    Carroll said the poem was about nonsense. He was right. He was being precise. The poem is nonsense. Every element is a demonstration of the referential machine running without the load. And it is simultaneously about nonsense, in the same way that a photograph of fire is about fire. The form and the content are the same thing.

    Only a logician would think to do that. To make a self-demonstrating argument. To write the thing and write about the thing in the same gesture.

    Which means the poem is the one thing in itself that is not a self-referent. It points accurately at something real. It points at the structure of nonsense itself, from the inside, with complete precision.

    Carroll made a map that actually works. He just made it of the territory everyone else was pretending wasn’t there.

    That is why it is so funny.

    And that is why my young sailors, reading it for the first time, keep finding things. They are not sure what they have found yet. But they know they have found something. They can feel the gap between the form and the missing referent, even if they don’t have words for it yet.

    They noticed the forks. They noticed the map. They noticed the solemnity.

    They are better equipped for this hunt than the Bellman’s crew.

    They are sailing with something other than hope.

  • The Pattern Hunter’s Journey

    The Pattern Hunter’s Journey

    There are moments, as a mother, when you experience terrifying bouts of clarity. Your child has to live their life on their own. You have either prepared them well or not.

    The Problem of Knowledge Transfer

    When my oldest was 13, we sat at the kitchen table. He handed me a math assignment, and his score was 60%. An F. An F after having had time to correct it. I was furious. And the story I told myself was that he wouldn’t graduate high school; he’d never get into college; all of his future prospects centered on his ability to get the right answers on these 30 problems.

    Doug Wilson said in a lecture that boys discover, around age 13, that their mothers can’t make them do anything. Who were these boys? What sorts of women birthed them? My boys figured that out by age 3.

    While I was telling myself that my child didn’t care about school or his future, my son was telling himself that I didn’t care about him. I just cared about this stupid assignment. I just wanted him to get good grades so I could brag to my friends. I cared only about math.

    He was wrong, of course, but not exactly. He was wrong about my motivation, but as Dr.Swartz of the Bronx Charter School for Better Learning said, my fear was so big, it took up all the space in a room. There wasn’t room for anyone else.

    I would love to tell you I figured it out. But I didn’t then. The wound just festered. We can call it the math wound. I did not know how to repair it. By the time I figured out how deep it was in my son, it was no longer about math; it was about me. He was angry.

    When my son was 14, I became pregnant with my second child. Because, you know, I believe in spacing. My first response was, “How can this happen? I’m 42?” After that thought came, “Oh dear, we have to do math again.” I was on a mission to solve the math problem.

    Within a few years, I’d read nearly every teacher’s manual available. I was a classical education fan, so I hunted the curriculum recommendations on forums, classical school websites, and curriculum providers. I read them all. My fear continued to grow.

    The Structure of Math Curricula

    Basically, all math curricula are variations of the memory plus mastery or spiral methods. Some are a combination. They have different bells and whistles, but you must pick between them. I vacillated between delaying math education and game schooling math. This, at least, would stir his natural competition instincts. Little did I know my youngest wouldn’t have a competitive bone in his body.

    I settled on game schooling. Then I’d panic. What was I doing to my son? I could hear the doors of opportunity closing. In the middle of the night, visions of my toddler’s future flashed in front of me, and my panic friend came banging on my door.

    And that is when I found it. Caleb Gattegno. His work on math and awareness. Gattegno said, “We don’t teach math; we educate awareness.” We educate a person on how to see on purpose. Math is a tool. Then he did this crazy thing. He started with algebra first. He started with the relationships. I didn’t know how, but I knew my life had changed.

    For months, I read everything I could find by Gattegno. I used the Wayback Machine to hunt down missing links. I hunted down and read the books in the bibliographies. Sleep was not part of my usable vocabulary during that time. In the middle of the night, I sat at my table playing with the rods, describing relationships with symbols, making transformations, and watching them come alive in the expressions I wrote, and making the connections I should have made in high school. I was finally getting math. It was like seeing math for the first time.

    It seemed that if Charlotte Mason had known Gattegno, they would have been fast friends. They both discussed observation, reflection, and relationships. Both agreed that children arrive with certain faculties for learning and that education should be fit for human persons. The first workshop I offered was “Charlotte Mason and Gattegno Have Tea.” I blogged my way through Gattegno Mathematics Textbook 1. I offered my insights. I thought, “No one will need me to help them anymore.” Except they did.

    Then I wrote a quick start guide to base-ten blocks, and thought, “Now no one will need me.” But they did. I didn’t understand what other moms didn’t understand. What became obvious is that if we asked enough questions, they’d give me the answer. That didn’t mean I had a solution, but it gave me ways to think about the problem. I was noticing patterns in where people struggled. I could walk them through it, but I couldn’t explain to them what I was doing.

    Several years into my relationship with a school in New Zealand, my friend Victory, a teacher there, mentioned Feuerstein. Reuven Feuerstein was a Romanian Israeli cognitive psychologist. His escaped to Palestine during WW2 following the war he worked with child survivors. His premise was that while trauma is real, it is a distant cause of mental affliction and poor performance. The proximate cause is poor mediation. By mediation, he meant coming between the learner and the world to help shape their thinking. Mediators help learners gather, make sense of, and express information. By information, he meant the stuff of the world. Everything. That was a giant puzzle piece. Huge.

    By then, Denise Gaskins had pointed me to Anne Fetter, who had distilled what Gattegno was saying in noticing and reflection into “Notice and Wonder.” Immediately, I took that and ran. It is what Charlotte Mason and Gattegno were also getting at. What is this thing? What does it do? How does it work? Feuerstein gave stages of cognition, or, broadly speaking (Iain Mc Gilchrist would disagree with this), thinking. I kept Annie Fetter’s Notice and Wonder idea. This choice wasn’t because of liking it or its pleasing sound; rather, “Wonder” matched Socrates’ term with Feuerstein’s concept. They were tracking the same animal. 

    What Is Notice, Wonder, Discover?

    This middle stage of cognition is sense-making. Socrates called it wonder. Feuerstein called it elaboration. Wonder is not merely awe or curiosity. It is the work of determining significance. The Latin word is mirari – to look at with astonishment. It belongs to a family of words that mean “to look at” or “to aim at”. We get admiration from that word. Ad means “to move toward” – to move toward the thing you want to see. It is the process of taking what you have noticed and asking the kinds of questions that make a space navigable. Which details matter? Which relationships matter? What kind of situation am I in? How should I act in relation to it?

    If I walk into a funeral home, I notice people are somber. Wonder asks what those observations mean and how they relate to one another. What kind of place is this? What is happening here? How should I participate in this reality? If I have wondered well, I will discover that now is not the time to smack my brother with a hymnal.

    It was my friend Victory who gave me the word discover. We call Discover what Feuerstein called expression. Some people say that they don’t like that word. I kept it for several reasons. Discover means to uncover; to lift the veil off what was concealed. It has the idea of a roof inside it, but also other types of covering. I have kept it because the expression phase presents the thing you uncovered to the world. It is holding up the roof in a way that others can peek inside. The Greek word for discover is apokalypsis. The Book of Revelation is the unveiling, you can nearly hear the word Apocalypse in the Greek. Revelation is the book where everything is shown, and what is shown carries enormous consequences. The unveiling was intentional. The presenter was intentional, the recipient was intentional.

    Every genuine discovery is a revelation, an apocalypse. Small scale, but the same pattern. That discovery requires a response from the one who discovers. The ancients knew this. I had to hunt for these ideas but they lived inside a world where reality was already charged with meaning and address. A thing revealed, of course, required a response. The idea that you could witness a revelation and simply note it, file it away, and move on would have been incomprehensible.

    Just a few hundred years ago, people lived inside seasons. The length of the day changed. The weather changed. There were years of famine and years of plenty. The fig tree put out leaves when summer was near. Animals migrated. Rivers flooded. The stars moved across the sky. Reality continually interrupted you, demanding your attention.

    Finding Patterns Across Domains

    We set our houses to the same temperature as our cars, offices, grocery stores, and restaurants. The lights are always on. Night arrives, but we scarcely notice. Until COVID, stores were open twenty-four hours a day. There is so much light that the stars are barely visible. The rhythms that once formed attention are easy to ignore.

    We have to argue for what they simply inhabited. For them, the cosmos was not a collection of neutral facts. It was a place where things were shown to you by someone, for a reason.

    I didn’t learn that from Feuerstein, Charlotte Mason, Dorothy Sayers, or Doug Wilson. I had to go to Chesterton, Tolkien, and then finally to St. Maximus the Confessor. Because they brought in the last missing piece. Patterns. But I’m getting ahead of myself. We’ll come back to this.

    As I was redoing my math materials, considering the three phases of learning. I was excited. This could now be passed on to parents. There was an easy-to-understand framework. But then a mom wrote me and said, “I still don’t get it.” Again, I didn’t get what she didn’t get. I asked more questions: Tell me about, ‘I don’t get it. Where don’t you get it?’ I could hear her frustration. She said: I don’t know how to do what you do, and I don’t know if my child is learning without testing numbers.

    Knowledge Transfer Is Not Information Transfer

    I kept bumping into the transfer problem. How can I take what I am doing and seeing and transfer it to others? Every frustrated mom who wrote me helped me hunt for another piece of the puzzle. I’m grateful for all of them and their patience with me as I tried to figure out what I didn’t get. As I was working on some new materials, I discovered Aristotle’s categories. My mind exploded. Noticing well could be systematized. It was sitting in front of me all along. Gattegno knew it. He even wrote about it. If your child can speak, they can do math. If they speak, they are operating at high levels of abstraction. They are already sorting the world into categories. Aristotle’s categories. But Aristotle didn’t discover them. He named them. I added Aristotle’s categories to noticing, and that made a huge difference. Now, I say to myself. I am done. I have found “the things.” Everyone can implement this: You have a manual. You have the pieces of the puzzle: “Go, be fed.”

    Then I reworked all of my manuals and course lessons around the now-clearly defined movements of learning. I have Aristotle’s categories. I make the lessons match the foundation documents of NWD. I put in a huge Bibliography in the back of the Pattern Hunter’s Toolkit. Now, says I, “People will no longer need me.”

    It was during this time that I developed a spiritual relationship with a priest, Father Athanasius. I sent questions. Lots of questions. He was gracious and answered them. As I continued to rebuild my materials, the puzzle pieces dropped into place – puzzle pieces I didn’t even know were in my box. I realized that orientation isn’t just to something. If NWD is about developing the skills to see what is true, and in my belief system, Truth is a Person, and not just a person but a Trinity of persons, that would mean that orientation is to Someone. And that perhaps every act of noticing, every act of right naming, and every revelation is a small ‘s’ sacramental act. And that has implications everywhere. I emailed Father in the middle of the night, “Father Bless – here is what I am seeing…..I’m afraid. Is this possibly true?”

    His response was very gracious.

    “Yes. Call me when you get a chance.”

    That is when I made my acquaintance with St. Maximus the Confessor. St. Maximus took 10 years of struggle and gave me the insight I needed. This is my best layperson’s attempt at what I took away. I am not a theologian; I am a mom on a hunt:

    Yes, we have to notice. Yes, we have to wonder. Because that is how we perceive the world. All pattern hunting is a search for the logi. Everything that exists has a reason for being — not just a cause that made it, but a meaning that it carries. A purpose written into its nature. The logos of a thing is what it is at the deepest level — the thought of it in the mind of God, which is also the structure of it in reality. That is what I meant when I said in The Pattern Hunter’s Toolkit that pattern reveals structure and structure reveals purpose. Maximus named it in its fullness.

    The world is patterned from top to bottom, and the patterns repeat. They tell you about the world and the shape of reality. A wise person understands these patterns. Attends to them: Go to the ant…you sluggard. From the fig tree learn its lesson: as soon as its branch becomes tender and puts out its leaves, you know that summer is near. He is like a tree planted by streams of water that yields its fruit in its season, and its leaf does not wither. In all that he does, he prospers. The Scriptures send you to the patterns of the world and points: Look! Do you see what kind of thing it is? How does it work? Act wisely now that you have seen.

    The last thing that St. Maximus taught me was the thing I was missing: Feuerstein was right about mediation. Not only was he right about mediation, for St. Maximus the Confessor, mediation is the defining purpose of humanity. He taught that human beings are designed to act as a microcosm of the universe, uniting all divided realms of creation within themselves and lifting the entire world into loving communion with God. As parents, we are, to the best of our ability, supposed to help our children to become priests of creation, gathering the rational principles (or logoi) of all things and offering them back to God in a “cosmic liturgy”. By bringing creation into harmony with the Divine, humanity achieves its own ultimate destiny.

    Our problem is that we are not born mediators. Maximus confirms this. It is something we have to be shown, and we grow into it. We need mediation ourselves. The transfer problem is real. My son didn’t need more math, he needed better mediation. I didn’t know how.

    That is why I no longer push more courses and more content. You will not become a mediator by reading about it. Cuisenaire Rods are not magic. You become a mediator by watching it. You learn the patterns because someone came along and offered you mediation. What I offer now is not the promise that your homeschool will get some quick wins this year in math, but a community of people committed to noticing, wondering, and discovering a world that is patterned from top to bottom, and some of the help you need so that you can pass that world on to your children.

    You can join us here. No pressure. Nothing to buy. You get my free orientation course on Notice, Wonder, Discover.

    SUMMARY:

    What Is NWD?

    Notice, Wonder, Discover (NWD) is a framework for learning to see reality more clearly.

    • Notice is about reality becoming visible.
    • Wonder is about reality becoming intelligible.
    • Discover is about reality becoming unavoidable.

    The goal is not the accumulation of facts but proper orientation to reality. NWD emerged from years of studying the work of Caleb Gattegno, Reuven Feuerstein, Charlotte Mason, Aristotle, Socrates, St. Maximus the Confessor, and many other thinkers while helping homeschool parents overcome the transfer problem.

  • Unlocking Learning: A Journey Through Gattegno’s Four Stages

    Unlocking Learning: A Journey Through Gattegno’s Four Stages

     

    In my recent podcast with Debra Childers, we delved into the concept of thinking—what it is and why social interaction is essential for thinking well. Debra admitted that she uses the word “think” without fully understanding what she means when she says it. I fear the same can be said when we use the word “learning.” What is learning? How does it happen? Is it merely regurgitating facts from an arbitrary curriculum, or is it something more profound?

    None of what I share in my classes, blog, or podcast is original. It is a running joke that I have no original thoughts. That is a perfectly acceptable way to live a life. I’m a mom. But what I am good at is taking ideas from multiple places, breaking them down, making connections, and spitting it all back out for popular consumption.

    One of my go-to thinkers is Caleb Gattegno, who defines learning as developing cognition or educating awareness. According to Gattegno, learning occurs in four distinct stages, each characterized by a specific type of awareness. Understanding these stages can help us guide our children effectively, ensuring they not only learn but also retain and apply their knowledge in various aspects of their lives.

    Stage 1: Realization

    The first stage of learning is realization, which involves basic awareness—the moment when we recognize something new to explore or learn. Think about a time when your child first showed interest in something new: like their hands, a color, or a toy when they were babies. As they grew, their interests might have shifted to bugs, Legos, a musical instrument, a sport, or drawing. Regardless of when it happened – it is that initial spark of curiosity that is the hallmark of this stage.

    As parents, our role is to nurture this curiosity by providing opportunities and resources for exploration. However, we often unintentionally shut down curiosity when we’re too busy or dismissive. Creating an environment where curiosity is welcomed and encouraged is crucial. Modeling curiosity ourselves can also inspire our children, even if we lost that curiosity long ago due to disinterested adults in our own lives. Learning and teaching become more complicated if we don’t have curious students.

    Stage 2: Exploration and Experimentation

    True learning begins in the second stage. This is where your child engages with a new concept but is not yet an expert. Mistakes are not only common but are crucial, offering learning opportunities and a chance to adjust and try again. For example, when your child is learning to ride a bike, they will likely fall a few times and struggle to maintain balance. These errors are part of the learning process.

    As parents, it’s important to provide a safe space for mistakes, offer encouragement, and remind children that mistakes are steps towards mastering a new skill. Supporting their perseverance and resilience is key, as is avoiding rescuing them when they get stuck. This productive struggle helps them become independent problem solvers.

    As parents, our focus should be less on doing things right and more on learning from the process and learning to develop efficient processes for learning. This is a struggle for us. Most of us see education as the ability to answer questions correctly. We take tests. Lots of tests. And tests have a big score at the top that tells you whether or not you answered questions correctly. Big red checkmarks tell you everything you did wrong. The sheet of paper tells you learning took place. This is the measure of our learning. But it isn’t. It doesn’t tell you if your child has the ability to solve novel problems. It doesn’t tell you if the mistakes are mistakes in thinking, understanding the problem, or carelessness. Nor does it tell you if you child understands or is simply regurgitating memorized facts. Wise parents and students will notice what doesn’t go right and be curious about what went wrong. Just as they are curious about what they got right and determine how it is related to what they got wrong. This is how we learn and how we develop the ability to persevere.

    Stage 3: Transition

    In the transitional stage, your child can perform a new skill if they concentrate fully. Over time, with practice, this skill becomes more automatic, requiring less focused effort. At this stage, it’s essential for parents and teachers to avoid repeating instructions, as it can distract and interrupt concentration. Constant repetition teaches children they don’t need to pay attention the first time.

    Using the bike-riding example again, after a period of practice, your child will ride without thinking about every move, allowing them to enjoy the ride rather than focusing on staying upright. Our role as parents is to provide opportunities for consistent practice and give them space to think and work things out until the skill becomes automatic.Unfortunately, most of us never allow our children to make it to Stage 3. We assume that right answers in Stage 2 means “education happened”. Parents will often announce to me in frustration, “But we did this last week, and they got all the right answers.” I believe them. I do. And so, it is frustrating when you come to the same material this week and they look at you with a blank stare. They are not being rebellious. The material wasn’t mastered. It takes time. Less time than you think. But it will take more time if you allow yourself to become frustrated by the learning process. (I know – I have a particular gift in this area.)

    Stage 4: Transfer

    The final stage is transfer, where the learned skill becomes a foundation for acquiring new skills. Knowledge and abilities developed can now be applied to other areas, a concept known as domain transfer. For instance, the balance and coordination learned while riding a bike can help with other physical activities like rollerblading or skiing. At this stage, learning becomes a lifelong asset.

    As parents, we must help our children recognize these connections and encourage them to apply their skills in new contexts. Celebrating the transfer of skills and showing them how hard work pays off in various areas of their lives is the process of mediating meaning. Why do they have to do this thing in the first place? 

    Conclusion

    Understanding and supporting your child’s learning journey through these four stages—realization, exploration, transition, and transfer—goes beyond good grades or passing tests. It’s about building the foundational of cognitive skills that will serve them throughout their lives.

    Learning is a journey of developing thinking skills. With the right support, our children can achieve mastery and beyond. If you enjoyed this post, leave a comment, and share it with other parents who might benefit. Until next time, keep nurturing that curiosity! And go play some math. 

  • How Blurred Perception Affects Everything

    How Blurred Perception Affects Everything

    Every time I go to open my son’s bedroom door, I first take a deep breath so that I’m prepared for what I’m about to see. Usually, as soon as I open the door, I develop instant anxiety, sometimes I get a headache, and I used to get angry. What is going on with me?

    UNDERSTANDING PERCEPTION

    Cognitive Scientist Ian McGilchrest would say that the anger and anxiety comes from my inability, in that moment, to orient myself in that situation. What do I mean by orient myself? Essentially, that means I can make sense of my surroundings, of the place I find myself, and as Gattegno would say, I am aware enough that I can act and move myself forward in the world.

     

    BLURRED AND SWEEPING PERCEPTION

    When I open that door, I’m paralyzed by the mess. I can’t see anything individually, I see it all at once. It is one big thing – a giant mess. And the only thing that will move me forward on a bad day is a garbage bag, shovel, and a dumpster.

    But this temper tantrum isn’t helpful for anyone. Nor is it a good medium to long term strategy for winning friends and influencing people. It tends to make your children terrified of you. Fortunately, I don’t respond that way anymore (well most of the time.)Feuerstein called the initial cause of my melt down blurred and sweeping perception. What do we mean by perception – it’s the way we interpret and understand sensory information. It’s not just about seeing, hearing, or feeling something; it’s more about the way we organize, interpret, and consciously experience sensory information.

    It helps us navigate our environment, decide how to act, and understand the world around us. Our perception is greatly affected by the stories we tell ourselves, the assumptions we make, and our intuitions about how the world works – even if we’ve never given them a lot of thought. In the words of Ken Myers – they are givens. We will come back to these given in future episodes of the notice and wonder podcast.

    Ian McGilhchrist

    -Author-

    Perception is not the same as attention, and not at all the same as thinking. But the world we choose to attend to, indeed choose whether and how to attend to, is nothing without perception.

    -The Matter With Things: Our Brains, Our Delusions and the Unmaking of the World

    Blurred and sweeping perception is not about the information itself. It isn’t a limitation in information gathering, like say, spatial recognition, but rather what it is that I do with the information once I have it.

    The way we perceive things can be blurry, which means details are unclear, borders are imprecise, and the overall quality is poor. I may see a tree, but I don’t recall if it has leaves or needles. I may notice a car, but don’t recall its color or the model.

    One thing runs into another. You may notice this when you go through a traumatic event. Details and times become blurry. It’s like you are in a fog or a haze. This blurriness can affect both wonder (the making sense phase of NWD) and discover (how we communicate that information and move forward in the world around us.

    SPEAKING FROM EXPERIENCE

    Blurred and sweeping perception is really about the inability to focus and persist in looking at an object, event, or stimulus – the better we get at persisting and focusing the more accurately we perceive it. It is a lack of attention.

    I’ve long prided myself that I’m a big picture person and the details don’t matter to me. But, the devil is in the details. And missing them has caused no small amount of consternation in my life. Not just for me, but for those that have had to deal with me. My ability to deal with information used to be highly dependent on my motivation.

    The speed and rhythm at which we process information also plays a role in perception clarity. When there is something I’m interested in, or I’m curious about it, I can gather a lot of information quickly. But in the case of the messy bedroom, this slower processing requires way more effort for the same or even less information.

    When the perceptual process is slow and unfocused, it can lead to a blurred perception and the resulting negative emotional response follows. The anxiety is a danger signal from your brain that everything is not all right with the world. When your children get into situations where there is too much detail for them to handle, they experience the same anxiety and frustration. They may, like me, become angry.

    The nature of what we perceive, such as how simple, complex, familiar, or new something is, affects how much attention and effort we invest in focusing on it. This ability to adapt and accurately discriminate between different stimuli is important.

    Regrettably, this has been a hard road of learning for me as an adult. What this looks like is that I don’t have an intrinsic need for appropriate perceptual functioning. When I don’t see something clearly, I’m not bothered by it. I’m content to say the sunset was pretty and not be able to describe it to you. I once had a friend who had terrible acne – I never noticed until someone pointed it out to me. The next time I saw my friend, I looked at her face for the first time. I noticed that indeed, she really did have bad acne.  

    My investment in effort, attention, focus is generally situation specific. If it is something I want to do or see the need to do, even if I don’t like it, I will make the effort investment. If it’s not I won’t. I’ll sweep over information/stimuli indiscriminately. It’s not a problem that this is my disposition. The problem was that I wasn’t properly mediated as a child. No one came between me and the information coming at me to help me make sense of it.  That means, for me, there was no such thing as domain transfer. I couldn’t take the skills that came naturally when I was interested in something and transfer them to a situation that I wasn’t interested in even if I knew it was important. Nor could I transfer those skills when it was something I wanted to do but found difficult or didn’t understand. This meant that large portions of my world were off limits simply because I couldn’t make sense of them.

    THERE IS HOPE, IT CAN BE FIXED

    This all sounds depressing, doesn’t it. But it’s not. Because, while I’ll never love dealing with details in domains I don’t have curiosity about or don’t enjoy. Now, I can deal with details even when it is something I don’t want to do or don’t like without a meltdown. I know how to ask myself the kinds of questions that help me make sense of all the stimuli coming at me without a breakdown. I know how to focus my attention and I know how to bring myself back to focus if it is lost.

    The good news is that you can properly mediate yourself. It’s never too late. The good news for your children is that you can become a great mediator for them. I would suggest that this is your primary role as a teacher. The content of your curriculum is simply a tool that you use to help you in the mediation process.

    How do we do this? That’s what we’ll talk about on the next episode of Notice and Wonder shorts. But, in general, we need opportunities to practice and refine our perceptual skills through guided learning experiences. You know, opportunities like cleaning bedrooms. Besides, this helps you reframe the messy room. It is no longer

    a thing that the child has done wrong, but rather an opportunity for both of you to deal with your broad and sweeping perception. Or an opportunity for to learn how to mediate your child through it. It’s education. 

    Charlotte Mason

    -EDUCATOR-

    Education is life. 

    Opportunities like these help establish the necessary habits, attitudes, and techniques early on, ensuring their perceptual abilities can function well in various situations. We also need to learn how to ask the right kinds of questions. If you struggle as a parent or teacher, the opportunities to practice that your children need are the same ones you need. And the questions you ask your students are the same ones you’ll need to ask yourself. These are the tools in your tool kit. They become your superpower.Thinking you want to teach this way but aren’t sure where to start? Join my email list and get access to members only content. If you’d like to teach math using Notice, Wonder, Discover but need a little hand holding – check out our academy here.Do you have a 5th – 7th graders who’s behind and you are starting to panic? Go to my calendar and book a session. We can do an assessment and talk about tutoring options.

  • Notice, Wonder, Discover

    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

    -eDUCATOR-

    “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. Who/What

    • 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?

    When?

    • 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.

    Where?

    • 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?

    Relationships?

    • 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.