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.
