Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

Humanity exists to fully understand the universe.

Yati
Today’s topic is “Hands and Work.” Let me introduce some quotes from Maria Montessori: “The hand is the instrument of intelligence. Children learn by touching and moving things.” “Children play with their hands, come to work with their hands, and through accumulating such experiences, they form their personalities.” “Children teach us that we must use our hands to continue developing intelligence.” “Hands and Work” are important for both mental development and human intelligence.

Hiro
Right.

Yati
Before we discuss “Hands and Work,” I want to define “work.” What is “work”? Maria Montessori said it’s “changing the environment” or “creating something supranatural,” but I find that a bit hard to understand.

Hiro
That doesn’t really say anything. We need to define it more physically. There’s a physical definition of work too. What corresponds to work is energy.

Yati
Right. In physics, work is defined as force times distance, and its unit is energy.

Hiro
Energy exists for doing work. It’s a physics term. What Montessori calls “work” isn’t about earning a living. I think it’s physical work. Physical work is, for example, moving an object from here to there, or from a low place to a high place. Energy is used in the form of potential energy, kinetic energy, and so on. And in this universe, no matter how much energy you use, it doesn’t decrease. It doesn’t decrease, and it doesn’t increase.

Yati
The law of conservation of energy.

Hiro
Energy is transformed. What was potential energy here becomes kinetic energy there and does some kind of work. Cosmically, it’s like equivalent exchange. Generally, when people say “work,” they think of it as something to “earn a living,” but that’s the common-sense definition in human society. Human civilization has been advancing and getting smarter, but it’s still inferior.

Yati
What do you mean?

Hiro
In a perfectly physical world, “earning a living” isn’t part of it. The compensation for work in nature is different from the human world. Nothing in nature earns a living. Things simply do work.

Yati
For example, what does this mean for plants?

Hiro
When we say plants, there are trees, grass, all kinds. This is also a human classification. There’s a huge tree with grass underneath it.

Yati
And climbing vines.

Hiro
Right. There are small ones and big ones. And they’re all doing work. Each one blooms flowers. Respiration and photosynthesis are also work. This relates to the Constructal Law, a new law I’m currently studying. Let me introduce it briefly. It’s a law of design.

Yati
Tell me more.

Hiro
The design of this world is progressing in a certain direction according to physical laws. We call that “evolution.” What direction is it going? The law says it’s “progressing toward greater efficiency.”

Yati
What does efficiency mean here?

Hiro
Efficiency means “making the flow that flows through you flow even more.”

Yati
So the universe is evolving so that flow flows even more. What does that mean concretely?

Hiro
For example, with plants, you can’t see inside a plant, but water flows through it, and oxygen too. When photosynthesizing, leaves open their stomata. At the same time, water and oxygen flow out as gas. Conversely, plants absorb carbon dioxide from the atmosphere, convert it to carbohydrates through photosynthesis, release sugars from their roots, and pass them to microorganisms. That’s the work they’re doing.

Yati
There’s flow.

Hiro
This has become clear recently with the advancement of science and technology. Before, we just looked at plants blankly and wondered, “Why is it here?” But thankfully, we can eat them, burn them for warmth, and there are all sorts of uses. From a human perspective, we thought plants were doing work for us.

Yati
Right.

Hiro
But actually, when science and technology let us see the micro and macro worlds, we find that just by being there, not moving, they’re doing work just by existing.

Yati
And on a macro level, they’re increasing the efficiency of Earth’s cycles?

Hiro
Not Earth. The universe. In this case, they live on Earth but are doing work for the universe. Why? Because energy isn’t conserved per planet. It’s conserved across the entire universe.

Yati
This is what’s fascinating about physics.

Hiro
It’s amazing. The same laws govern tiny, tiny, invisibly tiny microorganisms and worlds far larger than galaxies.

Yati
Getting back to the topic. In this cosmic evolution, what is humanity’s work?

Hiro
What I want to say, and this is a bit of a leap, is that the work given to humanity as intelligent life is to achieve complete understanding of the entire universe.

Yati
What lies beyond understanding the universe?

Hiro
By understanding the universe, we become able to increase efficiency further. We help nature.

Yati
I see. We’re pushing forward the evolution of the universe.

Hiro
To properly connect this to today’s theme: humans have hands. Having hands means we can manipulate our environment. There’s also the philosophy of operationalism, the idea that the meaning of a concept comes from how we operate on it. For example, beavers build dams too. They block rivers. Beavers gnaw on big trees, conifers, with their teeth.

Yati
With their big front teeth.

Hiro
Right, they’re rodents. And they gnaw on trees that are still standing. They stop partway so they don’t get crushed when it falls. Then at some point, strong wind shakes it and it finally breaks. Then they gnaw it smaller to use. They’re forest carpenters. They’re called a “keystone species.”

Yati
A species that’s important for the ecosystem.

Hiro
They have a big impact on rivers and forests. By damming rivers, fish can’t swim upstream, which creates habitats for various birds. When water overflows, tributaries form. Water seeps into the soil and vegetation changes. By disturbing the ecosystem like this, they make it more diverse and stable.

Yati
But for beavers, they’re just building their own nests, right?

Hiro
Exactly. Beavers probably aren’t thinking, “I’m going to improve the forest environment.” They want a home, so they fell trees, gather them, build a safe place to sleep, and that becomes a natural dam.

Yati
And humans are the same?

Hiro
Yes. Humans also act on self-interest, drilling for oil, doing things for survival. Once they can ensure their own survival, they scale up for the survival of their community. Sometimes science goes too far and causes environmental destruction, sometimes we learn from nature, going back and forth in balance, developing like climbing a spiral.

Yati
So with that human mission in mind, what should we do during ages 0 to 3?

Hiro
Spend time in nature.

Yati
I thought given this theme, you’d say “use your hands to work in nature.”

Hiro
No. If you don’t interfere with children in nature, they’ll start using their hands on their own.

Yati
Why is spending time in nature important?

Hiro
Because no matter how hard humans try, what they create can’t beat the designs nature produces. Great designers usually come from the countryside. Biological design evolves according to cosmic laws. It’s efficient, and it’s about cooperation, not competition. When you touch a pill bug and wonder why it rolls up, you’re sensing those laws. Noticing the seasons naturally is also natural.

Yati
I was worried our older daughter would be bored on the long kindergarten bus rides, but she was moved by how Mount Iwate, in northern Japan, changed through the four seasons.

Hiro
Right. If I had to say what to be careful about when spending time in nature, it’s “don’t let them die.” Nature is harsh.

Yati
What else is important besides spending time in nature?

Hiro
Walking, eating, sleeping.

Yati
As a Montessorian, once children can walk and use their hands, they can do things for themselves and household tasks, so I tend to want to recommend that. But yes, walking is important. Children around 18 months to 2 years who can walk well really walk as if walking is their job. Including eating and sleeping, it’s about building the foundation for the brain and body.

Hiro
By the Constructal Law I mentioned earlier, bigger is advantageous. Speaking of hands, humans have longer thumbs than other great apes. Because this thumb opposes the other fingers, we can grasp things. Large, dexterous hands are a characteristic of Homo sapiens. The magnificence of the thumb might be proportional to intelligence.

Yati
Maybe so. Whether it’s finger length, physique, or brain size, there are individual differences, but everyone can aim for their personal best.

Hiro
Speaking of brains, the current Homo sapiens average is about 1,130 cubic centimeters for women and 1,270 cubic centimeters for men, but some famous Russian writers had nearly 2,000 cubic centimeters.

Yati
They say Einstein’s was surprisingly small. It’s mysterious.

Hiro
AI could solve math problems relatively quickly early on, but only recently became able to produce literary writing. Writing text that makes people groan is that difficult. It probably requires thinking about how the world works and how people feel, activating many different parts of a large brain.

Yati
A large brain seems necessary for understanding the universe too. We’ll cover “eating” in a future issue. As for “sleeping,” I recently watched videos of sleep researcher Professor Masashi Yanagisawa, and I really think everyone should sleep more, not just children.

Hiro
Right.

Yati
Sleep regularity and quality are important, but securing enough sleep quantity is the top priority. For adults, around 8 hours; for elementary schoolers, about 10 hours; so for ages 0 to 3, it’s even more.

Hiro
Children who sleep grow well.

Yati
There’s also research showing differences in hippocampus size based on whether children got enough sleep in early childhood.

Hiro
That’s significant.

Yati
Also, when you get enough sleep, you become more altruistic. Even just 1 hour of sleep deprivation makes people less altruistic. This is evident from charity donations clearly decreasing on the day daylight saving time starts.

Hiro
Religions should let their followers sleep rather than preaching about altruism.

Yati
Toward humanity’s mission of “complete understanding of the entire universe,” during ages 0 to 3, let’s spend time in nature, eat well, walk plenty, and sleep well.

Hiro
With smiles and good spirits.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

The children begin to use an entirely new coordinate system.

Yati
I want to talk about “Why learn mathematics through discovery?” But first, I’d like to define mathematics. Galileo Galilei famously said, “the universe is written in the language of mathematics.” What do you think?

Hiro
Mathematics can be defined as “the study of structure and pattern.”

Yati
Does that mean it describes the universe?

Hiro
Essentially, what we call “mathematics” is the correspondence of the universe’s structures and patterns to symbols. If you don’t map the universe to numerals, numbers, and mathematical symbols, but instead just speak in ordinary language and turn it into a story, it becomes mythology.

Yati
Is “the mathematics that humanity has developed” the same as “the mathematics that describes the universe”?

Hiro
There are two kinds of mathematics. One is human mathematics, the mathematics we learn in education. The other is cosmic mathematics, the mathematics the universe has. The history of human mathematics is a history of corrections to human mathematics. We hypothesize “Maybe there’s a law like this” and verify it, but eventually it turns out to be wrong and gets corrected by later generations.

Yati
Like relativity theory to Newtonian mechanics.

Hiro
That’s physics. For a pure mathematics example, Euclidean geometry to non-Euclidean geometry.

Yati
Right.

Hiro
The history of mathematical development is mostly like this: first you have some illusion, like “Isn’t this the pattern?” Then the next generation says, “Wait, that’s wrong.” It gets corrected. Like Gauss or Euler. But some people hit the right answer from the start, like Pythagoras, discovering that triangles have certain properties. The Pythagorean theorem. For other people, the next generation, they can’t deny it. It’s too useful. Even ordinary children can calculate area with base times height divided by 2. But we couldn’t use it with confidence if Pythagoras or earlier generations hadn’t discovered the law, or if no one had verified it. However, even things used that way for a long time might still have errors. That’s both the fascination and the terror of mathematics.

Yati
That’s true. Is there a pattern to when corrections happen?

Hiro
Usually corrections come through technological development. What I mean is, for example, when you want to see far into the universe, you build large telescopes. Space telescopes. First you have to think about how to launch them. You need mathematics and physics for the launch. Then you also need technology for seeing farther, and that uses mathematics and physics too. And then how to handle the data you get, what patterns to find from it. You need to answer propositions like whether the universe is round.

Yati
The shape of the universe was actually solved using mathematics and physics with the Poincaré conjecture.

Hiro
Right. And there are various unsolved problems that need proof, like Fermat’s Last Theorem.

Yati
Like verifying whether the proof of the ABC conjecture is correct.

Hiro
Right. And to solve these more efficiently, new mathematics is sometimes needed. And that new mathematics is actually undiscovered cosmic mathematical principles.

Yati
Like Edward Witten doing new mathematics while researching superstring theory.

Hiro
Here’s a spoiler for readers. That “coordinate system” you learned in education is called “Cartesian coordinates” because Descartes created it, and it’s very convenient. When drawing graphs, you say X axis, Y axis for 2 axes. For 3 axes, you add Z axis. This Cartesian coordinate system is not correct cosmically.

Yati
That’s a “What?!” moment. [laughs]

Hiro
It doesn’t work in the universe.

Yati
Since Earth is a sphere too, you can’t express it. When you go to the edge, you have to come out the other side.

Hiro
Right, even on Earth we’re approximating calculations quite a lot to get answers. We’re forcing it, quite a lot actually. GPS calculations, for example. Approximating curves with straight lines, using the squeeze theorem and limits to cleverly handle complex differentiation. The calculations are incredibly difficult.

Yati
Right.

Hiro
Since computers were invented, it’s fine if the computational load is enormous. Or rather, computers were developed because of that computational load.

Yati
Right. [laughs]

Hiro
Being able to do all sorts of things with computers is a really great thing. But really, if there’s a way to reduce computational load, that would be better.

Yati
Mathematical proofs sometimes use computers to brute-force things. Like the four-color map problem. If it could be proven without computers, that would be beautiful.

Hiro
Right. Computers would use less electricity too. Now with AI development, they’re consuming enormous computational resources, and there’s even talk of needing nuclear power. Electricity shortage is a problem. Data centers are running at like 100% capacity, constantly operating. Electricity becomes a problem. Then you’re consuming fossil fuels. Why is this happening? It’s because the mathematics is wrong. The underlying mathematics.

Yati
That’s really true. Whether global environmental problems get solved depends on the evolution of mathematics.

Hiro
Right now we’re calculating in extremely inefficient ways. With the cosmic approach, computational load becomes one-third.

Yati
Is that the power of cosmic mathematics?

Hiro
In other words, because we’re calculating in Cartesian coordinates, computational load is 3 times what it would be cosmically. This is essentially an assumption—people think Cartesian coordinates are always correct. Most people think mathematics has no errors and is always correct. They feel mathematics never changes forever, or that it doesn’t change because it’s been proven.

Yati
So separate from whether something is proven or not, there’s the discussion of whether it’s efficient.

Hiro
Right. We know it can be solved that way. For example, there’s brute force—giving random values, trying lots of random things when solving calculation problems, and if you hit the answer, lucky. Just repeating like “Please let tomorrow be sunny.” That method exists.

Yati
AI is a type of that too. Generating images from random seed values, hoping something good comes out. Or when you want new materials with specific properties, you generate randomly and pick what’s probabilistically likely. Same with shogi moves.

Hiro
If you do that, eventually you’ll solve it. Brute forcing. But if you do that for every problem, it’s game over. In the end, “because it’s proven” isn’t really a reason. The legitimacy of human mathematics is simply how much it matches cosmic mathematics. And the more it matches, the more you can predict the future. This is a bit of self-promotion, but Polymath School, which started in April 2025, defines “intellectual” that way and aims to be “the most intellectual school.”

Yati
Right.

Hiro
“Calculation” layers inferences. Like the Japanese proverb, “When the wind blows, the barrel maker profits.” It’s a saying about chains of unlikely cause and effect. You go through about 10 inference steps from wind blowing to the barrel maker profiting. Mathematics is about becoming able to layer inferences. There’s all sorts of randomness. So people immediately start talking about chaos, saying “We give up, we can’t predict the future.” But including that, you can still produce prediction accuracy. You can express it as probability.

Yati
That’s how AI has been developing too.

Hiro
Weather forecasting too. It keeps evolving, using AI to predict more accurately. This is the Laplace’s demon story—if you could accurately predict the state of all particles, you could always predict the next state.

Yati
The idea that the future is determined.

Hiro
We’re approaching that. In other words, cosmic mathematics is that direction. If you understood all of the universe’s state and principles, you could predict the universe.

Yati
That’s where quantum physics comes in.

Hiro
The idea that things are probabilistically determined, so the future is uncertain. Two states superimposed. But that’s human understanding—it’s not that the universe decided superposition is uncertain.

Yati
This discussion is getting complicated.

Hiro
Simply put, as an efficiency of representing information, superposition is good, so you could say the universe uses it. An interesting point here relates to “The Power of Folktales” from the previous issue. For example, in “The Crane’s Return of a Favor,” a crane secretly weaves cloth disguised as a young woman, and children naturally understand superposition. The crane in the weaving room is in a superposition state of daughter and crane.

Yati
Same with the big wicker basket in “Tongue-Cut Sparrow.”

Hiro
Richard P. Feynman said “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” Elon Musk said “Quantum mechanics is the most difficult.” Jeff Bezos said “I was going to become a physicist but gave up at quantum mechanics.” Meanwhile, in Japan, 5-year-olds readily accept it. Entanglement, the Urashima effect—there must be many more folktales if you look. And it’s not because some great scholar thought them up. They’ve been passed down among farmers since ancient times, and people listen because they’re interesting.

Yati
So children are given all sorts of patterns, and much later, they can discover on their own “Oh, this is that pattern.”

Hiro
“Straw Millionaire” is also the law of conservation of energy. Straw = lotus leaf = miso = sword = millionaire.

Yati
But straw does not equal millionaire, right? Isn’t that mathematically incorrect?

Hiro
That’s being tainted by human mathematics. Buckminster Fuller said mathematics must include time, gravity, and temperature. In cosmic mathematics that includes time, the equality holds.

Yati
It’s hard to escape human mathematics. Please properly teach me about how calculations become one-third without Cartesian coordinates.

Hiro
You’ll discover that yourself. That’s what learning through discovery means.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

Reliving the history of human mathematics through Montessori math materials.

Hiro
Many people think the essence of Montessori education is the materials, but the first thing I need to say is that materials are just one element that makes up the environment. They are not absolutely necessary. For example, there is essential work for living, like cooking, growing plants, or caring for animals. The parts directly connected to daily life are the necessary and sufficient conditions. If you do those properly, you will naturally acquire the abilities you need.

Yati
Right.

Hiro
When cooking, some people do it by feel without looking at a recipe, but if you try to follow a recipe, you use quite a bit of mathematical ability. You measure quantities, and the ratios of seasonings determine the spiciness, saltiness, and sweetness. That can only be understood through the senses, and robots still cannot do it. But even small children can do such difficult things. They can slice bread, add their favorite fillings and ham, and eat it. So doing that kind of “work” is what is important first.

Yati
This does not change from ages 0 to 3.

Hiro
Materials are convenient tools for environments where such work is not possible, like when you want to cook but cannot, or when you live in the city and cannot touch plants. Now, with smartphones and tablets and lots of digital apps, I personally think Montessori materials are quite similar to them.

Yati
What do you mean?

Hiro
Materials are tools made of wood and metal that allow children to deepen their thinking and discover various things through play. But without technology, you cannot cut wood to the same length. They standardize natural wood, paint it all, and harden it. In a sense, that is industrially produced while ignoring the nature of the wood. It is quite digital. There is no drama of how that wood grew and was transported, so it ends up extremely inorganic. There is no handmade warmth; it is symbolic.

Yati
I see. But there is still an appeal to materials as concrete objects that digital apps do not have.

Hiro
The drawback of digital apps is that you do not use your hands. Just swipes and touches. Video game controllers also have low diversity in how hands are used. With Montessori materials, you can play by arranging large objects, picking up small things, and transferring liquids, using your hands in diverse ways. That is the fundamental point. There are not many systematically prepared things like that, so if you can use them, you should.

Yati
Right.

Hiro
But it is true that they are expensive. Too expensive to introduce at home. They cost a lot because they standardize specifications, ignore the nature of wood, and do metal processing and painting. They are forcing something that is not natural. Shipping is also difficult and not environmentally friendly. So please understand that materials are not perfect either.

Yati
Right.

Hiro
“Montessori education equals materials” is not correct. That said, compared to conventional kindergartens and elementary schools, materials provide much higher learning efficiency and essential understanding. So let’s examine that.

Yati
This time we will look at math materials, which are designed to repeat the history of human numbers. Stanislas Dehaene, the researcher who proposed “number sense,” said in his book “The Number Sense” that ideally every child should be able to retrace in their mind a greatly condensed version of the history of mathematics, along with the motivations that drove it. Why? Because the evolution of mathematics is also the evolution of the brain.

Hiro
What do you mean?

Yati
The latest research uses technologies like fMRI to roughly identify where in the human brain the primitive number sense that animals also have is located. It is thought that through evolution, humans developed from this primitive number sense brain region as a starting point, deepening connections with various brain regions governing vision, hearing, language, space, and time, eventually developing highly abstract mathematics like modern mathematics. In other words, ideally children develop their brains and number sense by repeating human history. And math materials make that possible.

Hiro
So it is aligned with brain development.

Yati
The first math material is called “Number Rods.” There are 10 wooden rods, ranging from 10 centimeters up to 100 centimeters in 10-centimeter increments, color-coded in red and blue every 10 centimeters. What is amazing about this is that it simultaneously provides children with two concepts at once: quantity, meaning how much, and ordinal numbers, meaning what position. There is often debate among math experts about whether to introduce quantity or ordinal numbers first, but Number Rods introduce both at once with a single material.

Hiro
Two birds with one stone.

Yati
Furthermore, before these Number Rods, children become familiar with length using “Red Rods,” which is a version of the Number Rods that is all red. This is another excellent point.

Hiro
Excellent how?

Yati
Here, try to picture a small number, “1.” Now picture a large number, “100.”

Hiro
Okay.

Yati
Actually, we unconsciously have brains that map numbers to space. For small numbers, we become aware of the lower left, and for large numbers, the upper right. There is a number line in our heads. That is why at Paris Charles de Gaulle Airport, where higher gate numbers are arranged to the left, many people get lost.

Hiro
I see.

Yati
In short, “space” and “numbers” are closely related in humans. Getting back to the point, when the Red Rods used to introduce spatial length are upgraded and used to introduce numbers, it is smooth for a brain that is trying to connect space and numbers. It also looks like a number line extending. By the way, in some cultures the direction is reversed, with larger numbers on the left, but Number Rods can accommodate either culture just by changing the arrangement.

Hiro
So spatial perception is also being used.

Yati
And as an activity, children trace these long Number Rods with their fingers while counting “1,” then “1, 2,” then “1, 2, 3,” then “1, 2, 3, 4,” matching quantity with number names.

Hiro
Even someone who cannot see can understand numbers.

Yati
Indeed. The next material can also be understood without sight. It is called “Sandpaper Numerals,” which are wooden boards with numerals cut out of sandpaper and pasted on. Children trace them to learn numerals. After that, they match the numeral boards with the Number Rods, connecting numerals to quantities. This allows children to accurately match quantity, number words, and numerals from 1 to 10.

Hiro
That is well thought out.

Yati
Actually, this method of introducing numbers is also effective for chimpanzees. A chimpanzee named Sheba succeeded in matching quantities zero through nine with numerals over 2 years, according to Boysen and colleagues in 1996. Sheba started by placing biscuits one at a time on a tray divided into 6 sections. In the next stage, she learned to match the number of black dots on cards with the number of biscuits, and eventually could match the number of dots on cards with numerals. Another chimpanzee could even do fraction addition, and the tool used to express the answer was a divided disc, according to Woodruff and colleagues in 1981. This also matches the Montessori material for learning fractions. The fact that it is effective for non-humans too shows how user-friendly Montessori materials are.

Hiro
So they are monkey-friendly too.

Yati
Getting back to Number Rods. Because they are simple, they allow children to discover various number concepts on their own depending on their stage of number sense development. For example, combining the 5 rod and the 3 rod makes 8, so they can do addition. Finding combinations that add up to 10 is number composition. Making all combinations of 10 hints at the formula for the sum of consecutive natural numbers.

Hiro
Hmm. Like a universal seasoning.

Yati
After Number Rods, we use “Spindle Boxes.” This is an activity where you count spindles and bundle them with rubber bands to make a group. After bundling, you place them in the corresponding numbered compartment of the box. Defining 1 spindle as “1,” you learn by moving your hands that collecting, say, 3 of them into one bundle is “3.” Nothing goes in the compartment marked 0. In other words, you learn that “0” means “nothing.”

Hiro
Using small stones as tokens, matching 1 stone with “1” to count is human history itself. Representing 10 small stones with 1 large stone is acquiring the “base principle.” Combined with the “place value principle” of assigning positions, like ones place, tens place, and so on, the acquisition of these two major principles is extremely important in the history of human mathematics. For children to discover this themselves by moving their hands with materials is essential. If you realize that the “base” of a logarithm is just that “large stone” idea, college entrance exams get a lot easier.

Yati
Right. After Spindle Boxes comes “Cards and Counters.” This involves arranging small counter-sized balls in 2 rows corresponding to each numeral. It is a material for discovering odd and even numbers.

Hiro
Discovering parity, an important theme in number theory, around age 4 would make for an enjoyable life.

Yati
Next is the “Memory Game of Numbers.” It is a game for multiple children. You draw a slip with a number written on it and bring back that many of something. In other words, you let children define what counts as 1. This completes the introduction of the numerals 0 through 10.

Hiro
In human history, people counted and recorded wheat and cattle, but in modern times, we can freely count all sorts of things. How fun.

Yati
After the numerals comes the decimal system, then consecutive numbers, mental arithmetic, the process toward abstraction, and fractions. Materials in the three-to-six-year-old environment cover up to 7-digit arithmetic operations and fraction operations. There are finely graduated steps leading up to those 7-digit calculations.

Hiro
How does it start?

Yati
First, 1, 10, 100, and 1000 are provided with “Golden Beads,” where the physical size is proportional to the quantity. What is provided along with the Golden Beads is the material for the place value principle I called one of the two major principles. This is also interesting. They are numeral cards. For example, to express 2025, you stack the card for 2000, then the card for 20, then the card for 5. Together, they read 2025.

Hiro
I see, the cards literally line up.

Yati
In the stage after Golden Beads, the shape differences by number disappear, and everything becomes same-sized squares, called “stamps,” with 1, 10, 100, and 1000 written on them. The next stage represents 1, 10, 100, and 1000 with just dots. After that, the abacus is introduced. Step by step, from concrete to abstract, we trace the evolution of human numbers.

Hiro
The evolution of arithmetic technique from abacus to written calculation is inevitable, but you should not skip steps.

Yati
Also, though I cannot cover it all here, geometry is included in “Sensorial Materials.” For example, geometric solids like spheres, cylinders, and triangular pyramids start with lots of touching and feeling.

Hiro
Not with worksheets.

Yati
Getting back to math materials. Since numbers depend on language, there are stumbling points by culture. Another noteworthy aspect of Montessori materials is how brilliantly they avoid these.

Hiro
How so?

Yati
For example, in English, the words for eleven, twelve, and thirteen are irregular. Japanese is much easier to understand because it is based on the decimal system: ten plus one is “juu-ichi,” and ten plus two is “juu-ni.” So even in English-speaking countries, they introduce eleven and beyond with regular naming like Japanese. Using Golden Beads, when counting groups of 10, you count “one ten, two ten, three ten.” So 11 is understood in English first as “one ten and one.” After that, a different material called “Seguin Boards” is used to teach the correct reading, “eleven.”

Hiro
Interesting workaround.

Yati
There is actually research that asked American and Chinese children how high they could count. At age 4, Chinese children could count to an average of 40, while American children could only count to about 15. It was clear they stumbled on the irregular naming of 13 and 14, according to Miller and colleagues in 1995. Montessori education considers even these fine details.

Hiro
That is interesting. Because English speakers are at a linguistic disadvantage for calculation, they invented computers and actively use them. In the West, they have no hesitation in having AI solve calculation problems.

Yati
Similarly, Chinese and Japanese number names are short, easy to say, and easy to remember, so calculation is faster and memorizing multiplication tables is not that difficult. Furthermore, in China, the approach is to remove the “1 times” table, and by rearranging so smaller numbers come first, you only need to memorize half. If you memorize “two times three equals six,” you do not need to memorize “three times two equals six.” Such shortcuts in mental arithmetic are actively incorporated in Montessori education.

Hiro
That is rational.

Yati
Foreigners describe Japanese multiplication tables as being like poetry. I realized again that I love Japan’s number culture. For example, the square root of 5, which is two point two three six zero six seven nine, is remembered with the phrase “Fuji san-roku ni oumu naku,” which literally means “parrots cry at the foothills of Mount Fuji,” where the syllables encode the digits.

Hiro
That is a great mnemonic.

Yati
Learning that English speakers struggle greatly to memorize multiplication tables, and that recalling them takes more time and effort than for Japanese or Chinese people, really changed my view of brain training. For English speakers, it really is harsh training. In Japanese, “seven times eight is fifty-six” is recited as “shichi-ha gojuu-roku,” a quick rhythmic phrase. The English version, “seven times eight is fifty-six,” is much longer and harder to chant. That difference adds up over hundreds of multiplications.

Hiro
Just as parrots do not actually call at the foothills of Mount Fuji, Westerners do not like brain training. Though they do like strength training.

Yati
So as I said at the beginning, materials are not everything, but because they are symbolically organized, they are perfect for organizing the sensory experiences accumulated from ages 0 to 3, and they also compensate for disadvantages from cultural and language differences. I hope you have understood that they really are well designed.

Hiro
In the sense of advancing mathematical understanding more intuitively without depending on language, it would be great if the Montessori approach became standard. It would have very positive effects on preschool education, elementary education, and even higher education. There would be fewer people who hate math. I also found it convincing that the founders of technology companies like Google and Amazon, which handle astronomical volumes of data, came from Montessori backgrounds.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

The world’s most advanced mathematics education begins at age zero.

Yati
Today’s topic is the “mathematical mind.”

Hiro
What does “mathematical mind” mean in Montessori education? Is it the ability to arrange things in size order with materials or to do matching?

Yati
No. The mathematical mind is involved in everything and is considered a characteristic that humans have from birth to death. In other words, it’s close to a sense. Moreover, it connects with all other senses.

Hiro
So it’s a sixth sense. That means it’s like any sense. If you use it a lot, you become able to use it; if you don’t use it, you lose the ability. The same can be said for all five senses.

Yati
Right.

Hiro
I’m not entirely sure whether “number sense” is a comprehensive ability of the five senses or something else. But since it’s connected to the five senses, I think what underlies number sense is, in a word, “pattern recognition.”

Yati
In the international course, measurement, comparison, contrast, calculation, reasoning, ordering, and sequential processing (executing procedures correctly) were given as examples of the mathematical mind. I don’t think it’s strange to consider that these are executed through sensory pattern recognition.

Hiro
Let’s proceed assuming it’s pattern recognition. Recognizing patterns by sight, by hearing, by smell, by touch. The same goes for taste. With taste, for example, “this is bitter,” “this is delicious,” “red foods are sweet,” “orange means sweet,” “yellow means sour.” That continuous process of recognition like this forms the foundation of mathematical ability. So in the end, using mathematical sense well means organizing within yourself the patterns of things you’ve experienced through various senses.

Yati
That’s exactly what Maria Montessori said about sensory education. During ages 0 to 3, you experience and accumulate various sensory experiences, and during ages 3 to 6, you organize them. Number sense is no exception.

Hiro
I’d like to think about this more scientifically, though.

Yati
I researched various studies and discussions about mathematics education. First, what Maria Montessori said doesn’t contradict the latest research. Babies just hours after birth already have number sense. Also, it’s becoming clear that all senses are connected with number sense in the brain. As for mathematics education discussions, they only go as far as elementary school and preschool. Children, without special education, naturally come up with various algorithms by around age 6.

Hiro
I see.

Yati
Like when counting objects by pointing, the total doesn’t change regardless of the order you point. Or when subtracting, for 8 minus 2 you count 8, 7, 6, but for 8 minus 6 you realize it’s faster to count 6, 7, 8. So the conclusion is that we should use this number sense in both preschool and elementary education. That’s why board games are being introduced in preschool, and Montessori materials for ages 3 to 6 are being reconsidered. But before all that, there’s no discussion about having lots of sensory experiences during ages 0 to 3.

Hiro
We might be talking about the world’s most advanced mathematics education here. For example, in preschool education, they might ask, “When the water level is the same in a tall thin beaker and a short wide beaker, which has more water?” This is completely unsolvable without sensory experience. If you haven’t poured water or juice into a cup yourself and experienced spilling it, you don’t understand what spilling means, and you can’t understand the volume or capacity of that cup.

Yati
I see.

Hiro
At that time you don’t know “this is capacity” or “this is volume,” but later you intuitively understand “which one has more.” So what’s important for ages 0 to 3 is using those senses a lot, and the more you use them, the more the mathematical mind will flourish in the future. Not “flourish” exactly. More like “develop further.” But even “develop further” is really just using abilities you already have.

Yati
Right.

Hiro
Basically, it’s pattern recognition. Various information comes in through the senses. For example, we perceive differences in light frequencies with our eyes and distinguish colors. But colors are something we create ourselves. How things look differs slightly from person to person. Some can’t see green, some have difficulty seeing red, and so on. As information, light reflects and enters our eyes. We perceive that something exists, that there’s a shadow, that there’s light. If light reflects back from every angle, we understand there’s something that reflects there. Confirmed by another sense, we might hear sound, or touching it, “there’s something here.”

Yati
I see. That’s interesting.

Hiro
This “exists or doesn’t exist” heavily emphasizes the tangible aspect of touch. Things you can touch “exist,” things you can’t touch “don’t exist.” But going further, there are things that can’t actually be touched but exist. Small things, for example, electricity, magnetic fields, electric fields. You can’t touch them, but they exist. That’s interesting and scary at the same time. You have to unlearn that once to reach a correct understanding of the universe. Does that make sense?

Yati
It does. Those invisible, untouchable aspects are dealt with at ages 6 to 12. After imagination develops and you can imagine, you explore the micro world and the universe.

Hiro
Right. First, you experience “exists or doesn’t exist” with the five senses, and you make various assumptions, including misconceptions. “This is this,” “this is this,” deciding on your own. At ages 3 to 6, you get a bit cleverer. “Since it’s always like this, this should be like this,” “Since this is like this, it should be like this.” You start being able to calculate a bit: “1 and 2 together make 3.” And “There were 3 but I ate 1, so there are 2 left.” The next stage is that what you processed only through senses, you can now extend in your mind and do something like simulation. You can imagine and act as if “something is there even though it’s not in front of you.”

Yati
Yeah, that’s right.

Hiro
But that’s actually an ability that transcends the limits of the senses, and senses have limits. No matter how much you improve your vision, there are things you can’t see. Small things or distant things are invisible. Stars at the edge of the universe. I want to see them but can’t. But if you increase resolution, you can see more. So “developing imagination” means “imagining things that don’t exist and developing that,” but also externalizing the senses as tools, and if you develop that ability, what you imagined turns out to be correct. That’s the “imagination” trained from ages 6 to 12 onward. Imagination means becoming able to imagine more in accordance with the reality of the universe.

Yati
So, the power of imagination is growing.

Hiro
Ages 3 to 6 come before that. Recognizing patterns and using those patterns to estimate a bit. Being able to calculate. Starting to organize. Ages 0 to 3 aren’t about organizing, calculating, or estimating at all. It’s completely about experiencing various patterns: “If I do this, this happens,” “If I touch here, this happens,” “That was hot,” “That was cold,” “That was spicy,” “That was bitter,” “That was sweet.” Experiencing those sensations and patterns is what’s important.

Yati
For example, cookie-making can start from around 18 months, and this involves truly various elements of the mathematical mind. When measuring, large numbers with units like “150 grams” appear, and “2 tablespoons” might come up too. You mix and the dough becomes one mass. When you rest it in the refrigerator, you feel the cold temperature of the dough. With cookie cutters, you handle various shapes, and while cutting out shapes, you experience counting how many cookies you’ve made. When baking, you experience temperature and time like “180 degrees for 10 minutes.” When they’re baked, children think “I want to share equally with everyone,” so they naturally start doing division. When they repeat such experiences many times, children understand this sequence of steps and start planning and executing on their own.

Hiro
I see.

Yati
It’s actually very important that this is something like cookies that you can actually eat and enjoy. In one experiment with young children, it was found that children could compare numbers more accurately with chocolate than with abstract objects.

Hiro
That’s interesting.

Yati
Our 3-year-old second daughter, who usually struggles to count coins accurately beyond 3, can count caramels accurately up to 15.

Hiro
[laughs]

Yati
Come to think of it, when our daughters were 2 and 6 years old making a tart, the recipe said “roll out the dough to 30 centimeters diameter.” The younger one was rolling with a rolling pin while the older one measured with a tape measure, saying “It grew 1 centimeter. It’s 25 centimeters now. 5 more centimeters to go!” They were doing it together on their own, completely absorbed. They were doing addition, subtraction, and units intuitively. I’m the type who doesn’t worry about those little details in recipes, so it was just when the older one had learned to read and knew how to use a tape measure that she started spontaneously. That’s why she could get so absorbed, I think.

Hiro
Yeah.

Yati
There’s a program called “Rightstart” developed by American educational psychologists. Using board games and such, children of low-income immigrants surpassed the math scores of children in conventional education in just one semester. It’s research that’s like a rediscovery of Montessori education. They had children count the movement of game pieces, calculate the distance to the goal by subtraction, and compare who was likely to win. This is the same thing as “if the tart stretches 5 more centimeters, it’ll be 30 centimeters.” So if you cook and do daily household tasks, you don’t need to prepare special toys or materials.

Hiro
Right.

Yati
I think you can easily include children when adults are casually using their mathematical minds in everyday life. When counting things, point and slowly recite “1, 2, 3.” Show how to count by folding fingers. Show that you can represent “1” with one finger up and “2” with two fingers. In the elevator, say “Let’s press 2” while pressing the button together. Read the calendar or clock together. The same goes for babies. When shopping, you might be carrying them in a baby carrier or pushing a stroller, but you can narrate “We’re buying 2 carrots” while showing them each carrot going into the basket one by one.

Hiro
It’s fascinating that babies can grasp numbers.

Yati
Research has shown that 10-month-old babies, after watching 1 to 3 crackers being put into each of two boxes, can choose the box with more. Don’t underestimate them thinking “they’re still small.” If you properly show them what you’re doing, they understand more than you’d expect.

Hiro
Right. Intuitively.

Yati
I’d be happy if I’ve conveyed that you don’t need to prepare some contrived numerical environment. Our lives are overflowing with numerical elements, and adults just need to naturally introduce interactions with numbers in daily life.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

The history of the universe, the Earth, life, humanity, and language begins.

Yati
In the Montessori elementary curriculum, we first trace the history of the universe, then the history of Earth, the history of life, and the history of humanity, in that order, and then we trace the history of language.

Hiro
Right. There’s a flow where we present the big picture first, then move toward the details.

Yati
Why do we learn this way during the age six to twelve period?

Hiro
Because it’s more efficient for learning. In conventional education, it’s the opposite. There’s an arrow going from familiar things to the world, and with effort, toward the universe. That’s inefficient.

Yati
When you learn about your local area, then Morioka City, Iwate Prefecture, Tohoku, Japan, Asia, the world, people overseas feel like very distant beings. But in the opposite direction, universe, galaxy, solar system, Earth, people of the world feel very close.

Hiro
Right. In the universe, if you live within one parsec, you’re like “neighbors.” One parsec is about 30.8 trillion kilometers, but in the universe, that’s “quite close.”

Yati
Right. [laughing] It’s not just spatial distance. There’s a similar sense with temporal distance too. When you think about the history of life, the origin of language must have been just recently.

Hiro
So even when we say “global,” within the universe, Earth is a “local” planet, and events that happen here are “local” events. Learning things with that awareness helps maintain intellectual humility.

Yati
Because you realize you don’t understand anything at all.

Hiro
In Socratic terms, “knowing that you don’t know.” In Buddhist terms, “avidya,” meaning ignorance.

Yati
Right.

Hiro
Trying to understand even a little of that cosmic unknowability is cosmic inquiry, and the education and learning that happens everywhere daily is trivial in comparison.

Yati
What is language from a cosmic perspective?

Hiro
There are various definitions of language, and first it’s difficult to determine “what language is.” Academically, there are more than twenty different definitions.

Yati
I see. I want to unravel the history of language, but what is language in that context?

Hiro
The simplest definition is “language as a medium of information exchange.” Following this definition, facial expressions, gestures, attitudes, whistles, hand signals, writing, mathematical language, and programming languages, that is, computer languages, are all included in the concept of language. Ants’ chemical language and honeybees’ dance language are included too. So it refers to all forms of communication expression.

Yati
With that definition, we can also address non-human communication.

Hiro
Following this definition, the numerous bioacoustic information exchanges made at frequencies inaudible to humans, that is, organisms producing sounds, also count as language. For example, the audible range of an average fifteen year old human is about ten octaves, from thirty to eighteen thousand hertz. Birds, frogs, dogs, and others all produce sounds within this range. However, some organisms produce infrasound, below thirty hertz. For example, blue whales, elephants, and crocodiles. Sounds produced by ocean waves, volcanoes, and earthquakes are also in this frequency range.

Yati
Maybe the elephants at the zoo were greeting us in voices we couldn’t hear.

Hiro
Maybe. Also, in the ultrasound range, above eighteen thousand hertz, insects, bats, dolphins, and shrews produce sounds. But language includes not just vocal communication. It includes much broader things. Like affection, for example.

Yati
Like grooming.

Hiro
Worrying about someone. Caring. When we talk about the history of language, we humans unconsciously think of the history of human language. But if we consider the “communication media” used by organisms as language, then amphibians have their own history of language, and fish have their own history of language. This has become clear through recent bioacoustics research.

Yati
How can we unravel that history? It can’t be excavated like writing.

Hiro
Sound doesn’t remain. Humans encode it digitally and inscribe it on stone tablets and such, reproducing and preserving sound based on that code. That became possible through the advancement of modern science and technology. Historians from this point forward can trace the history of sound, but they can’t trace history before the invention of sound recording technology.

Yati
So it hasn’t been researched?

Hiro
Actually, humans are clever. From bone structure and such, we estimate muscle attachment and reveal what kinds of sounds could be vocalized. There’s also a method of tracing biological evolution in reverse. Specifically, the history of human language might be unraveled through research on the language abilities of great apes.

Yati
What do you mean? That apes have evolved to use language?

Hiro
Great apes are the animals closest to humans, a general term for apes with well developed cerebral cortexes. It refers to gibbons and hominids, that is, orangutans, gorillas, chimpanzees, bonobos, and humans. When orangutans were taught sign language, they learned about twenty signs.

Yati
They can communicate.

Hiro
When gorillas were taught sign language, they learned about one thousand words. There was a female lowland gorilla named Koko who had over five hundred active vocabulary words, meaning words she could use, not just understand, and five hundred receptive vocabulary words, meaning words she understood but couldn’t use. This is about the same as a human toddler. And it’s not just a rich vocabulary. She also had high empathy. When she saw “a horse with a bit in its mouth,” she signed “horse, sad.”

Yati
She understood feelings other than her own.

Hiro
Right. When chimpanzees were taught sign language, they also acquired hundreds of vocabulary words. However, while they can communicate, they can’t articulate words because they can’t properly control their lips and tongue. That’s because the laryngeal structure of great apes can’t produce aspirated sounds like humans. They can only produce very simple vocalizations using the larynx, like “boo boo,” “kee kee,” “hmm hmm.”

Yati
So it might have been a very long time from when humans started using language like sign language until they could vocalize.

Hiro
This research on the language abilities of gorillas and chimpanzees made clear that great apes do have language ability. However, it was unclear whether this was actually an ability to use language, or whether it just showed that advanced training was possible, such as wanting rewards, or performing tricks in response to non verbal cues.

Yati
That’s true. There are dogs that do tricks and parrots that talk, and trained monkey performances too.

Hiro
However, language research with the bonobo Kanzi brought a breakthrough. To give you the conclusion first: great apes have the ability to use language. Not only that, but it was also shown that they have the ability to make stone tools, the ability to use fire and cook, and the ability to play games.

Yati
Wait, that’s a lot of information. [laughing]

Hiro
That’s what a breakthrough means. [laughing] The bonobo Kanzi was given an artificial language called “lexigrams” by Doctor Sue Savage Rumbaugh, a researcher of primate language in America. Lexigrams are a keyboard with symbols representing words or actions, and he uses this to converse.

Yati
I see.

Hiro
What’s interesting is that Doctor Sue draws out the bonobo’s language ability using a Montessori style approach. Kanzi manipulates hundreds of symbols and enjoys spontaneous, creative communication with humans and other primates.

Yati
So Montessori education extends beyond humans.

Hiro
Right. This is the story of Montessori education for primates. Kanzi’s language ability wasn’t acquired through operant conditioning like teaching tricks, so he’s clearly using language through intrinsic motivation. In other words, it was proven that he uses language for communication just like humans.

Yati
That’s thought provoking.

Hiro
Once, Doctor Sue had her keys stolen by one of the chimpanzees at the research facility. She asked Kanzi, “Go get the keys back for me.” Kanzi went to the culprit, muttered something quietly, and came back with the keys.

Yati
So he interpreted for her.

Hiro
Right. Bonobos are famous for loving peace and are endangered great apes found only in the forests of the Congo. When you actually see them moving, it evokes indescribable emotions. I’d like everyone to search “bonobo Kanzi” on YouTube.

Yati
I watched it too. The image of him walking on two feet while carrying things with both hands was impressive.

Hiro
Personally, I think bonobos are positioned somewhere between apes and hominins, before Australopithecus in our human ancestry. I think research on bonobo language ability is essentially research that traces back and reveals the history of human language.

Yati
I see. I hadn’t thought of that approach!

Hiro
So I want to mention two discoveries and insights gained from this. One is Doctor Sue’s approach. What Doctor Sue did to get bonobos to use language naturally was to prepare an environment where the humans around them “normally” used language in daily life. She didn’t use direct rewards or punishments to force language acquisition like a trick. She lived together with them and respected their spontaneity.

Yati
That’s exactly the Montessori approach. Can adult bonobos do it too?

Hiro
That didn’t work. Doctor Sue first tried to teach language to an adult female named Matata, but Matata showed no interest at all. However, her son Kanzi, who was watching, started using language purely out of intellectual curiosity, so they decided to implement the education program with Kanzi.

Yati
So bonobos have something like a sensitive period for language too.

Hiro
Probably. Getting back to the point, the other insight is that the habit of combining many sets of symbols to express one’s intentions and thoughts is essential for intellectual development.

Yati
What do you mean?

Hiro
All great apes can’t speak and converse because their skeletal structure doesn’t allow pronunciation like humans. But if they have a set of symbols like lexigrams, they can combine them to express complex concepts. That’s the essence of the language activity that humans engage in. In other words, we communicate by combining not just sounds, but all “symbols,” such as gestures, facial expressions, and writing, as “expression signs.”

Yati
I see. When our three year old second daughter watched the Kanzi video with us, she got hooked on combining words to express what she wanted to say, like “night, not sleep, bad kid” or “alone, sleep, good kid,” and she seemed to be having fun.

Hiro
Like “room, mess up, sad.”

Yati
[laughing]

Hiro
So language is made of combinations of simple symbols, and I think the experience of playing with combining them in daily life develops language ability. There are pattern differences derived from geography, culture, and customs, like Japanese, English, Chinese, and so on, but the essence lies in wanting to “convey” and wanting to “understand.” If you value just that, I think language ability will become refined.

Yati
As a human environment, it’s important for the adults around to communicate using proper language. Adults deliberately handwriting text or writing letters can spark children’s interest in written language.

Hiro
Right. Unlike the Congo forest, civilized society has libraries, and books are readily available anytime. By making use of that blessed environment, just as we evolved from great apes to humans, I’d like us to evolve from humans to the next species.

Yati
Right. [laughing]

Hiro
Reading and understanding Scientific Montessori is also quite an advanced language activity. We’d be happy if you read it thoroughly and it helps with your daily child rearing. So with that, “today, talk, finished.”

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

Folktales are music, the memory of humanity, and mathematics heard by the ear.

Hiro
Today I want to open the door to folktales. I’d like to invite you into the world of folktales.

Yati
You can’t hide that you’re a fan of Toshio Ozawa. [laughs] In Montessori education, we’re taught to choose picture books with “content grounded in reality.” Things like “a mouse wearing clothes” or “an elephant with big ears that can fly” should be avoided because children might think they’re real. Are folktales grounded in reality?

Hiro
That’s quite a blunt question to start with. I’m a self-proclaimed folktale researcher who informally studies the works of Professor Ozawa, a researcher of folktales and legends.

Yati
My apologies. So, are folktales grounded in reality?

Hiro
There’s a program called Folktale University. They’re not running lectures now, but they have handbooks and such, and you can study folktales academically. To give you the conclusion first: folktales “transcend reality.”

Yati
[laughs] What do you mean?

Hiro
So it’s not whether folktales are grounded in reality, but whether reality is grounded in folktales. Whether the essence of folktales is being preserved.

Yati
What do you mean?

Hiro
This is borrowed from Professor Ozawa, but “folktales are humanity’s cultural heritage of oral tradition.” Folktale research began around the end of the 19th century and apparently flourished as a discipline in Germany, Denmark, Norway, Sweden, and Finland.

Yati
I see. And then?

Hiro
A European named Max Lüthi studied the texts of European folktales and revealed characteristics of their narrative style: using the same words when the same scene appears, synchronizing time, and not narrating realistically. Professor Ozawa in Japan collected Grimm’s fairy tales from Germany and Japanese folktales, spending about 13 years carefully reading and analyzing about 60,000 Japanese folktales. As a result, he confirmed that Japanese folktales share these same characteristics. Additionally, from his experience translating folktales from around the world, he confirmed that folktales from Africa, China, Siberia, South America, and other regions share these features too.

Yati
I’d like to understand this commonality more concretely. Can you give a well known example?

Hiro
Let’s take Jack and the Beanstalk. First, “once upon a time, a poor widow lived with her son Jack. They had nothing left but a cow.” Then, “Jack’s mother told him to take the cow to market and sell it.” Clean and simple. You immediately know who the characters are and what the situation is.

Yati
What do you mean?

Hiro
It’s not a complicated story like “Jack had three siblings and they argued about who should sell the cow, and the mother was thinking about getting a job.” It’s told with a clean structure. So anyone listening can easily picture the scene. There’s no mishearing.

Yati
It’s mathematical.

Hiro
Exactly. “Poor” contrasts with “rich,” “down below” with “up above,” “Jack” with “the giant.” Everything is in clear opposition.

Yati
I never noticed that.

Hiro
So actually, folktales are “mathematics for the ears.”

Yati
I’m good at math, but I never noticed.

Hiro
Continuing the story: on the way to market, Jack meets a mysterious man who offers him magic beans in exchange for the cow. What are the chances of that happening?

Yati
[laughs]

Hiro
If he’d left five minutes earlier or later, he never would have met the man. This is “synchronization of time.” It’s convenient.

Yati
I see.

Hiro
Then his mother throws the beans out the window in anger, and by morning a giant beanstalk has grown up into the clouds. Does that happen?

Yati
[laughs]

Hiro
And then Jack climbs the beanstalk. The naming is simple too. Magic beans, beanstalk, Jack. Easy to remember.

Yati
That’s why listeners can remember it easily.

Hiro
Right. Here’s where the repetition comes in. Jack climbs the beanstalk the first time, sneaks into the giant’s castle, and steals a bag of gold. He comes home. Then he climbs the beanstalk a second time and steals a hen that lays golden eggs. He comes home. Then he climbs a third time and steals a golden harp. Each time, the giant wakes up and chases him, shouting “Fee, fi, fo, fum!” The same scene told with the same words, three times.

Yati
That’s “using the same words when the same scene appears.”

Hiro
Right. And at the end, Jack chops down the beanstalk, the giant falls, and Jack and his mother live happily ever after with their treasure. But there’s no vivid description of the giant hitting the ground, or blood, or anything graphic. The violence is passed over quickly.

Yati
This is “not narrating realistically.”

Hiro
Right. Another important thing: folktales start with “Once upon a time,” signaling “I’m about to start a folktale now, this is a made up story so please don’t take it too seriously.”

Yati
That’s kind.

Hiro
At the end of the story, it ends with phrases like “and they lived happily ever after.” In Grimm’s fairy tales, it’s a bit more elegant, ending with something like “And if they haven’t died, they’re living there still.” This signals the end of the folktale.

Yati
This is like “end of proof,” isn’t it?

Hiro
Right. Like “Q.E.D.”

Yati
So in the end it’s “a made up story,” but what happened to whether it’s grounded in reality or transcends reality?

Hiro
That’s why it’s mathematics. Mathematics is the abstraction of reality, right? Mathematics describes the universe, right? So folktales describe reality, and they transcend it.

Yati
I see! Did you realize that yourself? Is Professor Ozawa saying this?

Hiro
I’m saying it on my own. But no one considers folktales as mathematics. That’s why they get arbitrarily made into animations or embellished unrealistically. Those aren’t authentic folktales. I think they’re the type of fantasy that Maria Montessori was concerned about.

Yati
Not many people read folktales aloud with that level of understanding.

Hiro
Not many. More like zero. Many families do it for vague reasons like “it’s good for emotional education” or “it’s good for the brain.” The saving grace is that there’s still a habit of parents reading aloud to their children in their own voice. Apparently there are products now that project animations on the ceiling with a projector to put children to sleep.

Yati
I don’t have many memories of being read folktales, and when I became a parent, there were so many folktales I was learning for the first time. I really empathized with them and even cried. Like the Japanese folktale “The Mice’s Sumo.”

Hiro
I see. The time parents can read aloud to their children is only a few years in a lifetime, so I think we should treasure it more.

Yati
Right. I was surprised when you said the Japanese folktale “Straw Millionaire” explains the essence of Montessori education in a way children can understand.

Hiro
Did I say that?

Yati
Usually people interpret it as “even with just straw, if you keep trading, you can become wealthy.” What you said was, “The main character boy encounters environments where he can give everything he has at each moment, and through that, he can grow.”

Hiro
Did I say that?

Yati
You did! I was so convinced. Folktales are grounded in reality! Folktales are amazing! That’s what I thought.

Hiro
I don’t really remember that, but folktales are parables, so they’re also a medium for conveying various ways of thinking and lessons.

Yati
It makes you think you shouldn’t do bad things. Also, what I find fascinating is that things like the “Urashima Effect” are scientifically correct but counterintuitive and hard to understand in daily life, yet they appear in Japanese folktales, so Japanese people accept them readily. While Westerners struggle with quantum mechanics like “it’s in a state of superposition and you don’t know the contents until you observe,” Japanese people just accept “the big wicker basket, perhaps?” in the Japanese folktale “Tongue-Cut Sparrow.”

Hiro
Right. So there are two things I want to say here. In the original Grimm’s fairy tales, there are descriptions that modern readers find disturbing, like the stepsisters cutting off parts of their feet to fit the glass slipper in Cinderella, or the wolf eating the grandmother in Little Red Riding Hood. There’s a trend of changing these stories because they’re considered too cruel. But this ignores the fact that these stories have been passed down through many people’s mouths and ears over centuries. I think this forgets the essence that folktales speak to the true nature of life and are meant to pass on to future generations how humans should coexist with nature.

Yati
I see.

Hiro
Nature is harsh. Eat or be eaten. Everyone is equal. So I think it’s also a reflection of humanity’s increasing distance from nature.

Yati
In folktales, humans and animals are close enough to talk and communicate.

Hiro
The other thing is that folktales exist only during the time they’re being told.

Yati
Not “existing in books.”

Hiro
Right. Written text and oral narration for the ears are different things. When you transcribe oral narration into writing, it often feels boring when read with the eyes. But that’s because there are techniques so that listeners won’t mishear, so characteristics are easy to remember, and so scenes are easy to picture. That’s why there’s a lot of repetition and simple language is used frequently.

Yati
It’s similar to songs.

Hiro
Right. Professor Ozawa says folktales are music. He emphasizes the importance of voice and rhythm. And the message.

Yati
There are skilled and unskilled storytellers.

Hiro
I want to be careful about that too. When telling folktales, don’t act. Narrating plainly without emotion is considered refined.

Yati
I didn’t know that.

Hiro
Tell it as if you’re passing on a story you heard. The importance of folktales lies in the simplicity of their logical structure. As I said earlier, they’re “mathematics for the ears,” so any age is fine to start, but there’s something called “recursive structure of language” that needs to be acquired by around age 5. So until age 5, I think it’s better to read aloud authentic folktales. If the recursive structure of language isn’t acquired, there will be struggles with tasks related to linguistic logic. For example, in programming or writing, situations requiring multi level logical development will be difficult.

Yati
Can you give me a concrete example of recursive language structure that’s acquired by age 5?

Hiro
There’s a simple test called LEPS. In technical terms, it measures the development of prefrontal synthesis, or PFS. PFS is said to be the brain function that forms the foundation of language ability and imagination, and there’s a critical period for this development, reportedly before age 5.

Yati
So the foundation of language ability and imagination is determined by age 5.

Hiro
Right. As a concrete example of the test, it’s things like “Put the orange cup inside the green cup” or “Put the red cup on top of the blue cup.”

Yati
That sounds easy.

Hiro
Neurotypical children over 4 can pass this test with almost no problem. Many children with ASD score low regardless of age, showing delays in PFS development.

Yati
I see.

Hiro
PFS is the ability to freely combine multiple objects or scenes in your head, and it’s considered the foundation for advanced imagination, grammatical understanding, and creative thinking.

Yati
So real world experiences along with reading aloud become important.

Hiro
Ages 6 to 12 is a period of expanding imagination, so how you spend the 3 to 6 age period is important for laying that foundation. Especially whether there’s a rich language environment or not affects one’s entire life.

Yati
So we should start by reading folktales aloud?

Hiro
Yes. There are authentic and inauthentic folktales, so who retells them is important. Please read aloud stories retold by people who properly understand the function of folktales.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

A bold hypothesis regarding the history of human language development, the brain, the relationship between apes and birds, and ASD.

Yati
Today’s topic is “language development.” In Montessori education, brain development and language development are understood as connected. The basic idea is to prepare the environment according to this development. For example, the “sensitive period for spoken language” introduced in the previous issue begins at 7 months of fetal age, around 26 to 28 weeks of pregnancy, and the basis for this is that myelination progresses in the brainstem during this period and the fetus’s auditory function begins to work in earnest. That’s why we’re encouraged to talk to the baby in the womb.

Hiro
Right. What’s the most important thing for language development in ages 0 to 3?

Yati
What I realized when learning Montessori education is that the sensitive period for order forms the foundation for language acquisition. Around age 2, children become sensitive to set ways of doing things, routines, and things being in their designated places. I think these become the foundation for naturally understanding and using the rules in language too.

Hiro
So what is language for humans?

Yati
It’s what we speak and write.

Hiro
For ages 0 to 3, very few children communicate through writing, so I think body language and spoken language are what we mean by “language” during this period.

Yati
That’s true. Crying, laughing, pointing. Even babies try to communicate their intentions. And while they look at picture books, they don’t focus on the text.

Hiro
Right. When we talk about language, it can actually be divided into body language, spoken language, and written language. Body language is something we become able to use somewhat instinctively. After that, we acquire spoken language, then written language. Language ability develops in that order. This order probably doesn’t change for any language.

Yati
I see. So you can listen and speak before you can write and read.

Hiro
It’s so obvious that no one thinks about it, but I think understanding this is fundamental to language development. Spoken language is acquired first, then written language.

Yati
Right. What changes when you’re aware of this?

Hiro
For example, during the 3 to 6 age period when written language is being acquired, children make mistakes like spelling “said” as “sed” or “night” as “nite,” writing words exactly as they sound. If you understand that written language is acquired after spoken language, you don’t need to correct these mistakes.

Yati
What do you mean?

Hiro
They’re just writing down spoken language. They’re in the middle of acquiring written language, so you can leave it alone. For example, even if a child says “pasghetti” instead of “spaghetti,” it will naturally become “spaghetti” without adults correcting them. Correcting them each time only damages the child’s self-esteem, so I’d like to leave them be until they self-correct.

Yati
Right. In Montessori education principles too, the idea is that “all errors should be noticed and corrected by oneself.” However, there is the point that adults shouldn’t imitate “pasghetti” just because it’s cute. They should speak correctly.

Hiro
So serious! [laughs] Don’t think about it so seriously. Just try to make conversations more fun, right? It’s a one-time thing. That period.

Yati
I didn’t talk much with my parents, and at school I had little time to talk freely, so my vocabulary is poor and I can’t make my stories interesting.

Hiro
So, about human language acquisition. When we look at Homo habilis fossil skulls, we can see that Broca’s area is prominent. Broca’s area is the part of the brain that controls speech production, located in the left frontal lobe. It’s called the motor speech center. It’s named after the French neurologist Broca, who reported cases of aphasia in patients with damage to this area. When Broca’s area is damaged, you can understand the meaning of spoken language and have an idea of what you want to say in response, but you cannot put what you want to say into words. Speech isn’t very fluent, and rhythm and stress become inaccurate.

Yati
How is this relevant?

Hiro
We know that Broca’s area is a brain region related to language, speaking and writing, but interestingly, as the term “motor” suggests, it’s also activated when moving the hands with intention.

Yati
So it activates even when doing craftwork silently, without using language?

Hiro
Yes. Brain regions including Broca’s area are activated by hand movements during work and by observing one’s own hands. It’s not just a speech production center. It’s involved in understanding the meaning of hand movements and in verbalization without speech. For example, when observing piano playing hand movements, Broca’s area activates when viewing unfamiliar melodic movements.

Yati
How should we interpret this?

Hiro
Essentially, this is probably a region for understanding hand movements, and as this region develops, we become able to speak words as well.

Yati
I see.

Hiro
Anthropologically, Homo habilis was the first human species discovered with stone tools, called Oldowan tools, simply chipped stones. They’re said to have used these to scrape meat from animal carcasses. Besides stone tools, sticks have also been excavated, showing they made and used tools. By the way, “Homo habilis” means “handy man.”

Yati
So Homo habilis used tools and also spoke?

Hiro
It’s thought they couldn’t speak. There are various theories that speaking began with Homo erectus. Since sounds can’t be excavated, we can only estimate from archaeological evidence. When analyzing Homo habilis skull fossils, as I mentioned, the Broca’s area in the prefrontal cortex shows a bulge, so the beginning of human language development is thought to have started there. In any case, there’s a flow: hands develop, tools are made, speech becomes possible, hands develop further, tools develop, and speech becomes more refined.

Yati
We now know that birds also have language and grammar, but do birds have a brain region corresponding to Broca’s area? Birds don’t use hands, so how did their language develop to the point of having grammar?

Hiro
Bird wings are arms, right? So if we include arms as hands, I think a Broca’s area like region probably activates when flying. If birds learn to fly through observation and imitation, the logic of language development might be the same.

Yati
Looking into it, birds do acquire flight through observation and imitation. Also, regarding tools, New Caledonian crows use wooden sticks to get insects and combine parts to make tools. And it seems birds do have brain regions corresponding to Broca’s area. Broca’s area is included in what’s called mirror neurons. Those capable of learning through imitation include primates including humans, birds, and cetaceans, which have mirror neurons. It seems that if you have language, you definitely have mirror neurons, but having mirror neurons doesn’t necessarily mean you have language.

Hiro
I see. What I thought about with the mirror neuron discussion is that for humans, being able to “imitate hand movements” seems to have a major influence on acquiring spoken language.

Yati
Right.

Hiro
This is at the hypothesis stage, but there are research reports that ASD, Asperger syndrome, shows structural characteristics in Broca’s area that differ from neurotypical individuals. Personally, I suspect it’s a language area issue.

Yati
If we consider that mirror neurons don’t function well, the symptoms reported in ASD do make sense. Not being able to empathize, not being able to understand others’ emotions, and so on.

Hiro
Empathizing, understanding emotions, understanding intentions, motor imitation. These are gifts of mirror neurons.

Yati
I’m aware that I have ASD, and it’s interesting to start understanding where the problems might have been in my early childhood.

Hiro
Sesame Street, children’s TV shows, hand play songs. In a sense, they’re developing Broca’s area through imitation of hand movements.

Yati
There’s a photo of a baby macaque imitating a human sticking out its tongue, and apparently this is only seen for a few days. In other words, there’s a critical period. There might be a critical period for the human Broca’s area too.

Hiro
Right. That’s why the environment from ages 0 to 3 might influence one’s entire life.

Yati
In Montessori environments, we do what’s called a “presentation,” showing hand movements slowly so even small children can imitate them. By showing hand movements slowly, even 1 year olds can dress and undress, cook, clean, and do laundry.

Hiro
So moving your hands slowly is important. It’s activating the child’s Broca’s area. Also, Broca’s area is the region for verbal communication, located in the left prefrontal cortex. Symmetrically, brain science research has revealed that the right prefrontal cortex is involved in nonverbal communication, understanding emotions from facial expressions and such. It’s been found that children’s prefrontal cortex is highly activated when talking with parents, but when talking with unfamiliar people, the right prefrontal cortex isn’t activated as much. By the way, it’s known that in ASD, the left right network structure of the brain is asymmetric. From this, I infer that very early daycare use might contribute significantly to ASD.

Yati
I was put in daycare before age 1, so this hypothesis concerns me greatly. And the difference in prefrontal cortex activation between parents and strangers is shocking. This scientifically demonstrates the importance of time spent with parents and reading aloud to children.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

An educational approach grounded in the 13.8-billion-year history of the universe, the 4.6-billion-year history of Earth, and the 3.8-billion-year history of life.

Yati
Montessori education for ages 6 to 12 isn’t very well known. I’d like to talk about “Aid to Life (preparing the environment for natural development)” for this age group.

Hiro
In a word, it’s about “survival.”

Yati
What do you mean?

Hiro
Sorry to jump straight to the conclusion, but since this topic takes a while to explain, I thought I’d start with the main point. By the way, we don’t hold the international teacher certification for the 6–12 age group. What we’re discussing is based on reading all of Maria Montessori’s works and all the elementary-level texts published by AMI and AMS, combined with our own developmental theory research.

Yati
We’ve also read research papers on Montessori education from around the world. And we’ve done our own investigations into Montessori elementary graduates.

Hiro
That’s right. We know which school Larry Page attended, which school Sergey Brin attended, and about Jeff Bezos’s elementary school years. As for Will Wright’s games, I’ve probably played them more than anyone else in the Montessori community.

Yati
I actually knew Will Wright’s games before I knew about Montessori education, so I was amazed when I started recognizing the Montessori materials his games were based on.

Hiro
Personally, I was shocked that almost no one in the Japanese Montessori community knows about Will Wright. SimCity, SimEarth, and Spore.

Yati
And The Sims and SimAnt.

Hiro
When you play them, you get a window into how someone raised in Montessori elementary thinks.

Yati
For example, in Spore, we simulated 500 million years of life’s history.

Hiro
Right. It was an epic journey, starting as a single-celled organism and heading toward the center of the galaxy. We even experienced terraforming.

Yati
I remember thinking things I’d never normally consider, like “I’m really glad humans are omnivores.” And “Ideals like non-violence alone won’t make running a nation work.”

Hiro
Some of that is due to game design choices. But as an opportunity to think about problems you’d never consider in everyday life or gain perspectives you’d otherwise never have—and as materials for 6–12 elementary—Will Wright’s simulation games are unparalleled.

Yati
SimAnt is an ant simulation game, and the manual includes not just controls but an encyclopedia-like section on ant ecology. It’s a difficult game, so at first things don’t go well. When you get stuck and read the manual to understand ant ecology, you mysteriously get better at the game.

Hiro
All real knowledge is used, and it connects to reality. I heard Will Wright say in a lecture, “There are some game design adjustments to make it more fun, though.”

Yati
I played The Sims so much when I was in elementary school. It’s a life simulation game. Basically a digital version of playing with dolls, but you can see various human needs quantified, and you arrange furniture and adjust the environment to satisfy them.

Hiro
Fundamental human needs.

Yati
Exactly. It’s a major theme in elementary education, and it’s a simulation of the “preparing the environment” aspect of “Aid to Life” that we’re discussing now. From this game, I learned and resolved, “When I grow up, I’m definitely going to sleep in a good bed.”

Hiro
I see. SimCity is probably known by more people—it’s a simulation game where you become mayor.

Yati
Since it was released for Super Nintendo, many people know the game, but I don’t think they know it was created by a Montessori elementary graduate.

Hiro
Setting aside the game content, what Will Wright said about game design was: “You learn more by actually becoming a mayor than by reading a book like ‘How to Become a Mayor.’”

Yati
That really sums it up. I agonized so much over “where to put the waste treatment plant.” Now I understand how the current mayor of Morioka feels.

Hiro
Right. You start thinking about real political issues as if they were your own. Your perspective on urban planning and city design changes.

Yati
I learned that cities grow over time and that you always have to be aware of the fiscal situation. I was a notorious mayor who drove my city to bankruptcy many times. [laughs]

Hiro
When you’re too particular about things, you can’t manage effectively. [wry laugh]

Yati
And when the management target becomes the Earth, that’s SimEarth.

Hiro
First of all, it’s hard just to create an environment where life can emerge.

Yati
Starting from there. [laughs]

Hiro
“Aid to Life” really is difficult. Not too hot, not too cold.

Yati
With carbon dioxide and oxygen in the right proportions.

Hiro
Right, you have to pay close attention to atmospheric composition. The wonderful thing is that you can think childish thoughts like, “Octopuses have taken over the Earth, so should I hit it with an asteroid and reset?” and actually try it.

Yati
It makes you think about the real dinosaur extinction too. I’d love for today’s children to play this.

Hiro
Exactly. But all these games are old now, hard to find, and there are technical issues. I’d be grateful if someone would remake them. But it seems like no one will, so maybe I should do it myself.

Yati
Various people have tried, but I think you really can’t make them without understanding Montessori education and developmental theory. They’re essentially modern Montessori materials.

Hiro
Yeah. It requires knowledge plus sensitivity plus technical skill. It’s difficult.

Yati
The SimEarth manual was written by Hitoshi Takeuchi, a geophysicist and professor emeritus at the University of Tokyo.

Hiro
The “Age of the Professor.”

Yati
Montessori described the 6–12 stage as the “Age of the Professor.”

Hiro
Yes. But personally, I think “Age of Survival” is more appropriate.

Yati
We’ve come back to your initial conclusion. Why is that?

Hiro
Looking at the four planes of development, ages 6 to 12 correspond to the second plane. In the first plane, it’s a phase of integrating senses and movement, and through that integration, imagination expands.

Yati
Moving from concrete to abstract.

Hiro
Then the question arises: what should that imagination be used for? Looking at what happens in the third plane, it leads to Erdkinder (Children of the Earth). That’s a program where students learn practical self-sufficiency from life on a farm.

Yati
The “Secondary” of the third plane. Secondary corresponds to a time when hormonal balance is unstable, so the idea is to calm down by working with the soil. This stage is also called the “social newborn.”

Hiro
The fourth plane corresponds to university age, a time to prepare for entering social life, but personally, I think of it as the “Age of Natural Philosophy.”

Yati
Since the first and third planes are similar enough to both be called “newborn” stages, and the second and fourth planes are similar enough to both be called “professor” stages, your interpretation seems to fit.

Hiro
Yes. So the fourth plane has a very academic feel. Elementary in the second plane is a phase of broadly and deeply learning about nature at the scale of the cosmos, Earth, and life—knowledge needed for the third plane. To do that, you need to develop literacy in numbers and language. In other words, you need to acquire real knowledge that can withstand the self-sufficiency of Secondary.

Yati
Where does the “survival” aspect come in?

Hiro
In Secondary, you’ll be dealing with many plants and animals, so you need to understand natural ecosystems. You need to understand how the Earth works. Natural phenomena and so on.

Yati
That’s true. As with Will Wright’s games, after learning at a macroscopic scale, you could approach farming and animal husbandry with new perspectives from the viewpoint of the cosmos and ecosystems.

Hiro
Rather than that, knowing “how life was created” before engaging with actual nature versus not knowing changes the difficulty level.

Yati
That connects to the SimAnt discussion.

Hiro
The organism in front of you is an Earth organism, a life form in the universe. It plays some role in the ecosystem. For example, if you know that honeybees pollinate flowers, you’d want to use fewer pesticides.

Yati
Right.

Hiro
Just because something isn’t toxic to vertebrates doesn’t mean you should spread neurotoxins that affect invertebrates in nature. On a planetary scale, that definitely has negative impacts.

Yati
Tracing the 3.8-billion-year history of life would inspire reverence for life.

Hiro
Absolutely. It’s a desecration of all life. I think it stems from ignorance of that miraculous history.

Yati
You mentioned atmospheric composition earlier. There’s lots of nitrogen in the air, and there are microorganisms in the soil that can convert atmospheric nitrogen into forms plants can use. Ignoring that and spreading chemical fertilizers should also feel wrong.

Hiro
Mycorrhizal fungi. In short, I think people who think they’ve learned just by memorizing right and wrong answers from static textbooks can’t grasp nature’s dynamic equilibrium. The real test comes in Secondary, where you find out whether what you’ve learned actually works in nature.

Yati
That’s harsh. Nature passes judgment.

Hiro
Current mainstream education keeps moving further from the real thing. It’s like a simulation of a simulation of a simulation.

Yati
There’s no real work.

Hiro
Spending lots of time there won’t make you wiser. I feel like the fundamental things that should be learned aren’t being learned. Being good at entrance exams isn’t really an essential measure of intelligence.

Yati
I know of overseas Secondary examples where they also function like universities. Teachers act as facilitators, bringing in university professors for opt-in lectures. They also encourage internships at companies. Since students can already do university-level work, being good at entrance exams isn’t really the point.

Hiro
Right. They normally use university research labs too.

Yati
Teachers also teach how to read academic papers, and the children conduct research in agriculture and natural sciences. They also do activities like designing and building cabins. They do real work and learn the knowledge needed for it.

Hiro
Elementary is the preparation period for that, so students need to gain as much real knowledge as possible. The curriculum that provides an intuitive understanding of the roles of humanity, language, and numbers from the grand perspective of cosmic, Earth, and life history exists only in Montessori education. We want to steadily evolve and spread it.

Yati
I’ll continue the research.

Hiro
Having the foundational knowledge that civilization was built from the beginning of the universe, through galaxies, the solar system, Earth, and life—learning various things with that background versus without it changes both learning efficiency and the conclusions reached in discussions.

Yati
That’s right. Though spreading this isn’t easy.

Hiro
It’s not that difficult. If you know history, you realize we’re just following the law of inertia, moving in a certain direction. Once you notice that, it happens quickly.

Yati
Children might be more receptive since they have fewer prejudices.

Hiro
Exactly. World peace begins with children.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. CEO of Motherhand and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

Fulfilling the mind means empowering one’s capacity for learning.

Hiro
Today I want to talk about the child’s spirit. When we think about the components of life in animals, there are many ways to categorize them, but personally, the division into body and spirit feels right to me.

Yati
Go on.

Hiro
We still can’t fully replicate life physically. We’re gradually making progress on the body side, but the spirit side hasn’t caught up yet. There’s an ongoing debate about whether AI corresponds to the “spirit” of a robot. Personally, I think we need to discuss this more in physical terms. In other words, I want to clarify what the spirit is from a physical standpoint.

Yati
Where should we start to make this physically clear?

Hiro
Personally, I think the spirit can be approximated by learning ability. In animals, it’s closely related to the capacity of the brain.

Yati
What do you mean?

Hiro
For example, today’s robots are measured against benchmarks like whether they can complete tasks a 5-year-old can do: figuring out how not to be found in hide-and-seek, stacking blocks with a robotic arm, or walking in a park without falling.

Yati
Sounds like they’re doing what toddlers do.

Hiro
On the other hand, AI has been defeating world champions in games like chess and Go. That’s what’s happening in the field technically called “machine learning.” What’s fascinating is that these systems no longer need human data. In fact, research shows that “self-play” without learning from human data produces far more capable and intelligent systems. It’s quite surprising.

Yati
Using that approach, AI has surpassed humans as Go players and is now approaching human-level performance in mathematics too.

Hiro
In autonomous driving as well, AI can now drive far more safely and efficiently than humans. The key point is that humans aren’t teaching it—once you set up the environment, it becomes smarter on its own. No teacher needed. In other words, the teacher was actually limiting its potential.

Yati
The same is true for human children. Especially with children’s spirits, it’s natural for them to be cultivated through self-education. Maria Montessori was the one who emphasized the importance of building an environment for this purpose.

Hiro
Watching AI progress, I think we could say that the maturation of the spirit means becoming able to solve complex and difficult problems. There’s a natural developmental stage of the brain where children move from solving only concrete problems to being able to solve abstract ones. That’s why the Montessori method of progressing from concrete to abstract aligns well with this.

Yati
Right. In Montessori education, children ages 3 to 6 learn abstract concepts like numbers, language, and culture through sensory and motor experiences.

Hiro
In short, the ultimate mission for ages 3 to 6 is to do plenty of integration training between the brain’s sensory input and motor output. Put simply, if there’s an environment where children can immerse themselves as much as they want in self-correcting learning through “trial and error,” their spirits will be fulfilled. As a result of being fulfilled, they reveal their more developed selves. It’s like a program activating that transforms a chrysalis into a butterfly.

Yati
Just as we can’t see what’s happening inside a chrysalis from the outside, we can’t see what’s happening inside a child from the outside. So we can only imagine—but science has actually identified what happens inside a chrysalis. We now know that the chrysalis liquefies parts of its body to rebuild itself into an adult. Similarly, science can help us see a child’s inner development.

Hiro
Everyone pays attention to physical development, but we’re often blind to mental development. When it comes to children’s spirits during this chrysalis-like period of ages 3 to 6, society tends not to place much importance on inner development. In many countries, kindergarten is available, and elementary school starts after age 6. But there isn’t yet a strong movement to make early childhood education mandatory as a social institution and improve its quality.

France lowered the compulsory education age to 3 starting in 2019, and Hungary made kindergarten mandatory starting in 2016. There are also examples from Mexico and Sweden, but globally, we still have a long way to go.

Yati
In Japan, preschool has been made free but not mandatory.

Hiro
That’s right. Japanese nursery schools are classified as “preschool education” by OECD and other international standards, but that was only achieved through 2015 system reforms to align with global standards. In practice, since teachers weren’t required to obtain new licenses, it’s become somewhat hollow. Even with the “integrated centers for early childhood education and care”, the actual quality of education varies considerably.

Yati
I think quality needs to improve along with accessibility. How can we raise quality?

Hiro
Let me proceed on the assumption that if educational quality improves, the learning environment improves, and children’s spirits are fulfilled as a result. In that case, should we measure educational quality by literacy acquisition rates, or is there some other indicator? What do you think?

Yati
Well, I think literacy in reading, writing, and arithmetic can be acquired even with “low-quality education” in the sense of using “the carrot and the stick.”

Hiro
True. But literacy acquired that way doesn’t lead people to use it spontaneously for meaningful purposes as adults—for example, reading lots of books, writing extensively, or engaging in mathematical thinking. This shows up in statistics like reading rates and book purchase rates. The correlation between these indicators and income or assets has also been established. In the end, literacy that was forced on someone reluctantly versus literacy acquired voluntarily affects life outcomes differently, don’t you think?

Yati
That’s true. When you consider the long-term impact, we can’t really say they’ve fully mastered literacy. If we could measure acquisition rates with that in mind, it would become a good indicator of educational quality.

Hiro
Exactly. If we measure literacy acquisition rates at the end of preschool, primary, secondary, and higher education, and then continue measuring during young adulthood, middle age, and old age, I think we’d find that some literacy gets lost. So while we tend to assume literacy is acquired once education is complete, we shouldn’t ignore that unused literacy is easily lost. Including that factor, literacy acquisition rates could serve as an indicator of educational quality.

Yati
In fact, recent neuroscience research shows that people with reading habits or habits of mathematical thinking maintain those abilities even past their 50s, while those without such habits start declining from their 30s, according to Hanushekand colleagues in 2025.

Hiro
Acquiring literacy in childhood is extremely important, but we need to discuss educational environments while considering how the method of acquisition affects motivation to learn in adulthood. So adults don’t struggle later.

Yati
Preschool education isn’t mandatory in many countries yet. But if it becomes mandatory, does that mean educational quality has improved? Does it mean children’s spirits are fulfilled?

Hiro
Their spirits will be fulfilled if it creates an environment where children can freely engage in trial and error.

To understand the impact of making education mandatory, we can look at times when primary education wasn’t mandatory.

Yati
I see. Making something mandatory can meet resistance, but learning from history is important.

Hiro
Compulsory education in Japan began with the School System proclamation in 1872. The turning point was in 1907 when the compulsory education period was extended to 6 years of elementary school. Enrollment rates improved significantly. After World War II, the School Education Act of 1947 extended it to 9 years total: 6 years of elementary and 3 years of middle school. This forms the basis of the current system.

Yati
I see. Before that, were there no educational opportunities? People couldn’t read, write, or calculate?

Hiro
Before that was the Edo period (1603 to 1868), when private educational institutions called terakoya spread throughout the country. There, children learned reading, writing, and the abacus as practical knowledge for daily life. Literacy rates vary by source, but it’s believed to have been over 60% in urban areas and under 30% in rural areas.

Yati
What about before that?

Hiro
In the medieval period (Kamakura through Muromachi), education for noble and samurai children was mainly conducted at temples. Temples were centers of learning, and monks taught not only Buddhist doctrine but also classical Chinese, waka poetry, and calligraphy. The samurai class emphasized reading and writing education alongside martial arts. Literacy among common people was low.

Yati
So historically, new forms of education were for a small elite, and over time they spread to the common people. Most people until recently didn’t have the opportunity to learn letters and numbers.

Hiro
That might be true. So we modern people are having quite a luxurious discussion. “Will making preschool education mandatory actually fulfill children’s spirits?!” [laughs]

Yati
Is this discussion scientific? [laughs]

Hiro
Okay, then let me talk in an even larger historical frame. In the history of life, we originally had no “brain” at all.

Yati
[laughs]

Hiro
We were so tiny we couldn’t be seen, couldn’t move freely—we could only drift. From there, we settled in certain places, photosynthesized, preyed on other organisms, got absorbed by others, grew larger, and became more complex. We came up from the sea onto land, grew legs, and learned to walk. Some learned to fly; others returned to the sea. We climbed trees and came back down. We laid eggs, then hatched eggs inside our bodies. And somehow, now here we are discussing whether to make preschool education mandatory.

Yati
That was quite a sweeping look back. [laughs]

Hiro
Yes. Within that grand flow, we had no brain until relatively recently, and now we’re discussing how to use and develop our enlarged brains. That’s impressive. Look how far we’ve come. So first, I want to give a round of applause to all life for making it this far.

Yati
True.

Hiro
With that perspective, we can then ask about the merits of preschool education. I want to discuss the cultivation of children’s spirits on that kind of macroscopic scale. The idea of “adaptation to environment through learning” might be valid across the entire history of life.

What is nourishment for the spirit? At first I thought it was “language” and “dialogue,” but that wouldn’t apply to all life. When I reconsidered, “trial and error” and “discovery” felt right.

Yati
So “Aid to Life” was actually “Aid to All Life.” When thinking about children’s education, we need to consider whether it only applies to humans.

Hiro
In many ways, I think education will evolve by moving away from “human-centered” thinking. In the world of machines, this is already happening.

Yati
So we’re at a crossroads between being the ones who use machines or being used by machines.

Hiro
Rather, it’s a fork between competing with machines or cooperating with them. Whether we continue the current competitive approach or transition to a cooperative one. Discussions about mixed-age grouping and diversity are becoming outdated.

Yati
That’s interesting. A paper published in March 2025 scientifically suggests that the mixed-age, competition-free experience in Montessori education forms a fundamental worldview that “people are cooperative,” which enhances trust in society and well-being in adulthood.

Montessori-educated Larry Page and Will Wright are positive about AI, and Jeff Bezos is focusing on preschool education for low-income families through the Day One Fund. It’s an initiative to establish free Montessori schools across the United States. Elon Musk’s Ad Astra (a kindergarten and elementary school) is also based on Montessori education.

Preparations are steadily advancing toward a future where all life and AI cooperate.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. Research Scientist at StudyX and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

What does it mean to prepare the environment?

Yati
Today’s topic is “Aid to Life”, a cornerstone concept you’ll discover whenever you explore Montessori education.

Hiro
Right. How should we understand it?

Yati
To summarize the international teacher training course lectures: “Life” means natural development, and “Aid” means preparing the environment.

Hiro
Okay. Does that mean raising children outdoors in nature? Like, for example, Waldkindergarten emphasizes spending time in the forest.

Yati
Of course the outdoors plays a vital role in the environment. But it extends far beyond nature alone. Language, using tools, exposure to numbers and culture, all of these are necessary parts of the environment too.

Hiro
So “natural” here doesn’t just mean “nature” in the outdoor sense. I’m thinking the environmental requirements would change depending on how we define “natural development.”

Yati
Natural development means allowing the innate developmental blueprint within each child to unfold as nature intended. Maria Montessori discovered this through observation: children around the world show the same developmental tendencies. She observed these changes both physically and mentally.

Hiro
Right.

Yati
Within this framework, Montessori education calls the emergence of mental developmental processes “sensitive periods.”

Hiro
How is that different from the brain’s “critical periods”?

Yati
They’re similar, but sensitive periods aren’t as strictly time-bound as the brain’s critical periods. For example, a classic critical period is imprinting, which happens only immediately after birth.

Hiro
Right. The language acquisition window closes around age 6 to 7, after which learning language becomes nearly impossible. Some say it might extend to around 12. Because it’s unethical to test directly, we infer this from tragic cases of children found after isolation who hadn’t acquired language. In cats, researchers did rather cruel experiments, like keeping one eye closed, to identify the critical period for vision.

Yati
This diagram (Figure 1) shows the sensitive periods based on the international teacher training course. Imagine sensitive periods like a wave: interest in acquiring a particular ability gradually builds, peaks, then gradually fades and disappears. Maria Montessori described them as “very strong sensitivity to certain knowledge or skills appearing during successive short periods of varying length.”

Hiro
Got it. So sensitive periods track the rise and fall of interest intensity, while critical periods mark windows when learning is structurally possible?

Yati
Exactly. I’ve summarized the comparison in Table 1.

Table 1. Comparison of Sensitive Periods and Critical Periods

Hiro
That’s clear. I wonder whether Montessori’s sensitive periods apply beyond animals with brains.

Yati
Let’s dig deeper into that in another issue. By the way, recent research has revealed that children raised in Montessori environments have different brain responses to errors (Denervaud et al., 2020).

Here’s what happens: when the ACC, the brain’s error detector, fires, Montessori children activate the right parietal lobe and dorsolateral prefrontal cortex to think of new moves on the spot. On the other hand, children in traditional education don’t show such responses during errors. Instead, during correct answers, their ACC strongly connects with the hippocampus and striatum, the memory and reward systems, showing a response of “burning the correct answer into memory.”(Figure 2). In other words, this suggests that growing up in traditional education makes you lean toward a strategy of “remembering and recalling correct answers.”

Hiro
That’s why Sota Fujii, the seven-crown shogi champion and one of the most famous Montessori-educated figures in Japan, is so incredibly strong, right? For other shogi players, it must feel like fighting an AI that thinks of moves on the spot.

Yati
Exactly. And there’s more recent research showing that Montessori children have various brain regions that cooperate more strongly with each other. They also develop brains that can sustain concentration better (Zanchi & Denervaud, 2024).

Hiro
Ah, okay. Now I understand why Google and Amazon are so incredibly strong. [laughs] In the end, it’s because the founders’ brains are on another level, right? If you don’t miss the sensitive periods, brain performance can increase that much?

Yati
That’s right.

Hiro
So I understand that sensitive periods are concepts that hold up even with the latest science, but what should parents actually do?

Yati
Don’t interfere with the child’s sensitive periods. For example, during the sensitive period for spoken language, if all the adults around are wearing masks and the child can’t see how mouths move, I think that had a considerable impact. Also, not letting them do what they want to do, not allowing failure, not letting them make choices. Telling them to be quiet, or keeping babies in confined spaces. There are so many restrictions on movement. The earlier discussion about brain connectivity is probably because Montessori education’s learning method always involves movement.

Hiro
That said, raising children in modern society is quite difficult, especially in cities.

Yati
That’s true. For example, due to space issues, it’s difficult to have children cook or keep children’s dishes within reach.

Hiro
So how should we solve that? Even if it’s not an ideal environment, there must be small things that can make it better just by being aware of them.

Yati
One thing is to understand developmental stages and sensitive periods (Figure 1). When the number sensitive period emerges, show them counting anything. Acorns or beans are fine, and counting in the bath works too.

Hiro
That seems doable for any household.

Yati
For the written language sensitive period, just prepare paper and pencils. Since children from 0 to 6 years old learn through imitation, it’s important to show them adults writing as a model.

Hiro
What about ages 0 to 3?

Yati
When it comes to babies in Montessori education, mobiles are iconic, but that’s also for visual development, in other words, the sensitive period for eye movement. You could also go outside and look at leaves swaying in the wind together. Mom and Dad’s faces peering at the baby’s face are also the best material for the baby’s eye development.

Hiro
Oh, really?

Yati
What to be careful about after birth is interfering with motor development by putting them in a crib or fixing them in a bouncer. It’s better to lay them on a wide futon from right after birth so they can move freely.

Hiro
Got it. For example, when you give birth at a hospital, they naturally recommend all sorts of things through marketing, like formula and diapers. There are tons of baby products, and information comes at you with this “everyone uses these” vibe. But you’re saying we shouldn’t just go along with that.

Yati
Right. Many things actually go against natural development, like pacifiers. Also, living in sync with natural light is surprisingly not well known.

Hiro
So blackout curtains aren’t good either?

Yati
Exactly. Even for newborn nighttime diaper changes, if you keep the light minimal, like draping a towel over an indirect light, then just nurse, the baby will calm down and fall back asleep. Living in tune with natural light naturally helps establish the baby’s circadian rhythm.

Hiro
Huh, interesting.

Yati
Also, babies have a grasp reflex in their hands from birth, so they can play with a light rattle. Even without a rattle, they can grasp family members’ fingers and play. I want people to try this when a baby is crying and you can’t figure out why. Sometimes they cry just because they’re bored.

Hiro
That’s a helpful tip. How should we respond to the terrible twos that start around age 2?

Yati
From a Montessori perspective, it’s a sign that they’ve developed their own ideas, so we respect the child’s viewpoint. First, acknowledge their feelings when they say no. Then offer choices between two options.

Hiro
That advice didn’t solve things for us, so I did some independent observation and experimentation. This is purely a personal hypothesis, but I think the terrible twos might actually be “a period of acquiring the logic of negation.”

Yati
That’s a fascinating hypothesis. It’s true that before this stage they didn’t understand negation, but now they’re using it precisely.

Hiro
So the response is to let them negate as much as they want. [laughs]

Yati
What do you mean?

Hiro
The child wants to put “not” in front of everything. Mom is not me, Dad is not Mom, what I want to do now is not that, what I want now is not that.

Yati
[laughs] So if adults don’t affirm their negation, the negation can’t be established.

Hiro
Right. If you respond to negation with negation, they start thinking, “Wait, is Mom me? Is Dad Mom? Is this what I wanted to do? Is this really what I want? No, that’s not it! Definitely not!” That’s what happens.

Yati
You’re totally simulating a 2-year-old’s brain. [laughs]

Hiro
So that first negation 2-year-olds often make is a pure negation for the purpose of acquiring negation itself. The continuous negations that happen, which we call the terrible twos, are negations that arise in response to the parents’ negations. I think parents confuse them by responding to negation with negation. When I tried this approach with my child, instead of a terrible two-year-old, they became a two-year-old learning logic.

Yati
If you get double-negated when you’re just starting to understand negation, that would definitely be confusing.

Hiro
I noticed this because my second daughter would often say “not this.” Like, “What do you want? Milk?” “Not milk.” “Water?” “Not water.” “Tea?” “Yes, yes.(nodding)” And she’d have this really satisfied look on her face. When language isn’t that developed yet, children can’t negate verbally, so I think they end up expressing negativity through emotional behavior. But I think overall this corresponds to a sensitive period for negation, though it’s embedded within language development.

Yati
I looked into this academically too, and the terrible twos period does overlap with the acquisition of cognitive negation, so your hypothesis might be right.

Hiro
I’m glad I wasn’t negated. [laughs]

Yati
To sum up what we’ve discussed, scientifically speaking, the Montessori principle of “Aid to Life” isn’t wrong. In fact, evidence supporting it seems to be accumulating.

Hiro
I’m glad we can continue “Scientific Montessori.”

Yati
Me too.

“What we need is a transparent will that embraces the galaxy,
Great power and heat” Miyazawa Kenji

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. Research Scientist at StudyX and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

How Old-School Drills Light Up Young Minds

Hiro
I’ve been researching the brain and discovered something fascinating. Traditional Japanese elementary schools actually have habits that are surprisingly good for the brain.

Yati
What do you mean?

Hiro
Take reading aloud, mental arithmetic, handwriting, especially writing characters beautifully and carefully. Brain imaging shows these activities create comprehensive neural activation. When they become habits, the prefrontal cortex develops. The elementary curriculum probably wasn’t designed with neuroscience in mind, yet it’s remarkably rational for brain development. Fascinating, right?

Yati
Montessori Elementary and other alternative approaches focus on children’s freedom and advanced content. Repetitive practice, reading, writing, arithmetic, gets dismissed as outdated, even unintelligent.

Hiro
Far from unintelligent, it’s brilliant. The brain develops through daily activation. Only habits create lasting change. Why? Synaptic circuits strengthen with frequent use. That’s basic neuroscience. Elementary schools function as social systems ensuring children regularly practice these brain-building activities: reading aloud, handwriting, calculating.

Yati
That makes sense.

Hiro
Brain training is like muscle training, no pain, no gain. Activation requires load, challenge, effort. I learned this developing a brain training app. People instinctively avoid mental strain. Consider this: cooking, walking, jogging, activities linked to longevity, all activate the brain. Yet forming these habits? That’s the hard part.

Yati
Guilty as charged. I skip the brain training exercises I’m bad at. Walking feels like a chore.

Hiro
Elementary education extends beyond the classroom. School transforms daily rhythms: early rising, breakfast, walking to school, greeting crossing guards, socializing with friends. These “non-cognitive” habits, they’re gold for brain development.

Yati
The research backs this up. Elderly people learning juggling increased brain plasticity (Boyke et al. 2008). Walking habits rejuvenated aging brains (Erickson et al. 2010). For children? Aerobic exercise boosted academic performance (Chaddock-Heyman et al. 2014).

Hiro
Very scientific. But here’s the flip side. Current schools are riddled with brain-hostile practices. Sitting for hours. Passive listening. Hands idle on desks. No wonder school refusal rates are skyrocketing, while there may be various reasons.

Yati
Look at Japanese school refusers’ daily routines. YouTube marathons. Gaming binges. Even learning center kids gravitate toward low-sensory, low-challenge activities. Minecraft. Coding. Comfortable, but not brain-building.

Hiro
That’s a serious problem for development. The root cause? Parents and learning center operators haven’t scientifically studied development. They confuse freedom with abandonment. Left to their own devices, literally, children disappear into digital worlds. Neglecting sensory experiences in the real world.

Yati
The research is terrifying. Internet-addicted children don’t just fail academically, their brain development halts (Takeuchi et al. 2018).

Hiro
It’s a cruel choice in Japan. If you avoid school, you have freedom, but smartphone, game, and internet addiction await. But if you go to school, you lack freedom, and unpleasant things like bullying, mental starvation, and military-style education await. International schools and alternative schools break through this dichotomy, but their tuition is ridiculously expensive. Currently, for most families, even if they wish for their children’s healthy development, their options are limited. So I think most people hope for reform in existing schools.

Yati
But reform faces resistance. The winners of the current system, those with prestigious degrees, comfortable lives, why would they want change? Their identity depends on the status quo.

Hiro
Right.

Yati
They’re myopic, maybe selfish. But can we blame them? The system trained them this way, compete, win, protect your position.

Hiro
True. The Japanese poet Miyazawa Kenji captured this perfectly in “An Outline of Peasant Art”. Let me read it here: “There can be no individual happiness until the whole world becomes happy. The consciousness of self evolves gradually from individual to collective society to universe.” What he wanted to say and the problems we’re sensing are similar. Essentially, our “consciousness is still small.”

Yati
People say education’s purpose is “to become happy.” Miyazawa Kenji ruined that simplicity for me. It’s the prisoner’s dilemma in action. Individual rational choices lead to Nash equilibrium, not Pareto optimality. Personal success doesn’t equal collective flourishing.

Hiro
I think intelligence is the spatiotemporal scale you can grasp, measured by predictive power. Like, sure, everyone can guess what’ll happen an hour from now, but a hundred years? That’s much harder. And if you keep stretching that to a thousand years, ten thousand years, a hundred million years, maybe that’s actually how we could think about developing intelligence in a more quantitative way. But then, how do you even do something that sounds like wizardry, or astrology, or alchemy? In the past, priests who served as advisors to kings had real power because they were skilled in astronomy and mathematics. They could predict things on Earth by reading the movements of the heavens, like nailing the timing of an eclipse, or changes in the seasons, or when snow or rain would come. And the reason they could do that was because they’d quietly been collecting data and working with hidden equations. There was always a trick behind it. But to ordinary people, farmers who had no education about the cosmos, it must have looked like magic, or some kind of divine oracle.

Yati
You’re always talking about these sci-fi kind of ideas, like what schools might be like a thousand years from now.

Hiro
Montessori Elementary curriculum centers on the history of the universe, Earth, and life, dealing cross-sectionally from macro to micro. Children learn the 13.8 billion year history of the universe, the 4.6 billion year history of Earth, and the 3.8 billion year history of life. That’s their foundation for predicting futures. Imagine the accuracy advantage.

Yati
Artificial intelligence follows the same principle. There’s a trend toward creating “smarter” AI by teaching it concepts that apply to larger spatiotemporal scales, like physics and mathematics, rather than just training it on internet data. This leads to more accurate predictions.

Hiro
These days, science and technology have given us access to massive amounts of historical data. But there’s still so much we don’t fully understand in fields like planetary science, geology, and archaeology. Huge parts of the record are still literally buried underground. And once we dig that up and start reflecting it in our knowledge, everything shifts. Academic systems, educational frameworks, all of it will need to be updated. And sometimes that means we’ll have to admit, “what we thought was true was actually wrong.” It’s like when people moved from believing in the geocentric model to adopting the heliocentric one. We should expect those kinds of Copernican revolutions. Knowledge is always moving. That’s why we need educational systems that can stay strong and flexible through constant change.

Yati
These revolutions are happening all the time, in big ways and small. Some people don’t wait for society to catch up. They bring these radical new truths into their daily lives before the rest of us even notice. Quite a few are already living through their own personal Copernican revolutions. The future is already here. It just hasn’t reached everyone yet.

Hiro
Montessori education itself isn’t mainstream in Japan yet. While some countries have made it public education, in Japan, there are almost no private schools offering it. With the declining birthrate and aging population, it’s easy to predict that establishing new schools using traditional school management models will be financially difficult. But since Montessori education is clearly superior in quality to existing education, I personally want to somehow bring it to standardization.

Yati
So we’re ignoring existing models entirely. We’re physically designing a new model from scratch. We’ve launched our experimental alternative school April 2025.

Hiro
Exactly. The school has a new model. The model is distributed, not centralized, and mobile. I think mobile is cosmic. We’ll discuss the details another time. At the societal level, it’s important to increase experiments with these new alternative models, even if they’re small. I think it’s important to regularly increase learning density, deepen education in the right direction, and actively try new things.

Yati
The brain research I cited earlier also says that acquiring new skills activates the prefrontal cortex.

Hiro
Sure, individual prefrontal development matters. But I think we also need to talk about something bigger, like the prefrontal cortex of society, maybe even of the universe. Between the ages of six and twelve, imagination really expands. That’s when independent thinking starts to emerge, and that’s crucial. Elementary school, at the very least, should train kids for that shift. Current schools do help kids build some healthy brain habits. That’s good and worth keeping. But we also need to move to the next stage, where the brain isn’t just active, it’s used more purposefully.

Yati
That’s why at our alternative school, Polymath School of Morioka, we emphasize both brain development support and Montessori-style cosmic education. There’s no other school with such good balance. Plus, it’s free without tax funding. [laughs]

Hiro
That’s right. We’re aiming to be “the most intellectual school on Earth.” [laughs]

“There is no punishment or reward in our schools to interfere with the joy in the work itself. The only reward is in the completion of the work–it is at this time that internal discipline establishes itself, and the foundations of character are laid. ” (Maria Montessori, “Maria Montessori Speaks to Parents”)

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. Research Scientist at StudyX and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

What neuroscience reveals about how praise affects the developing brain

Hiro
Today, let’s talk about praise and its effects on children.

Yati
What’s your take on praising children?

Hiro
I’ve been researching childhood developmental disorders for a brain training app I’m developing. Reading blogs about therapeutic education, I noticed a pattern: everyone gets praised excessively. The children, their parents, everyone gets praised like crazy. Staff at therapy facilities say things like “How cute!” or “Amazing!” at every opportunity. Many parents write, “At first it felt strange, but it saved my heart.” That really stuck with me. It’s as if therapeutic education equals praise. Maybe it’s not quite that extreme, but everyone seems to have strong reactions to being praised or watching their children be praised.

Yati
Preschools and kindergartens are similar, and it makes me uncomfortable too. Since learning about Montessori education, we’ve been careful about evaluating children, including praising. We don’t say “amazing” or “cute.” That probably makes the discomfort even stronger.

Hiro
The early childhood education world seems to treat praising as something wonderful, but personally, I think it’s a double-edged sword. Children might comply while being praised, but without it, they do nothing. There’s this sense of adults controlling everything. It feels like a technique to make children do what adults want rather than what children want to do.

Yati
There are bestselling books on praise techniques, but they’re ultimately about parents controlling children. That goes against the Montessori philosophy.

Hiro
Well, most parenting books are essentially manuals for controlling children to meet parents’ expectations. Actually, I recently read something fascinating in a neuroscience book. The brain region that responds to praise is different from the one that feels personal achievement. Even when you do something voluntarily, if you receive external evaluation, you start responding to the praise rather than the achievement itself. Then when the praise stops, you stop doing what you were doing voluntarily.

Yati
I looked for papers on this and found one. It’s research showing the “Undermining Effect” through brain activity data. This is a psychological phenomenon where people who were acting from intrinsic motivation lose motivation when they receive external factors like rewards or evaluation. (Murayama et al. 2010)

Hiro
That makes sense.

Yati
Here’s what they found. Even with tasks that seem interesting and engaging, when you add rewards, people start thinking “it’s meaningless without the reward.” Brain activity actually drops. In the study, it was a game people naturally wanted to practice. But with rewards, they stopped practicing voluntarily. When they learned the rewards would end, they practiced even less, and during the game, the brain stopped responding.

Hiro
Yeah.

Yati
This study used money as the reward. But other research confirms that monetary rewards and positive evaluation from others affect the brain in similar ways.

Hiro
Tell me more.

Yati
Think about what this means. Activities that should trigger “This looks fun!” get hijacked. They become “If I’m not praised, why bother?” And this rewiring happens at the brain level. Chores, writing letters, cooking... these naturally enjoyable activities become meaningless without praise. That’s terrifying when you really think about it.

Hiro
We made up a song with the kids called “Don’t Praise Me.” Our eldest wrote lyrics like: “Don’t praise me. When you praise, it’s not for myself anymore, and when I grow up I’ll become stupid.” I thought that was a bit extreme. But it turns out there’s actual scientific basis for it. [laughs]

Yati
Maybe that kind of simple, direct message is exactly what adults need to hear from children’s perspective.

Hiro
True.

Yati
This “don’t praise me” theme really resonates with me. As a child, I was completely driven by praise and good grades.

Hiro
I’m the opposite. I wasn’t praised growing up, so I don’t praise others either. I just keep challenging people. That’s why I’m good at developing people. [laughs]

Yati
Remember how you never praised my cooking? You’d only say things like “Try adding more salt next time” or “The timing could be better.”

Hiro
Did I? I don’t remember.

Yati
Then one day, I made something absolutely delicious. I asked “How is it?” and you asked back “What do you think?” When I said “It’s really delicious,” you said “If you think it’s delicious, isn’t that enough?” That’s when it hit me. I’d been cooking for praise, not for the joy of it. The real motivation should have been the pleasure of making food, enjoying it, and sharing it with someone I love.

Hiro
I don’t remember.

Yati
Something similar happened recently. I started cleaning days before guests arrived. The children joined in, and our eldest made the toilet sparkle. I thought “Now we can welcome our guests.” But she said “It feels good when it’s clean.” That made me pause. I was doing it for external validation again! She was doing it for the intrinsic satisfaction. I want to regularly value the feeling of “cleaning because it feels good”, so the children don’t end up thinking “We have to clean because guests are coming.”

Hiro
You’re so serious [laughs.]

Yati
[laughs.]

Hiro
If you genuinely think something is amazing, not to please the child, then praising is natural, isn’t it? Basically, I think it’s good to think once about “Why am I praising?” Making rules about everything like “don’t do this, don’t do that” is exhausting.

Yati
Let me share a failure from my Montessori training. During my AMI practicum at a Montessori preschool, I was careful with my words. I kept them simple: “You did it” or talking about specific efforts. But my trainer said my tone was too excited. It still came across as praise.

Hiro
Really?

Yati
Veteran teachers barely react. They just glance over with a neutral “Hmm.” Complete calm. No disturbance to the child’s concentration. It’s incredibly difficult. I’m still learning through daily practice with our own children. I’m gradually understanding what they taught me during practicum.

Hiro
Hmm. By the way, Maria Montessori said something perfect for you:
“A young student can become a great teacher or doctor if he is driven on by an interest in his vocation; but if he is motivated solely by the hope of a legacy or a good marriage or some other external advantage, he will never become a real teacher or doctor, and he will not make any great contribution to the world through his work. If a young man must be punished or rewarded by his school or family to make him study for his degree, it would be better for him not to receive it at all. Everyone has a special inclination or special secret, hidden vocation. It may be modest, but it is certainly useful.” (Maria Montessori, “The Discovery of the Child”)

Yati
That hits too close to home. Here’s another Montessori quote:
“It may happen, when we fall in love, or when a child has been conceived, or a book published, or a great discovery has been made, and we deceive ourselves with the thought that we are the happiest person in the world. And yet, if at that moment someone who is in authority, or who is over us like a teacher, should come up and offer us a medal or some other prize, he would rob us of our true reward. Disillusioned we would cry out: ‘Who are you to remind me of the fact that I am not supreme, that there is another so far above me that he can give me a reward?’” (Maria Montessori, “The Discovery of the Child”)

I think anyone who’s given birth can relate to this. After all that pain, when you’re holding your baby for the first time, in that fulfilled, quiet moment... If a stranger suddenly tried to give you a medal, it would ruin everything. Once you understand how praise can destroy these pure moments, you can’t carelessly evaluate children anymore.

Hiro
Ages zero to six are for coordinating senses and movement. Children need to experience as many failures as possible in the real world. But typical praise celebrates success, which makes them fear failure. What matters is their own trial and error, failing repeatedly, gaining insights. Parents should establish that cycle as a mindset. If you only praise success, children will hate failing and avoid real challenges. To borrow from Kenya’s Wangari Maathai, that’s “mottainai”, what a waste.

Yati
[laughs.] Adults think praise makes children like them more. But children see right through shallow praise, don’t they? The adults who calmly demonstrate, without fanfare, they’re the ones children really trust and admire.

Hiro
As a child, I knew there were aunts and uncles who praised excessively, so I think children observe adults’ reactions carefully to see if praise is genuine.

Yati
When you think about it, games are representative of things that don’t praise you. Children are absorbed in them even when adults tell them to stop. Really, housework and studying, if not praised, might have the same essential interest that makes you want to continue even when told to stop, like games. Actually, lately our second daughter won’t stop writing letters even when we say “Time for bed.”

Hiro
Think once about “Why am I praising?” And if you’re praising to please children, consider whether they’re really feeling genuine joy from it. Personally, I think having adults help clean up their messes is more valuable than easy praise from adults. When you take on a huge challenge, fail spectacularly, and make a complete mess of the table and floor, which adult would you prefer: one who gets really angry, or one who enjoys cleaning up with you? I think they’d prefer an adult like Curious George’s Man with the Yellow Hat. Even as an adult myself, I think so.

Yati
True. Remember when I first introduced you to Montessori’s ideas? You summarized the parent-child relationship perfectly.
The parent says: “I’ll take responsibility, so experiment freely.”
And the child responds: “I’ll do it myself, so watch quietly. If I fail, I’m counting on you.” That’s the essence of it.

Hiro
I don’t remember [laughs.]

Dos for the Developing Brain

1. Real-world, hands-on experiences

Children’s brains develop through actual experiences. Think cooking together, building with blocks, gardening, even folding laundry. These activities engage multiple senses and require problem-solving.

• Exercise

• Experiences in nature

• Cooking

• Handwork

• Conversation

• Reading

• Writing
  etc.

It is especially good to consciously incorporate activities that use the hands (tidying, cooking, origami, etc.). Hands are heavily represented in the brain’s motor cortex. Activities using hands literally build neural pathways.

2. Independence

Enable them to do things for themselves.
Enable them to make choices for themselves and experience the results.

3. Connection with nature

Nature provides endless sensory input and unpredictable challenges that indoor environments cannot match. Every season offers different learning opportunities.

• Interact with various living things.

• Observe.

• Feel the changes of the four seasons.

• Nature games.
  etc.

Exposure to natural environments lowers cortisol, supports attentional recovery (including improvements in selective attention and executive function), and offers rich multisensory experiences.

4. Sensory and movement exploration

The brain learns through the body. Movement isn’t just exercise, it’s how children understand space, physics, and their own capabilities.

• Use the five senses.

• Sports.

• Art activities.
  etc.

5. A safe-to-fail environment

Do not get angry even when they fail. Make it so they understand what to do when they fail. Be careful not to overpraise, and be mindful so that they can maintain a spirit of challenge and a desire to improve.

Don’ts for the Developing Brain

1. Yelling and fear-based discipline

When children face frequent yelling or threats, their amygdala (fear center) goes into overdrive. This floods their system with cortisol(stress hormones). Over time, this actually shrinks the prefrontal cortex—the part responsible for self-control and decision-making. It can lead to increased anxiety and impulsivity.

What this looks like:

• “If you don’t listen, I’m leaving without you!”

• Raising your voice to get compliance

• Using shame or humiliation

Try instead:

• Keep your voice calm, even when setting firm limits

• “I see you’re upset. Let’s figure this out together.”

• Create predictable consequences rather than threats

• Maintain an environment that provides a sense of security even when they fail.

2. Overprotection and overinterference

If parents do everything for the child or constantly issue instructions, the child has fewer opportunities to think for themselves, which may delay the development of problem-solving ability and self-efficacy. The brain’s executive functions (planning and judgment) become harder to cultivate.

What this looks like:

• The parent does all the toy tidying up

• Giving detailed instructions on how to play and how to behave

Try instead:

• Give time to try things on their own and prioritize a watchful stance.

• Limit assistance to the bare minimum.

3. Monotonous, under-stimulating environments

When sensory and motor stimulation is scarce, the formation of neural circuits in the brain becomes insufficient, and the development of sensory integration and motor abilities can be delayed.

What this looks like:

• Playing only with the same toys every day

• A tendency to stay indoors, with no nature or outdoor play

Try instead:

• Have them experience diverse materials (wood, nuts, cloth, stones, sand, etc.) and movements (running, climbing, etc.).

• Provide environments with nature and change.

4. Sleep deprivation

Sleep is essential for the brain’s memory consolidation and synaptic strengthening. If sleep is insufficient during this period, learning ability and emotional regulation may decline, and stress tolerance may also weaken.

What this looks like:

• Staying up late at night

• Naps that are irregular and too short

Try instead:

• For 2–3-year-olds, ensure 11–14 hours of sleep per day (night + naps).

• Create a regular daily rhythm.

• Consistent bedtime routine.

• Dark, cool, quiet sleep environment.

5. Excessive sugar and processed foods

Diets high in sugar and additives cause rapid fluctuations in blood glucose, which can adversely affect the brain’s concentration and emotional stability. Long-term nutritional deficiencies also affect neural development.

What this looks like:

• Giving mostly sweets and juice

• Meals with a skewed nutritional balance

Try instead:

• Center meals on natural ingredients (vegetables, fruits, whole grains).

• Keep processed foods to a minimum.

6. Social isolation

When engagement with others is limited, the development of brain regions responsible for language development, sociality, and empathy (e.g., the mirror neuron system) may be delayed. At this stage, much learning occurs through imitation and dialogue.

What this looks like:

• Hardly interacting with anyone other than the parent(s)

• Spending the entire day alone

Try instead:

• Have appropriate interactions with family members and nearby children.

• Create opportunities to naturally come into contact with people through parks and walks.

Profile

Yati Obara
Editor-in-Chief, Scientific Montessori
Based in Japan, born in 1989. Research Scientist at StudyX and Co-Director of the nonprofit think tank Polymath Research. Holds an M.Eng. and is an AMI-certified teacher. Focused on Montessori developmental theory and AI. Mother of two.

Hiro Obara
Publisher, Scientific Montessori
Based in Japan, born in 1990. CEO of StudyX and Co-Director of the nonprofit think tank Polymath Research. Works as a software developer and game designer. Father of two.

(Good for the brain ⇔ Good for parenting) ∧ (Bad for the brain ⇔ Bad for parenting)

Hiro
I’ve been thinking...what if there were some basic principles for parenting? Something like “follow these and you’ll be fine.”

Yati
That’s an interesting starting point. Where would you begin?

Hiro
Well, take Montessori education. It aims for “whole personality development1”, right?.
But not everyone who goes through it achieves that. And plenty of people develop beautifully without it. Let’s start by sorting this out and derive the necessary and sufficient conditions for the development of the whole personality.

Yati
I created a simple chart to visualize this, four quadrants showing Montessori education versus whole personality development (Figure 1).

Hiro
Looking at this figure, it’s clear that Montessori education is not the necessary and sufficient condition for cultivating the whole personality.

Yati
It’s fascinating to think about people who developed beautifully without Montessori. Who are they? Maybe children who spent lots of time in nature, using all their senses? People often fixate on Montessori materials, the pink tower, the golden beads, but this shows something important: the materials aren’t essential. They’re not what really matters.

Hiro
I think the necessary and sufficient condition for developing the whole personality is simple: develop the brain in a healthy way.

“The key: Healthy brain development equals healthy personality development”

Yati
That makes perfect sense. When you look at what works in Montessori education, it’s exactly the things neuroscience tells us are good for brain development. The connection is clear.

Hiro
In other words, if we list what’s good and bad for the brain, we get a simple parenting guide, follow these principles and you’ll be fine.

Yati
I’ve actually summarized what helps and harms the brain. We’ll share that next. From a Montessori perspective, it all makes perfect sense.

Hiro
Neuroscience gives us even more insights for parenting. Take the homunculus, the brain’s body map. Huge areas are devoted to hands and mouth. That tells us activities using hands and reading aloud are crucial for brain development.

Yati
Actually, the homunculus just got a major update from neuroscience (Figure 2) (Gordon EM, et al. 2023). The discovery, large brain areas are dedicated to integrated movements, movements that combine different skills. This explains why everyday activities, especially cooking with children, are so powerful for development. Think about what happens when a child helps make dinner: they crack eggs using fine motor control, carry bowls using gross motor skills, measure flour and taste the sauce engaging their senses. All these different types of movement happen simultaneously. That’s exactly the kind of integration the developing brain needs.

Hiro
Traditional Japanese arts are perfect examples too, tea ceremony and ikebana(the art of Japanese flower arrangement), both require this kind of integration.

Yati
Absolutely. In tea ceremony, the host carries a heavy water jar, gross motor skills. They fold the silk purification cloth with precise, delicate movements, fine motor control. Guests bow and recite formal phrases like “I humbly receive this tea”, language and social protocol. Then there’s the sensory richness: savoring tea from seasonal ceramics, tasting delicate sweets that balance the tea’s bitterness, feeling the bowl’s warmth in your hands, listening to water boil. Every sense is engaged. The brain must integrate all these elements seamlessly exactly the kind of complex coordination that promotes healthy development.

Hiro
Reading aloud works the similar way, rapid, fluent reading activates multiple brain regions and enhances plasticity.

Yati
People picture Montessori classrooms as perfectly quiet, but we actually encourage reading poetry aloud. Your speed-reading point is fascinating. Watch how children progress: they start sounding out letters slowly, “c-a-t.” Then they read whole words, “cat.” Eventually, full sentences flow smoothly: “The cat sat on the mat.” This progression mirrors brain development exactly. And here’s the breakthrough: pushing reading speed further actually accelerates brain development. It’s not just comprehension. It’s building neural efficiency.

Hiro
Montessori education can feel overwhelming, so many rules, different interpretations, complex materials. It’s tough for parents to implement at home. But here’s the simple version: do what’s good for the brain, avoid what’s harmful. That’s really all you need to know.