雅歌教育典藏站

Chapter 1

From Awakening to Realization

Many children struggle in school not because they lack intelligence, but because they cannot find an entrance into understanding. Others gradually lose motivation because they no longer know why learning matters to their lives. When learning loses meaning, children often seek emotional refuge elsewhere, retreating into virtual worlds, games, or temporary forms of belonging.

Arco Experimental School was founded in response to these two educational questions:

• How can children learn to understand?
• How can children become willing to learn?

Arco developed four foundational beliefs, summarized as ARCO:

• A — Awakening：an intelligence stage that helps children learn through different entrances.
• R — Realization：a life stage that helps children live out their gifts and become willing to learn.
• C — Circumstance：a decoding system that enables understanding to emerge.
• O — Offering：an ecosystem of love and models that allows life to flourish together.

To support awakening, Arco developed MINE (Multiple Intelligence Niche Exploration) based on the theory of multiple intelligences. MINE integrates language, music, images, movement, manipulation, roles, and situations into different entrances toward understanding. When children find an entrance, abstract knowledge begins to become meaningful, and understanding begins to emerge.

To support realization, Arco gradually developed Sim Life, a life-based learning environment in which children assume roles, complete missions, participate in relationships, and experience responsibility through meaningful situations. Learning is no longer separated from life, but becomes connected to identity, dreams, and future possibilities.

Arco further discovered that many children experience surprising breakthroughs when learning occurs through musical intelligence rather than only through linguistic intelligence. Rhythm, sound, movement, and embodied interaction often allow abstract structures to become tangible and emotionally accessible.

Through years of classroom exploration, Arco gradually organized a decoding framework called the CHARACTER Decoding System, consisting of nine learning conditions:

• C — Context：when abstract concepts are grounded in context
• H — Home：when an apprenticeship environment is present
• A — Affection：when learners desire to participate
• R — Read Aloud：when text is interpreted through voice
• A — Awakening：when learning is driven by questions
• C — Commitment：when content is refined to its essentials
• T — Transfer：when problems are represented through media
• E — Encoding：when answers are verified through structure
• R — Recognition：when learning is presented before others

These nine conditions are not a checklist, but a set of interrelated supports that help children enter understanding. Different lessons may activate different conditions; however, when these conditions consistently exist within a learning environment, children gradually develop the ability to decode abstract concepts.

Chapter 2
Classroom Examples of the CHARACTER Decoding System

This chapter presents classroom examples that illustrate the nine conditions of the CHARACTER Decoding System. These examples are not intended to show that every lesson contains all nine conditions. Rather, each example highlights one condition and demonstrates how Arco designed learning experiences to help children enter abstract understanding.

1. Context — Tile Shop and Square Roots
2. Home — Prime and Composite Numbers
3. Affection — My Treasure and Classroom Shops
4. Read Aloud — Turning Stories into Scripts
5. Awakening — When Music Tiles Speak Chinese
6. Commitment — Young Anchors and Young Reporters
7. Transfer — Solving Chicken-and-Rabbit Problems with Chess Pieces
8. Encoding — Exploring the Area Formula of a Circle with a Hundred Grid
9. Recognition — Research Presentations and Teaching Others

C — Context: When Abstract Concepts Are Grounded in Context

Tile Shops and the Embodiment of Square Roots

In teaching square roots, Arco does not begin with mathematical symbols. Instead, children first enter the context of a “tile shop.” Acting as shop owners, they use small square tiles to construct squares and explore the relationship between area and side length.

Children first describe the structure in Chinese:

“A square with an area of 9 has a side length of 3.”

They then express the same idea in English:

“The square with an area of 9 has a side length of 3.”

Only afterward does the teacher introduce the mathematical expression:

$\sqrt{9}=3$9​=3

At this moment, the teacher introduces “how masters say it,” helping children discover that there exists another language called mathematical language.

Children often react with surprise:

“It’s so short!”
“So powerful!”

Mathematical symbols are no longer unfamiliar marks, but become a condensed language that captures experience and structure.

Thus, the function of Context is to ground abstract concepts in meaningful situations before introducing symbolic representation.
H — Home: When an Apprenticeship Environment Emerges

Exploring Prime and Composite Numbers Together

In a lesson on prime and composite numbers, children from first through fifth grade explored mathematical structures together. Rather than beginning with formal definitions, the teacher first presented a number, such as 13, and invited children to divide it evenly using chess pieces or grid paper.

The children arranged the pieces into one row, then two rows, three rows, four rows, and so on, testing every possible arrangement up to 13 rows. They discovered that 13 could only be divided evenly into one row or thirteen rows; all other arrangements produced remainders. The teacher then demonstrated the number 12, showing that it could be evenly arranged into 2, 3, 4, or 6 rows.

Only afterward did the teacher introduce the terminology:

• Numbers that could be arranged into “rectangular boxes” were called composite numbers.
• Numbers that could not be evenly divided except by 1 and themselves were called prime numbers.

This lesson became a Home because it contained three essential conditions: mentor awakening, peer support, and accessible tools. The teacher guided learning through questions and awakening; children observed, imitated, and supported one another; and chess pieces and grid paper remained constantly available for repeated manipulation, revision, and verification.

Thus, Home is not unstructured freedom, but an apprenticeship environment in which understanding is allowed to grow.

A — Affection: When Learners Desire to Participate

My Treasure and Classroom Shops

In a sharing activity called My Treasure, each child brought a personally meaningful object to class. Rather than allowing free and unfocused sharing, the teacher guided children to focus on several key questions:

• What is its name?
• Why did you give it that name?
• Why is it important to you?

Because the objects genuinely mattered to the children, they prepared voluntarily and worked hard to express themselves clearly.

The same phenomenon appeared in classroom shop activities. When children knew they would bring products, set up stores, welcome customers, and complete transactions, they usually required no reminders from teachers. They prepared on their own initiative.

Thus, Affection is not simply about making learning “fun.” Rather, it emerges when learning becomes connected to life, and children begin to desire participation.

R — Read Aloud: When Text Is Interpreted Through Voice

Language Immersion and Relay Reading

In language immersion lessons, the teacher first told a story while inviting children to enter different roles and help build the situation together. When the plot required dialogue, children naturally needed to read the lines aloud.

The teacher transformed the story into a script and allowed children to choose roles they liked, including the narrator. Since the lines varied in length and difficulty, children could select parts that matched their abilities.

Through relay reading, text was no longer merely a set of symbols on paper. It was interpreted through pauses, tone, rhythm, and emotion.

Thus, Read Aloud gives text a voice. It allows children to enter understanding through sound, while also enabling them to choose roles they are able to fulfill.

A — Awakening: When Learning Is Driven by Questions

When Music Tiles Begin to Speak Chinese

In a music lesson, children sang Little Chick Drinks Water. In Mandarin Chinese, when a third tone is followed by a first tone, the vocal contour often forms a fourth interval. For example:

• xiǎo jī 小(3)雞(1) → E A
• hē shuǐ 喝(1)水(3) → A E

The teacher used music tiles labeled E and A. Children first recited “小雞喝水” in Chinese, and then played E A A E on the tiles.

When they discovered that the melody produced by the tiles matched the tonal contour of the Chinese phrase, they often responded with surprise:

“The music tiles can speak Chinese!”

At that moment, children were not merely receiving an answer. They were suddenly seeing a structure between language and music. Awakening, therefore, becomes the ignition point of decoding.

C — Commitment: When Content Must Be Refined to Its Essentials

Young Anchors and Young Reporters

At Arco, textbooks were often hidden from view. Instead, the teacher first designed an activity, sometimes even replacing the textbook with a video, so that children could enter a situation before organizing its content.

In the Young Anchor activity, the teacher first played a video for children to watch carefully. Afterward, children identified key words and wrote them on the board.

The teacher then guided children to reconstruct the event through those key words, form sentences together, remove unnecessary details, and preserve what was essential. Finally, each child expressed the event in their own words:

What do I feel about this event?

Another example is the Young Reporter activity. Before interviewing an expert, children first studied the expert’s background and identified the questions they truly wanted to ask. When facing the expert, they then verified whether their understanding was accurate.

Thus, Commitment is not merely effort. It is the ability to identify key points, remove distractions, and gradually form one’s own viewpoint.

T — Transfer: When Problems Can Be Represented Through Media

Solving the Chicken-and-Rabbit Problem with Chess Pieces

Transfer does not primarily address children’s inability to calculate. It addresses their inability to understand what an application problem is asking.

Therefore, instead of beginning with equations, the teacher first invited children to solve the chicken-and-rabbit problem with chess pieces.

• White pieces represented heads.
• Black pieces represented legs.

Children first arranged the heads, and then assigned legs to each head. Chickens had two legs, while rabbits had four. Through arranging, comparing, and verifying, children gradually understood the actual relationships within the problem.

A problem that originally could only be “thought through” became a structure that could be manipulated. Many children who could not solve the problem mentally began to solve it once they started working with their hands.

Thus, the core of Transfer is not simply changing the teaching method. It is transforming an abstract problem into a medium that children can see, touch, and manipulate.

E — Encoding: When Answers Can Be Verified Through Structure

Exploring the Area Formula of a Circle with a Hundred Grid

When learning the area of a circle, the teacher did not begin by giving the formula. Instead, children first drew a quarter circle inside a hundred grid, and then subtracted the squares outside the curved boundary one by one.

Gradually, children discovered:

A quarter circle occupies approximately 78.5 squares.

The teacher then guided them to organize the structure:

• 10 × 10 = 100
• 78.5% of 100 = 78.5
• Multiplying by 4 gives the area of the whole circle.

Through this process, children began to see that the area of a circle is related to “radius times radius.”

Only then did the teacher introduce the mathematical master language:

$A=\pi r^2$A=πr2

$r$r

$A = \pi r^2 \approx 28.27$A=πr2≈28.27

$C = 2\pi r \approx 18.85$C=2πr≈18.85r = 3.00

At this point, the formula was no longer a symbol to be memorized. It became a structure children had discovered through manipulation, approximation, and organization.
R — Recognition: When Learning Is Presented Before Others

Research Presentations and Turning Stories into Scripts

At Arco, research lessons always included presentation. Children did not merely complete research; they had to stand before others and teach them.

They needed to explain:

• What did I not know before?
• How did I find the answer?
• How did I verify it?
• Why do I believe this is true?

True understanding is not only being able to understand something oneself, but being able to help others understand it.

In another example, turning stories into scripts may appear to be a Read Aloud activity on the surface, but at a deeper level it is also Recognition. Children do not simply read a story; they must use roles, lines, and performance to help the audience enter the situation.

Thus, Recognition is not merely the display of results. It is the process through which understanding becomes visible, audible, and comprehensible to others.

Chapter 3

Sim Life: From Refuge to Realization

Many children do not reject learning because they lack ability. Rather, they cannot see how learning connects to life.

When reality becomes disconnected from meaning, children often seek refuge in virtual worlds. Games provide temporary belonging, identity, missions, rewards, and emotional compensation. They offer a place where effort appears meaningful.

Sim Life emerged from an important educational question:

Could education provide these experiences in real life rather than only in virtual worlds?

Instead of treating games merely as distractions, Arco began to ask what psychological and educational needs games were actually fulfilling.

As a result, Arco gradually developed Sim Life — a life-based learning environment without screens or keyboards, where children assume roles, complete missions, participate in relationships, face consequences, accumulate experience, and pursue realization through lived situations.

In Sim Life, learning is no longer separated from life. Mathematics becomes part of trade, construction, timing, budgeting, and verification. Language becomes part of reporting, storytelling, negotiation, and performance. Music becomes part of rhythm, cooperation, emotion, and cultural expression.

Children gradually discover that learning is not merely preparation for life:

learning itself becomes part of living.

In Chinese culture, calling someone “a stone” often implies that the person is emotionally numb, unable to feel or respond deeply.

One of the most remarkable legends in Chinese literature begins with such a stone.

In Dream of the Red Chamber (Hong Lou Meng), a stone was once refined by great masters and became spiritually awakened. Yet it failed to fulfill its original purpose of repairing the sky, and was left unused on a barren mountain for thousands of years.

Later, two masters encountered the stone. They gave it a name so it could be recognized, and brought it down into the human world to experience life.

What makes the story extraordinary is that, after entering the human world and experiencing love, loss, relationships, suffering, longing, and awakening, the stone eventually wrote a book.

That book became one of the greatest classics in Chinese literature:

Dream of the Red Chamber.

For Arco, this story became a powerful metaphor for education. Education is not merely the transmission of knowledge. It is the awakening of feeling. It is helping a child move from being untouched, unnamed, and unused, toward becoming someone who can feel, understand, respond, and finally tell the story of life.

In this sense, Sim Life is a way of bringing learning “down to earth.” Children do not merely study life from a distance. They enter situations, assume roles, experience relationships, face choices, and gradually learn what it means to live.

In Arco classrooms, a Sim Life lesson often began with one simple phrase from the teacher:

“Sim Life.”

Children would immediately ask:

“What are we playing?”

Here, “playing” did not mean entertainment alone. It meant entering a role, performing a life situation, and becoming part of a story.

Sometimes the teacher began simply by telling a story. Without being formally assigned, children would quietly step forward and become actors, taking up roles as the story unfolded. They did not know how the story would develop, but that did not matter. They enjoyed the act of simulation itself — becoming part of the world being created.

Context is therefore a crucial gateway in Sim Life. It may be close at hand, drawn from daily life, or it may be distant: thousands of years in the past, far away in another land, or even in a heavenly court.

When context comes first, even ancient language becomes accessible. In some lessons, as the teacher told a story and children acted it out, idioms were thrown into the unfolding situation. Children who might not have understood those idioms in isolation could immediately point to the correct phrase from an idiom list, recognizing where it belonged in the story.

The meaning did not begin with definition.
It began with situation.

The Stone: Being Named, Being Recognized

In Chinese, when someone is described as “a stone,” it often suggests a person without feeling, someone who does not easily respond to the world.

Yet Dream of the Red Chamber begins with a stone that gradually becomes capable of feeling.

This stone was once refined by great masters, but because it failed to repair the sky, it was left unused on a barren mountain for thousands of years. Later, two masters encountered it. They gave it a name, so it could be recognized, and brought it down into the human world to experience life.

This moment of naming is important.

A nameless stone is only a stone.
Once it is recognized, it becomes the stone—the stone with a story, a destiny, and a path into the human world.

In this sense, even the article matters.
Education also moves children from being one among many, unseen and unnamed, toward becoming someone recognized:

not merely a child,
but the child whose story, gift, and calling can be seen.

This is why Sim Life begins with context and role.
A child enters a story, receives a position, and begins to be recognized.
Only then can learning move from information to experience, and from experience to realization.

In this Sim Life mathematics lesson, Dream of the Red Chamber became the narrative thread through which children entered the concept of the number line. Rather than beginning with an abstract diagram, the lesson began with a stone.

The stone had remained on the Great Waste Mountain for thousands of years. It had a position, a direction, a distance, and a story. As children began asking:

• Where is the stone?
• Where did it come from?
• Where is it going?
• How long has it waited?

they were already entering the essential structure of the number line.

At this point, the teacher gradually introduced the elements of the number line:

• a starting point
• a direction
• a unit of measurement

The number line was no longer merely a line on paper. It became a representation of position, movement, distance, and time.

Children therefore encountered the stone through the number line, and encountered the number line through the stone. Mathematics was no longer separated from life, but became a language for understanding journeys, relationships, and existence itself.

The figure may be introduced as follows:

Figure 1. The Number Line as a Journey of the Stone

The figure shows a horizontal line with three essential elements: starting point, direction, and unit. These are not introduced as abstract mathematical terms alone, but as elements of the stone’s journey.

In the story, the stone was left on the Great Waste Mountain for thousands of years. It did not know how long it had waited. What it did know was the rhythm of each day: at sunrise, the tide rose until it was full, then slowly fell; at sunset, the tide rose again, and again slowly fell.

This became the entrance into the mathematical idea of number lines.

Children first observed the time line:
from 0 to 23, hour by hour across a day.

They then observed the tide line:
the water level rising from 0 to 6, then falling from 6 back to 0.

One line represented time.
The other represented space.

Through the stone’s long waiting, the abstract idea of a number line became visible. Time was no longer an empty sequence of numbers, and height was no longer an isolated measurement. The children could see how two number lines might meet: one moving horizontally through time, the other rising and falling vertically through space.

At Arco, instructional units were not primarily organized as lesson plans, but as activity designs. The purpose of these designs was not simply to deliver knowledge, but to awaken situations.

In conventional instruction, teaching often begins with concepts and explanations. In Sim Life, learning begins with context, rhythm, roles, relationships, and experience. Knowledge does not knock on the door first; the situation does.

Children first enter a world.
Only afterward do they begin to recognize its structures.

Thus, an activity design is not merely a sequence of tasks. It is the design of an awakening.

From this foundation, Sim Life gradually expanded into different professions and social roles.

Children did not merely study occupations from textbooks. They entered situations and became participants within them. A marketplace required shopkeepers, customers, accountants, and reporters. A hospital required doctors, nurses, patients, and caregivers. A research center required investigators, presenters, and evaluators.

Context naturally brought children into roles, and roles naturally brought them into qualifications.

A child who wished to become a shopkeeper needed to calculate correctly.
A child who wished to become a reporter needed to ask meaningful questions.
A child who wished to become a researcher needed to verify evidence before presenting conclusions.

In this way, qualifications were no longer external requirements imposed by teachers. They became meaningful abilities connected to participation and responsibility within the simulated world.

In Sim Life, television stations and newspapers became important learning environments. These settings required children to become young anchors and young reporters — two forms of training considered essential for Arco students.

Young anchors learned to observe events, identify key points, organize information, and communicate clearly before an audience. Young reporters learned to prepare questions, interview experts, verify understanding, and reconstruct meaning through dialogue.

These activities also cultivated the ability of Commitment within the CHARACTER decoding system: the ability to distinguish essentials from distractions. Children learned to identify what truly mattered, remove unnecessary details, and gradually form their own viewpoints.

Thus, media roles in Sim Life were not extracurricular activities. They were part of the core training through which children learned how to observe, interpret, organize, and express the world around them.

Beyond media roles, Sim Life designed many professions according to the abilities required in different intelligence domains.

An architect needed to see the structure within a drawing.
A musician needed to hear the rise and fall of spoken language.
A comforter needed to listen actively, ask meaningful questions, and help the speaker untie emotional knots.
A politician needed to recognize responsibility, judge situations, and make decisions.

Most Sim Life activities were designed from mathematics curriculum indicators. Different professions were created so that children could enter real-world roles and solve problems through different media.

In this way, ability was no longer an abstract requirement. It became a qualification for participation.

These five mathematical laws became foundational structures within Arco’s Sim Life mathematics curriculum.

The Identity Law helped children recognize that quantity and structure may remain the same even when objects change position or arrangement. Through moving blocks, beads, or patterns, children gradually sensed:

“The outside changed, but the quantity stayed the same.”

The Zero Law helped children understand that emptiness is also part of structure. When all objects disappeared, children began to recognize that “nothing” was not chaos, but a return to zero.

The Commutative Law allowed children to experience how rearranging order could make structures easier to process. By reorganizing cards and regrouping quantities, children discovered that changing sequence could simplify thinking without changing results.

The Associative Law further developed regrouping. Children learned to reorganize quantities into more manageable structures, often combining numbers that formed ten first. They began to feel that structure could be redesigned to support understanding.

For children, the distributive law was often experienced not as an abstract algebraic principle, but as the familiar act of making change.

When solving:

$99\times7=7\times(100-1)=700-7=693$99×7=7×(100−1)=700−7=693

children could immediately “see through” the structure because it resembled the logic of cashiers repeatedly giving change in Sim Life shops. Instead of calculating 99 directly, they naturally decomposed it into “100 minus 1,” then redistributed the operation.

Because of Sim Life, mathematics lessons at Arco could extend far beyond conventional textbook exercises.

In one activity, children running a fruit shop needed to record orders containing twenty different items. Using four rhythmic cards, children created different fruits through rhythm patterns, allowing them to experience how information and quantities could be recorded symbolically.

In another activity, young accountants needed to calculate the total of twenty transactions, even though they had not yet formally learned arithmetic notation. Each child received twenty playing cards along with ten-unit coins. Rather than writing equations directly, children searched for “friends of ten” — combinations that could form ten as a unit.

Gradually, children began reorganizing quantities into groups of ten in order to simplify calculation. Long before formal arithmetic expressions were introduced, they were already experiencing grouping, place value, and structural reorganization through meaningful activity.

Interestingly, children often preferred activities involving many items rather than fewer ones. The increasing mathematical complexity did not discourage them; instead, it fascinated them.

As the number of transactions grew, children became increasingly absorbed in discovering patterns, reorganizing quantities, and finding more efficient structures. The depth of the mathematics itself became engaging.

Rather than experiencing mathematics as repetitive drill, children experienced it as the pleasure of seeing through complexity.

At Arco, mathematics was understood as a language that allows human beings to communicate precisely with nature.

Sim Life therefore required children to use their own measuring tools to investigate the environment and discover where mathematics existed within lived reality.

When planning vegetable gardens, for example, children used ropes to divide planting areas into sections. They were not allowed to label plots with names. Instead, they needed to identify locations mathematically.

As children attempted to describe positions precisely, coordinate systems emerged naturally. Mathematics was no longer introduced first as symbolic abstraction, but as a necessary language for identifying, measuring, organizing, and communicating the world around them.

At Arco, mathematics always required verification. Answers were not considered complete until children could confirm them through another representation or structure.

For example, an arithmetic expression such as:

$4\times2=8$4×2=8

was not verified only numerically. Children were also asked to verify it geometrically by constructing the relationship on a hundred grid or with square units.

Similarly, inequalities involving square roots were explored visually and spatially. For example:

$\sqrt{5}>2$5​>2

Children verified the relationship through chessboards or square constructions, discovering that a square with area 5 must have a side length slightly greater than 2.

Thus, mathematical understanding did not remain within symbolic manipulation alone. Different representations — numerical, geometric, spatial, and embodied — were used to verify one another. Verification therefore became part of the culture of mathematical thinking rather than merely the checking of answers.