Academic Materials Explained: The Flat Bead Frame
Rebecca Lingo • December 1, 2025

The Flat Bead Frame is one of the most elegant bridges between the concrete and the abstract in our math curriculum here. Your children work with very large numbers on this academic material, up to the hundreds of millions, while still manipulating tangible representations of each place value.


Unlike many elementary materials designed for group exploration, this work is typically done individually or with a partner amid the classroom’s collaborative hum.


From the Large Bead Frame to the Flat Bead Frame


At a glance, this material may look similar to the Large Bead Frame that your children used during Kindergarten and early elementary grades at Wheaton Montessori School, but it represents a meaningful step forward in abstraction. The earlier frame is color-coded, with distinct beads that highlight the different periods of the decimal system. That approach reinforces the structure of tens, hundreds, thousands, and beyond.


The Flat Bead Frame, however, shifts the work in a quiet but powerful way. Its nine vertical columns of identical golden beads represent units through one hundred million. The categories are written across the top, and red zeros along the bottom show the multiplication patterns that come with each new place value. The golden beads signal something important: your child is ready to move from concrete color-coding toward pure numerical understanding.


Introducing the Material


When our teachers introduce this material, they begin by reviewing everything your child already knows as a foundation. It is both a continuation and a moment of assessment. Your child notices what is familiar and what is new: the vertical layout, the placement of numbers, the red zeros, and the uniform golden beads. The known supports the new. This careful transition is one of the qualities that make education in this school so effective.


Moving Toward Abstraction


The Flat Bead Frame is used to explore long multiplication and multiplication by powers of ten. When the multiplier involves tens, hundreds, or thousands, your child learns to shift the multiplicand to the left. The red zeros at the base make this idea visible. What can feel like a memorized rule in conventional public and private schools becomes something your child can see and feel. They understand why the number moves, not just that they are supposed to write an extra zero.


A Continuation of Pre-Kindergarten Foundations


This material builds on the work with the Golden Beads that your children experienced at younger ages, when they learned to exchange ten units for one ten, ten tens for one hundred, and so on. The Flat Bead Frame requires concentration, accuracy, and an understanding of the relationships between categories. These qualities from their preschool years help build the foundation for true mathematical abstraction.


The Mathematical Mind in Motion


Through this work, your children reinforce multiplication facts, internalize the commutative law, and become comfortable working with very large quantities. More importantly, they continue to see that mathematics follows a clear and consistent logic that they can and do understand. They gain the sense that numbers are not something to memorize for a test, but something they can work with, reason through, and take pride in mastering at a challenging pace that is right for them.


This is education that respects each human mind. At Wheaton Montessori School, we believe that the hand helps develop the intellect, and as your children move the golden beads across the frame, their understanding of place value deepens along with their confidence. Your children are not just learning math. They are learning how to think.


Come see how what begins as a physical exercise in moving beads becomes, over time, a quiet revelation and a process of mathematical thinking. This is Montessori math at its best!


You’re invited!


What: Open House
When:
Thursday, January 15, 2026, 6:00 p.m.

Explore our academic curriculum, from early childhood through the freshman year of high school, and connect with our expert teachers and school community. Tour our campus, natural playscape, and conservation areas.

Current families with children of all ages RSVP:

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Prospective Families with children ages 4 ½ and under* RSVP:

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*2026 Summer and Fall Openings
Openings are available only for new students under 4½ years of age and for current students to re-enroll. The waitlist for the
2025–2026 school year (kindergarten through freshman year of high school) is closed. Exceptions may be considered for students transferring from AMI-accredited Montessori schools with continuous attendance.


Students in classroom with headline
By Kelly Jonelis, Adolescent Program Director and Math Teacher January 12, 2026
Where Learning Supports Who They Become Inspired by the Deep Dive on Psycho-Disciplines by David Kahn and Michael Waski In Wheaton Montessori School’s Adolescent Program, learning is more than content acquisition; it is a Psycho-discipline. A psycho-discipline is the connection of each discipline to the psychology of the developing human. When children and adolescents engage in subjects in a way that aligns with their psychology and developmental needs, the learning becomes internalized, and since discipline's root meaning is connected to “accepting with love”, they are supported to love learning. At Wheaton Montessori School, every subject your adolescent studies, from math, science, language, and literature to economics, morality, and culture, is intentionally crafted to support who they are becoming. We don’t teach disciplines simply to transmit facts. We use the subjects of humanities, math, social sciences, language, and sciences to strengthen your adolescent’s confidence, character, and capacity to participate meaningfully in society. This approach is deeply rooted in the Montessori work of David Kahn and Michael Waski, both pioneers of adolescent training programs and adolescent psyche work. They describe these subjects as psycho-disciplines. Psycho-discipline can be defined as the order necessary for self-construction. When children and adolescents engage with subjects in a way that aligns with their psychology and developmental needs, the learning becomes internalized. It becomes part of your children and adolescents. And when the curriculum is deeply connected and part of each individual, the result is self-construction that is whole, complete, interdisciplinary, and integrated. Wheaton Montessori School staff are trained to understand and respond to developmental needs and to aid your children and adolescents in loving to learn across the curriculum. We do this for adolescents by connecting the academic topics we cover to real-life applications that are meaningful and relatable for the student. Rather than teaching facts and skills in a silo “just in case” students may need them, we first present students with meaningful context and then move to presenting lessons that give them the tools they need to engage with that context, “just in time.” Psycho-disciplines: • Engage intellect and emotion • Build purpose through real work • Support the drive for belonging and contribution • Empower independent thought connected to others • Spark passion and identity formation Your adolescents learn to navigate complexity by applying their advanced knowledge to real needs. They learn academics best and enjoy them most when they use what they know to strengthen their community and improve the world. This applies whether they are solving problems that arise within their immediate environment or finding opportunities to serve the broader local community. At Wheaton Montessori School, 7 th -9 th graders engage in learning that is meaningful to them. They begin with recognizing authentic needs around them, extending the growing season in their gardens, keeping their chickens and bees healthy through the year, and then working to address those needs. When we provide the “big picture” first, students enter academic lessons with a clear understanding of why the content matters. Instead of teaching unit conversions or graphing equations in isolation and waiting for the question, “When am I ever going to use this?”, we begin with harvesting honey and ask, “What do we need to know to bottle and sell this honey? How do we determine the right price?” This is psycho-disciplines in action. Thermodynamics becomes relevant as students prepare their beehives for winter. Through this work, your adolescents also come to understand their value and place in the broader adult community, whether they are partnering with organizations such as People’s Resource Center or volunteering at Northern Illinois Food Bank. Learning through psycho-disciplines supports who adolescents are becoming and engages the work of the hand, head, and heart. Wheaton Montessori School adolescents don’t learn by memorizing facts, but by engaging and immersing themselves in meaningful work. This provides the means to learn lessons that speak to who the students are and to stick with them for a lifetime. Why Learning with Purpose Your adolescents are forming their adult identity right now. They are asking: How do I contribute? Where do I belong? Why does this matter? At Wheaton Montessori School, psycho-disciplines answer those questions through: • Meaningful collaboration • Real-world application • Guidance from experts and highly skilled mentors • Leadership and ownership • Choice and autonomy Instead of prioritizing the mere transmission of knowledge, we open the doors to further study and provide the order necessary for the formation of maturity and self-respect.
Children at tables, parents interacting, Montessori school setting. Title: Lighthouse Parenting.
By Christine McClelland and Rebecca Lingo January 5, 2026
Lighthouse Parenting helps children navigate life with guidance and freedom, building the skills and confidence to grow into resilient, independent individuals.