Our Montessori Bookshelf: Mathematical Thinking

Montessori education has been in existence for over a century, but does it actually work? Dr. Angeline Stoll Lillard spent years researching this question, and her book, Montessori: The Science Behind the Genius, is a must-read. In her book, Dr. Lillard identifies eight principles at the heart of Montessori education. What’s key is that these Montessori principles align with what developmental science tells us about how humans actually learn. The remarkable thing is that Dr. Maria Montessori arrived at most of these insights through careful observation of children, decades before the research existed to corroborate how children learn. In this two-part blog post, we’ll examine these eight principles and the connected research. PRINCIPLE ONE: Movement and Learning Are Deeply Entwined In most traditional classrooms, children are still expected to sit still, as if stillness is a prerequisite for learning. In Montessori, we understand how movement and thinking are intertwined. And research backs this up. Studies have found that physical activity improves cognition, judgment, memory, and social reasoning. Moving the body isn't a break from learning. Rather, the movement is often the learning (and this is even more so for younger children!). Montessori materials are designed to be touched, carried, sorted, and manipulated. Children working with the knobbed cylinder blocks are actively perceiving, making judgments, and reasoning through their hands. The same is true when children sort fabric squares by texture, shake and compare sound cylinders, or lay out bead bars to represent quantities. Every material helps children integrate their minds and bodies. Practical life activities take this even further. When children learn to pour, button, fold, or prepare food, they are engaging in organized sequences of purposeful action that develop concentration and executive function skills. What the Research Shows A Milwaukee study found that high school students who had previously attended Montessori programs significantly outperformed peers on math and science assessments, subjects that rely heavily on the kind of reasoning that, in Montessori, is first built through hands-on materials. PRINCIPLE TWO: Choice Improves Both Learning and Well-Being The freedom to choose is at the heart of Montessori education, but this isn’t just about enjoyment. Having choice measurably affects how well children learn and how they feel about themselves. In a striking series of studies, children aged seven to nine were given anagram puzzles to solve. Those who chose their own category of puzzle solved twice as many as children whose category had been chosen for them, even though the actual puzzles were identical. Those who had a choice also spent far more time voluntarily working on puzzles during free time. The key finding is that the perception of control (even in small things) activates a fundamentally different relationship to the work. Children who feel in control tend to engage more deeply, persist longer, and take more ownership of their learning. In a Montessori classroom, children choose their own work throughout the day. Importantly, Dr. Lillard notes that this freedom is always paired with responsibility, and that too many choices can be as demotivating as none. The Montessori environment offers meaningful, bounded choice. Rather than an overwhelming array, each classroom has a selection of purposeful materials designed to match children’s developmental readiness. Choice and concentration are closely connected, too. When children choose work that genuinely engages them, they're far more likely to reach a deep state of focus, or what psychologists call a “flow state.” PRINCIPLE THREE: Children Learn Best When They're Genuinely Interested This sounds obvious, of course! It makes sense that we learn better when we are interested. However, think about this in terms of how classrooms are typically structured. If interest is one of the most powerful drivers of learning, then organizing a school day around a single curriculum delivered to the whole class at once works against almost every child in the room. Dr. Montessori understood children's interests as biological signals pointing toward what their developing minds most need to engage with at that moment in their lives. These windows of opportunity, or "sensitive periods,” are particular stretches of development during which children are uniquely primed to absorb certain kinds of learning. During these windows, learning that matches the child's inner readiness can be extraordinarily effortless and lasting. The role of interest is why Montessori materials are designed to be beautiful, engaging, and self-correcting. The sensorial materials, for example, aren't only teaching discrimination of size or color. They are designed to help children become more interested in noticing the world around them. The adult’s role is to observe carefully and offer new lessons at the moment a child's interest is most alive. PRINCIPLE FOUR: Rewards Undermine the Motivation They're Meant to Build Offering children external rewards (e.g., stickers, prizes, praise for being smart) for activities they already enjoy reliably reduces their intrinsic motivation to do those things later. What the Research Shows Researchers identified preschoolers who loved drawing with markers. They then told one group they would receive a "Good Player Award" for drawing (a fancy certificate with a gold star). Weeks later, the children who had expected the reward used the markers far less than they had before, and half as much as children who had never been offered a reward at all. Expecting a reward had turned something they loved into something they did for a prize. And when the prize was gone, so was much of the pleasure. Rewards like sticker charts, gold stars, and even grades and honor rolls, shift children’s relationship to learning from "I do this because it interests me" to "I do this to get the reward." When the reward is taken away, children’s inner drive has often already weakened. In Montessori classrooms, feedback comes through the work itself, which includes many self-correcting materials, so children discover their own errors without external judgment. The goal is to keep children's relationship to learning intrinsic, personal, and durable. This doesn't mean feedback is absent, though! What matters is the kind of feedback. Research by psychologist Carol Dweck found that praising children for effort (e.g., "you worked really hard on that”) produces dramatically better outcomes than praising ability (e.g., “you’re so smart”). Children praised for effort choose harder challenges, persist longer after failure, and actually improve their performance over time. Children praised for their intelligence begin avoiding challenges, fearing that failure will expose them as not as smart as they were told they were. In our following blog post, we’ll look at the next four Montessori principles outlined in Dr. Angeline Stoll Lillard’s book, Montessori: The Science Behind the Genius: Children Learn Powerfully from Each Other Meaningful Context Makes Learning Richer and More Lasting How Adults Interact with Children Shapes Everything Order in the Environment Supports Order in the Mind In the meantime, schedule a tour here in Old Saybrook, CT to see the principles in action! And let us know if you would like to borrow a copy of Montessori: The Science Behind the Genius by Dr. Angeline Stoll Lillard. It is one of the most research-based books on Montessori education, and we recommend it to anyone who wants to understand the deeper logic of Montessori!

In Part One of this series, we began exploring the eight Montessori principles that Dr. Angeline Stoll Lillard examines in her landmark book, Montessori: The Science Behind the Genius. As we saw, what makes these principles so compelling is that Dr. Maria Montessori's intuitions about children were a precursor to what decades of developmental science have since confirmed about how humans actually learn. In this second and final installment, we pick up where we left off, examining the remaining principles and the research that brings them to life. Whether you're a parent, an educator, or simply someone curious about what effective learning really looks like, these insights offer a fascinating window into the remarkable alignment between one woman's careful observations over a century ago and the science we have today. If you haven’t already, be sure to check out the previous four principles: Movement and Learning Are Deeply Entwined Choice Improves Both Learning and Well-Being Children Learn Best When They're Genuinely Interested Rewards Undermine the Motivation They're Meant to Build PRINCIPLE FIVE: Children Learn Powerfully from Each Other When you walk into a Montessori classroom, you’ll notice that children are almost always working near or directly with other children. Peer learning is one of the most effective forms of learning, and Montessori classrooms are deliberately structured to make it a constant. Much of this learning happens through observation. When a child watches a slightly older classmate work through challenging material, they're absorbing the technique and the possibility. They begin to see what they can do! Peer observation often drives a spontaneous "explosion" of writing or number awareness, spreading through a class (e.g., one child suddenly writing everywhere, then several more following). The mixed-age grouping in Montessori classrooms amplifies this. Younger children always have a visible horizon of what's coming next. Older children consolidate their own understanding by helping younger ones (which is one of the most effective learning strategies known). And the large, stable class community means children have time to build genuine relationships and observe one another across many contexts over several years. PRINCIPLE SIX: Meaningful Context Makes Learning Richer and More Lasting Children remember far more when what they're learning is connected to something real and purposeful. What the Research Shows In one study, three-year-olds were asked to memorize lists of items. When the lists were presented as shopping lists for a pretend store, the children remembered twice as many items as those who were simply told to memorize a list. Montessori education is built on this principle. Practical life activities such as cooking, cleaning, caring for plants and animals teach children that the skills they are learning connect to the real world. The Montessori curriculum is deliberately integrated. Vocabulary develops alongside sensorial exploration. Math concepts are entwined with concrete materials that make abstract ideas visible. Knowledge in one area consistently links to knowledge in others. This is why Montessori materials are not isolated exercises but part of a spiral curriculum that returns to the same ideas with greater depth and complexity as children grow. PRINCIPLE SEVEN: How Adults Interact with Children Shapes Everything The way an adult responds to a child's efforts has effects that ripple far beyond the moment. What the Research Shows Carol Dweck's research, now widely cited, demonstrated that a single sentence of feedback can set children on divergent trajectories. Children told "you must be smart" after succeeding at a problem later chose easier tasks, enjoyed them less, and performed worse after encountering difficulty. Children told "you must have worked hard" sought harder challenges, recovered from failure more readily, and improved their performance over time. The difference is in the delivery of one sentence! The implications are profound for how we talk to children about both their successes and their struggles. In a Montessori classroom, the adult’s role is carefully defined: to observe, to connect children to materials at the right moment, to step back when a child is productively engaged, and to step in only when something is genuinely unproductive or unsafe. This requires a great deal of precision and restraint. An adult who constantly intervenes, corrects, and directs trains children to look outward for approval. An adult who observes and offers at the right moment helps children learn to look inward. Consistency and long-term relationships also matter. The multi-age grouping in Montessori means that children spend multiple years with the same adults, building the kind of attachment and trust that research consistently links to stronger learning outcomes and healthier social-emotional development. PRINCIPLE EIGHT: Order in the Environment Supports Order in the Mind The Montessori classroom's distinctive aesthetic reflects a deep understanding of how the environment shapes cognition. What the Research Shows Research consistently shows that noise, clutter, and unpredictability are cognitively costly for children. When an environment is chaotic, children spend precious mental energy managing uncertainty rather than engaging in learning. Temporal order matters as much as spatial order. The three-hour uninterrupted work cycle (a hallmark of Montessori classrooms) gives children long enough stretches of focused time to move from initial engagement to deep concentration and, eventually, to the kind of absorbed flow that produces real intellectual development. Frequent interruptions (bells, transitions, whole-class pivots) train children to work in short bursts and to constantly reorient. The three-hour cycle allows children to go deep. Children in Montessori classrooms are also responsible for maintaining their environment by returning materials to their proper place, caring for plants and classroom spaces, and treating everything with consideration. This care builds the child's relationship to order as something they participate in creating rather than something imposed from the outside. Even noise levels matter in ways that go beyond comfort. What the Research Shows Research cited by Dr. Lillard found that across all ages, noise was one of the most consistently negative influences on cognitive development, partly because it interferes with the auditory discrimination that underpins both reading and vocabulary development. The quiet that characterizes a well-functioning Montessori classroom is the natural result of many children deeply absorbed in their own work. What makes Dr. Lillard’s work so valuable because it validates the Montessori method and gives the why behind practices that can otherwise seem puzzling from the outside. There are important reasons why Montessori teachers don't correct every error, why there are no gold stars, why the classroom is so quiet, and why children seem to do the same work over and over. This approach to education is deeply rooted in creating conditions in which children's natural drive to learn can develop as fully as possible! To learn more, visit our school here in Old Saybrook, CT. And let us know if you would like to borrow a copy of Montessori: The Science Behind the Genius by Dr. Angeline Stoll Lillard! It is one of the most research-grounded books available on Montessori education, and we highly recommend it for anyone who wants to understand the deeper logic of Montessori!