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Whether we embrace math or not, humans have a tendency to think in patterns, quantify, and make logical connections. Some even say we have a mathematical mind! Young children also have this innate ability and inclination, so in Montessori, we take advantage of this propensity for mathematical thinking and offer learning experiences that provide an in-depth understanding of math even at a young age. Organized into six general groups, the mathematical exercises in the Children’s House span from a foundational understanding of the numbers one to ten, to working with very large numbers and place value within our decimal system, to internalizing number facts, and even early work with fractions! Numbers 1 to 10 Although learning the numbers 1 to 10 sounds simple, it actually involves the integration of several distinct concepts. The beauty of the Montessori materials is that they isolate each separate concept so that children’s understanding grows in progressive steps. This first group of exercises in the Children’s House aims to teach the names, symbols, quantities, and sequence for the numbers 1 through 10. The youngest children first use the number rods, which are color-coded with alternating red and blue sections to designate the quantities of one through ten. As children work with the number rods, they solidify the concept of quantity as a single entity while also practicing one-to-one correspondence. The sandpaper numbers help children learn the symbolic representation of numbers. After children master the sandpaper numbers and can easily identify numerals, we help them connect the number cards with the corresponding number rods. Additional materials–like the spindle boxes, cards and counters, and the memory game–help children progress from understanding quantity as a single entity to grasping how quantity can be a set. Throughout this progression, we offer experiential exercises to help children learn the concepts of addition, subtraction, multiplication, and division. At this stage, we don’t provide the vocabulary but rather give an impression of the concept of each operation. The Decimal System Once children have mastered the numbers 1 to 10 activities, they are ready to begin exercises with the golden beads. Because there are never more than nine in a given place value, and children already know the quantities and the symbols, they are ready to learn the hierarchy of units, tens, hundreds, and thousands. As children set up the golden beads, the primary decimal system materials, they learn how to think through the process of each operation and the concepts of calculation. Are they putting quantities together or taking them apart and recounting the categories? The decimal system work gives children knowledge of the mathematical processes and solidifies their understanding of the mechanics of the decimal system. We focus on helping children understand the process of each operation. We aren’t looking for the right answer. We want the child to understand the operations and what adding, multiplying, dividing, or subtracting means. After children understand the operations with the golden beads, we offer other materials, such as the stamp game and dot game, to help them move away from a very concrete toward a more symbolic representation of the quantities. We offer word problems at the end of this series, which help verify whether children understand each operation's process. Continuation of Counting Through this group of exercises, children learn the name, symbol, and quantity of the numbers from 11 to 100, and consolidate linear counting up to 1,000. The work starts with the teen boards (11 through 19) and tens boards (20 to 100). We also introduce the colored bead stair, which gives a color-coded sensorial representation for quantities of one through ten, a pattern replicated throughout the Montessori math materials. With the golden beads, children experience the difference between 100 and 1,000, by weight and geometrical representation. In continuation of counting, children lay out the bead chains and see the dramatic linear difference between 100 and 1,000. Children also use the bead chains to practice skip counting, which lays the foundation for further studies in multiplication. We also make sure there is lots of counting in the classroom! Children can be taught to count by rote, but mental maturity helps them take the leap from rote counting to understanding quantities represented by numbers. Exploration and Memorization of the Tables Through a variety of materials–the addition strip board, addition snake game, subtraction strip board, subtraction snake game, multiplication bead board, bead bars, and unit division board–children have lots and lots of practice with the essential math facts. This concrete exploration establishes a visual understanding of what something like 5 x 6 looks like and helps children establish early neural pathways for memorizing these math facts. After children use different forms of bead material to practice, they move into more abstract representations of quantity and eventually even use blank charts to test their memory. All of the repetition in this exploration phase leads to memorization as children become aware of which combinations they know and which they don’t know. Eventually, after a lot of practice and repetition, children realize that it is faster to do the calculations mentally rather than with the materials. As children reach the end of their primary years, they want to be more efficient. At precisely this point, they are ready to begin the last group of exercises, called the passage to abstraction. Passage to Abstraction In the exercises for passage to abstraction, children connect the skills and concepts from the previous strands of learning, and their knowledge base shifts from understanding the concepts experientially to understanding them logically. With the small bead frame, children revisit the process of addition and subtraction. With the wooden hierarchy material, children get a sensorial and symbolic introduction to the quantities ten thousand, one hundred thousand, and one million. This material also prepares children for the large bead frame and experiencing the multiplication of large numbers with a single-digit multiplier. The racks and tubes material allows children to begin dividing with larger divisors and dividends. With all of this concrete experience working with larger quantities, children are well on their path to abstraction. Fractions The final material in the mathematical progression is fractions. In the Children’s House, we have already helped the youngest children explore fractions sensorially. They return to this material from a mathematical perspective to understand quantities smaller than one unit. In addition, children begin simple operations with the fraction material and start to explore the equivalence of fractions. In the Children’s House, the progression we use for all of these exercises helps children deeply solidify their mathematical understanding. We first ensure children have strong concrete experiences, followed by more symbolic representations. After children associate the concrete and the abstract, we offer lots of activities for practice, repetition, and verification. In the process, we support children’s growth in classification, comparison, and reasoning. We invite you to come see children’s mathematical minds in action. Schedule a tour today!

Most of us have had the experience of a child walking into the room and proclaiming, with exasperation and desperation, “I’m bored!” Without even thinking, we begin to offer suggestions. Despite our best intentions, this situation tends to not end well. Our brilliant ideas are often quickly refuted. We feel frustrated. Our children haven’t engaged. And we’ve missed an opportunity to help our children take responsibility. What Does it Mean to “Own the Problem”? It helps to think proactively about how to respond when our children face problems, choices, or situations. These aren’t necessarily the big issues, but rather daily moments that can help our children learn important coping skills that will be crucial in their lives. At its core, figuring out who owns the problem is about determining whether we or our children are the ones who are primarily responsible for addressing an issue. For example, when our children forget to bring something to school (a coat, gym shoes, snack, etc.), it’s their problem to own and solve because they are directly impacted. Plus, they are also capable of problem-solving (e.g. borrowing a coat, talking to their teacher, asking if there is any food they can have for a snack). Owning the problem helps children take more responsibility and learn from their mistakes. Whereas, if we rush to their rescue and bring anything that was left at home, our children learn that remembering to bring essential items isn’t really important because we take care of covering for them. The Challenges However, watching our children struggle can be heart-wrenching. We don’t like to see our children upset, in pain, or even frustrated. Often, without even thinking, we jump in and try to protect our children from whatever problem, conflict, or challenge they are experiencing. In addition to this urge to rescue, we may also experience time constraints, diminishing patience, worry about how others will perceive the situation, doubts about our children’s capability, and even pushback from our children. It may seem faster to tie our children’s shoes or clean their messy room than to wait for them to do it themselves. We may worry that our children won’t meet expectations with a school project or that teachers, other parents, or extended family members will judge the results if we don’t help. Or maybe we aren’t sure that our children will make the “right” decision or if our children are mature or skilled enough to handle a situation. We may even feel guilty about allowing our children to face the natural consequences of their actions, even though it’s a necessary part of learning. The Value All problems have owners. Being thoughtful about who owns the problem helps create a clear boundary between guiding our children and taking over their challenges, which is crucial for raising independent, confident, and capable individuals. If we take the time to think ahead about specific (and even recurring) situations, we can be prepared to empower our children to take ownership of the challenges they face, rather than automatically intervening. It’s also important to remember that if we regularly take ownership of our children’s problems, we are inadvertently teaching our children that they are not capable. The result? Our children grow more needy and dependent on (and sometimes even more demanding of) adults. If our children own the problem, we can let them handle the problem and provide support as necessary. This is a growth opportunity for us and our children! Steps to Take The next time our children express frustration or emotion in response to a problem they own, we can try a simple, three-step response. Tell them what we see When our children approach us, consider using detective skills to determine what emotion is at play. “It looks like you don’t know what to do right now,” or “It looks like you are disappointed,” or “It looks like you are feeling sad.” This simple first step provides acknowledgment and helps children accept that their feelings are normal and acceptable. For younger children, this also helps them learn to identify different emotions. In addition to validating our children’s feelings, active listening shows empathy and helps us avoid jumping to solutions. For example, if the upset is about an interaction with a friend, we can try saying something like, “That sounds really frustrating. Tell me more about what happened." Ask them what they can do Next, we can act as a coach rather than trying to provide solutions. This requires listening closely to determine the root cause of their problem and helping them come up with a solution (without doing it for them). For example, if facing the “I’m bored” statement, we can ask questions, “What do you think you could do on your own so that you would feel busy?” Even if they respond by saying, “I don’t know,” we can continue to focus on their ability to think through possibilities. Sometimes, even just replying with something like, “make believe you know,” grants them permission to use their imagination. Additional types of questions to have mentally prepared can include: “What do you think you could do to fix this?” “How do you think _____ might react if you explain?” “What’s the first step you could take?” Offer to help if appropriate Once our children have come up with a solution to their problem, we can offer to help without taking over and implementing the solution for them. Sometimes our children might need support with generating ideas. It’s okay to brainstorm together, which is different than trying to come up with solutions for them. If we do offer brainstorming support, it’s important to let our children choose the best course of action. For example, if the problem revolves around forgetting to bring something to school, we can help with some scaffolding, “Let’s think of ways you have remembered to bring your instrument for band. What’s one technique you’ve used before that worked well?” We can also offer support by providing access to tools or resources. For example, if the struggle involves organization, we can offer to provide a calendar or checklist and teach our children how to use this tool rather than organizing their assignments or chores for them. Role-playing can also sometimes help children practice the solution they’ve identified. Ultimately, we want to set clear exceptions by letting our children know what is expected and giving them the responsibility to follow through. Asking what their plan is is a great way to shift the focus to their ability to solve the problem. The best part is that the more often we allow our children to solve their own problems, the more capable they become. Are you curious to learn more about supporting children’s emerging sense of responsibility? Come visit our school!

Almost 120 years ago, when Dr. Maria Montessori created the first Children’s Houses in the slums of Rome, she saw a curious phenomenon. Young children, who not that long before had been considered street urchins, developed a sense of pride in their work and soon were eager to read and write. In fact, Dr. Montessori tells a story about how the children and their parents begged her to teach them writing and reading, despite the fact that, at the time society didn’t think that children under six were capable of this type of learning. Then Dr. Montessori did what she did so well: she observed the children, she identified what skills they needed, and she provided opportunities for the children to develop. The result? Dr. Montessori saw what she described as an “explosion” into writing and reading. In Montessori, we support children’s progression (and “explosion”!) in three aspects of language development: spoken language, written expression, and interpretive reading. Spoken Language Because spoken language is the foundation for all work in the language area, we offer rich, full, and beautiful language for young children through a variety of activities to cultivate conversation skills. Our enrichment of vocabulary exercises focus directly on expanding children’s receptive vocabularies and cultivating children’s experience and intelligence. As we engage children in language games, we also help increase their listening skills as well as their comprehension. As part of spoken language development, we also take the time to listen to children’s own spontaneous efforts of expression, so that they gain confidence in speaking and feel that their thoughts have meaning. Written Expression The act of writing consists of two separate elements: composing and recording. Composing is the mental work–thinking about what to say. Recording is the physical aspect of writing. In the Children’s House, we prepare these two elements separately by offering exercises to prepare the hand for recording and exercises to prepare the mind for composing. Writing is having a known thought that goes from sound to symbol, a process that is much easier than the process of reading. Because the development of the hand takes longer than the development of the mind, we use a material called the movable alphabet as a way for children to compose words before their hands are ready to write. The movable alphabet is a box containing the letters of the alphabet, essentially the building blocks of all the sounds in our language. Interpretive Reading In Montessori environments, unlike many traditional settings, reading is introduced after writing because the process of reading is cognitively more difficult. Writing is essentially an expression of thought. When we write something, we know what we are writing. When we read something, we don’t know what the author was communicating so we have to take the symbols, match sounds to them, blend them together, and then attach meaning to them. This is much harder to do. While the hand needs to be prepared for writing, the eye must be prepared for reading. This includes being able to follow a left to right, top to bottom progression across the page. In addition, the eye must recognize that the symbols in our language are lines creating a shape. So we have lots of activities with the geometry cabinet, as well as other sensorial materials, to prepare children for this visual discrimination. We also use the sandpaper letters to introduce the phonemes of language through three senses: tactile, visual, and auditory. Through games with the sandpaper letters, children get to practice the trace of the letter through gross motor movement of the whole arm and hand, see the shape, and associate the letter sound with its shape and their own movement. Once children progress from reading words (mostly nouns), to reading phrases and finally sentences and paragraphs, we offer activities to highlight how different words have different functions. These exercises also highlight the syntax or order of words (e.g. adjectives tend to come before the noun they are describing). Another set of exercises, called reading analysis, highlights the role or the order of parts of a sentence. In the process of understanding the components of our language, children are better able to interpret what the author is writing. The Pattern of Human Language Development The progression that young children go through – spoken language to written expression to interpretive reading – follows the pattern of early human language development. Early humans began with spoken language, then advanced into forms of writing (think of the first cave paintings and picture writing), and later moved into reading as a way to interpret the thoughts of others. How amazing that our young children do the same in a matter of years from birth to age six! One of the joys of the Montessori learning environment is how language learning is woven into all aspects of the children’s experience. When we present dusting, for example, we model a left to right, top to bottom pattern, which prepares the eye for tracking words on a page. When children use sensorial touch tablets and the rough and smooth boards, they develop lightness of touch and a relaxed hand necessary for writing. Every time children grasp a knob of the knobbed cylinders, they prepare their hand for holding a writing instrument. Through the sound game, children become aware of the fact that words are made of sounds and they begin to identify all of the sounds in a word and place them in order. Through the sandpaper letters and sandpaper phonograms, children associate the sounds of our language with their symbols. This is exciting work for the children because not only can they see the isolated symbols, but they can touch them, too! Through the moveable alphabet, children are able to write their thoughts even before their hand is ready to control a pencil. The genius of the Montessori approach is that it breaks down individual skills and abilities so that children can practice them in isolation. So by the time children have mastered these individual skills, they seem to spontaneously know how to write or know how to read. Once this explosion into writing and reading has occurred, then children are excited to refine their writing and access worlds of knowledge through reading. A new journey of discovery and learning begins. We invite you to visit the school to learn more about the “explosion” in language development and the joyous journey that unfolds!

Do you ever feel annoyed by throw-away apologies? So often, our children pick up the habit of tossing out “I’m sorry” like a used tissue. Completely overused, the expression begins to feel devoid of worth. They speak the words, but it seems like they don’t actually feel a sense of remorse or regret, much less a desire to make amends. In Montessori, we don’t insist that children apologize, especially right at the tail end of a heated moment. For goodness' sake, think about when we, as adults, are tired or hungry or stressed and make a snarky comment. We’re not usually feeling particularly sorry – more like ticked off and cranky! Later, after we’ve had time to take some deep breaths, or perhaps tend to low blood sugar, we often feel a deep sense of regret and desire to make things right. Because our children tend to replicate what they see in us, it helps if we decide to first make sure we aren’t just using “sorry” as an easy way out. To really model a different approach, it helps to use the framework of the “Three R’s of Recovery” from Positive Discipline. The Three R’s of Recovery When we make mistakes, we have an opportunity to make amends and even learn from the experience. In Jane Nelson’s Positive Discipline work, the “Three R’s of Recovery” offer steps to follow after calming down. The first R stands for recognize , and with this, we verbally acknowledge our mistake and take responsibility for our actions. To do this effectively, we must also be sure to keep any hint of blame out of the picture. So if we’ve snapped at our children and later cooled off, we might say something like, “I feel really bad about when I snapped at you. You don’t deserve to be treated that way.” Notice that these statements don’t weave in any know-it-all finger-wagging about things they did to push our buttons. Rather than blaming, we take responsibility for the choice we made in the moment. Next, we can reconcile by apologizing. This can be as simple as just saying, “I’m sorry.” When we’ve really taken responsibility, the reconciliation comes from a genuine and heartfelt place. And children are so forgiving and understanding. Perhaps we could learn a few things from them in this regard! Finally, the third R is for when we resolve the problem. At this point, we work together to find a respectful solution. After taking responsibility and reconciling, everyone often feels open and willing to collaborate. If the time isn’t right for a brainstorming session, it’s important to set and stick to a later date for problem-solving. When allowed to share ideas in a safe, respectful forum, children often can help come up with incredibly creative solutions. The Benefits When we try putting the “Three R’s of Recovery” into practice, our children are often able to be more mindful after their less-than-ideal moments. Our mistakes become less about what we did wrong and more about the kind of people we want to be. Because mistakes are an opportunity to learn and grow, our relationships with our children often grow stronger as we practice recognizing, reconciling, and resolving together. Mutual respect increases, and trust in each other becomes stronger. The Positive Discipline approach dovetails nicely with Montessori principles and practice. We’d love for you to visit our school to learn more. Contact us to schedule a tour!