Teaching Math Conceptually

For many people, children and adults alike, mathematics is a bane to be avoided. “Math anxiety” or even “math phobia” is on the rise in elementary and high schools across the country, and perhaps as a consequence, U.S. students notoriously score very low among developed nations on international math tests.

And yet, mathematics is not an optional activity. Handling numbers is a fundamental and necessary life skill, and a prerequisite for many careers, including those in engineering, the sciences and business.

So in relation to your own child’s education, what can and should you do about the distressed state of modern mathematics? The best thing you can do is to find a math program that works. If you want your child to be comfortable with numbers, and thrive in mathematics, you need to find him or her a curriculum capable of achieving these results.

At LePort, we believe that our approach, from preschool through 8th grade, enables students to not only master crucial math skills and concepts, but to develop into young people who are confident in their ability to tackle even the most challenging mathematical problems. 

In this newsletter, we give you three highlights of our math approach. For a fuller description of our math programs, please visit the relevant pages of our web site:

The “secret” of our approach is teaching math conceptually, first starting with a sequential, targeted introduction to concrete manipulatives, then enabling mastery through deliberate, focused, motivated practice, and then allowing the experience of efficacy through the application of skills in increasingly complex, real-life problems. How does this work? And how is it different from the approaches used in other schools?

In this newsletter, I’d like to share with you three important aspects of our approach:

  • We develop real understanding by using carefully structured manipulatives, and, more generally, by always progressing from concrete to abstract in a deliberate sequence.
  • We enable each child to attain mastery of math facts, at his or own pace,before we expect him or her to apply those skills to more complex problems.
  • Once a skill is learned, we explicitly teach mathematical problem solving, and advance, rapidly, to applying the skills learned to complex, real-life, meaningful math problems.

For each of these three principles, we’ll provide an example from our program, and compare it to the program used by the Irvine Unified School District (“Math Expressions”, by Houghton Mifflin publishers.) We’ll conclude by summarizing the value our students gain from this program: an advanced conceptual knowledge of mathematics, an earned confidence in their ability to handle mathematical problems, and enjoyment, rather than dread, of math class.

  1. Building understanding using carefully structured manipulatives, with a deliberate progression from concrete materials to abstract operations. Math is the science of quantitative measurement. It enables us to deal with quantities in all aspects of our lives. At LePort, our goal is to enable our students to really get the connection between real quantities on the one hand, and mathematical symbols and processes on the other.For example, consider the topic of place value and multi-digit addition. In our preschool classes, students learn place value into the thousands, using a material that concretely demonstrates this concept. This Golden Bead material includes individual beads or single “units,” strings of ten beads or “ten bars,” ten ten-bars combined into a “hundred square,” and ten hundred squares combined into a “thousand cube.” Number cards go along with these beads, with units printed in green, tens in blue, hundreds in red, and thousands in green.

    Using these cards and beads, 4 ½ and 5-year-old children build large numbers. For instance, a teacher may create a number with the cards, such as 3,574, and ask the child to bring her the corresponding number of beads: 4 Units, 7 Ten Bars, 5 Hundred Squares and 3 Thousand Cubes. After repeated exercises of this kind, students never confuse “1,006” with “1,060” or “1,600.” They clearly understand what each number stands for, and that a “zero” stands for no number in that category, i.e., no tens or no hundreds!

    With this specially-designed material, our students go on to explore addition and subtraction into the thousands, by Kindergarten. They simply “make” two large numbers with the bead materials, and combine them, exchanging units for tens, tens for hundreds and so on. For example, when they add 3,574 and 4,267, they first take the 4 units and the 7 units, and count them up, to get 11 units. They exchange 10 of those units for a ten bar, leaving them with one unit. Next, they add the 7 ten-bars, 6 ten-bars, and the “carried” ten-bar, to get 14 ten-bars. They exchange 10 ten bars for a hundred square, leaving them with 4 ten bars.

    Thus, “carrying” (and, later, “borrowing”) are more than mere abstract process steps to be memorized. In our students’ minds, these operations are real, forever tied to the Golden Beads they learned them with.

    In contrast, local public school systems introduce 3-digit addition in 2nd grade, using a purely “paper-and-pencil” approach, representing units, tens and hundreds with drawn circles, lines and squares, rather than actual quantities.

    The Irvine School District’s Math Expressions program encourages “children [to] do this with methods they invent themselves, or they [can] extend the drawings they did for 2-digit addition.” Then, students are introduced to different methods, such as “New Groups Below” and “Show All Totals,” and then encouraged to use “use any method they understand, can explain and do fairly quickly.” (Quoted from the family letter on Unit 6, 2nd grade Student Activity Book Volume 2 of the Math Expressions Program, which you can find here. You can also read about this paper-and-pencil approach to representing place value on Houghton Mifflin’s web site.)

    The problem with this method is that it expects students to learn about place value purely abstractly, with paper and pencil, without the benefit of experiencing the actual quantities that are represented by the symbols the students learn. Some children are, by second grade, able to learn this abstract progression, but many others understandably struggle. Also observe that by teaching this potentially concrete mathematical lesson in such an abstract way, the public schools are forced unnecessarily to delay this more abstract material to the higher grades, rather than teaching at a younger, more developmentally appropriate age.

    In contrast, our students readily learn the mechanics of multi-digit addition and subtraction in Kindergarten–which leaves them free to advance to multi-digit multiplication by 2nd grade. (Such multiplication lessons are learned through a series of unique materials that you can read about here.)

  2. Progressing at an individual pace, students achieve mastery of math facts before using those facts to solve advanced math problems. Whether in preschool or in middle school, our math program enables students to progress at their own pace, and to master what they learn before they move on to the next step. Take, for example, our elementary math program. With 24 students in her class of 6 to 9-year-olds, our teacher may give 10 or more distinct math lessons in any given week. Because Montessori consists primarily of small-group instruction, she may sit down with an advanced 7-year-old and two 8-year-olds to work on multi-digit long multiplication. She may introduce the process using a material such as the “Large Bead Frame” or “Checker Board” (see our web site, as linked to above, for more detail on these materials.)Once the students get the idea, they each go off to practice on their own for however long it takes them to master this new concept. (The teacher and/or assistant teacher are available to offer reinforcement, support, and oversight as necessary.) One student may get really intrigued, and spend several hours practicing with a given material, each day, for many days, until she has fully internalized how long multiplication works; another student may spread her work out over several weeks, revisiting the same concept and reinforcing it more deeply every time. Each child progresses at his own pace, practicing until he achieves mastery, and only then moving on. Notice also that an advanced first grader may work with second graders or third graders: in this respect, there is no leveling to the common denominator in our classrooms!

    The contrast to public education couldn’t be more pronounced. However dedicated a public school teacher may be to meeting the needs of her different students, by necessity she follows a one-size-fits-all approach.Here, for instance, is the introductory text, printed in red, bold, and underlined, on the Irvine Unified School District web site where the Math Expression student materials for grades K-5 are located:

    The links on this page are intended to support the classroom instruction that your child receives from his/her teacher. It is not appropriate to go ahead of the classroom instruction or to use this site to have your child work on math that is intended for use in subsequent grade levels.

    Your child’s math instruction and placement will not change as a result of working ahead in these materials. This means that your child will continue to work in the grade level appropriate math materials regardless of any work that is done from these materials and submitted to his/her teacher.

    The school district is understandably trying to ensure that parents conform to their system. The problem is not that they are doing so, given their system, the problem is the system itself. In this type of program, no matter how skilled (or challenged) your child may be in math, he must work on exactly the same problems as his classmates. Unfortunately, this means that children who complete a Montessori Kindergarten program, and have already mastered addition and subtraction into the thousands, will have to bide their time until 3rd grade, to again encounter such challenging work. By that time, their interest and excitement for math may have long atrophied and turned to boredom.

  3. Explicit instruction in problem-solving skills, which means the application of already-mastered computational skills to solve complex, real-life problems. Once our students have become familiar with basic operations and have automatized their math facts, we help them acquire a conceptual approach to math problems. For instance, we teach them how to diagram a word problem question. We start with problems with easy computations, and then, very quickly, move on to more sophisticated questions.As an example, our 3rd grade students, who have already mastered basic multiplication facts, may get this question from our Singapore Math workbook for 3rd grade:
    Singapore math, 3rd grade: A farmer has seven ducks. He has five times as many chickens as ducks. How many chickens does he have?

    We teach the student to represent this problem graphically, by drawing a box representing the seven ducks, and underneath it drawing a line of five equivalent boxes representing the chickens. Through this method, the student sees that there are 35 chickens.

    More importantly, the student learns a method of visually representing such a problem–a method that he may not even need for this question but that he will later apply to solve much more complex problems. For example, by 5th grade, they may encounter this problem:
    Singapore math, 5th grade: Sam had $85 and John had $220. They were each given an equal amount of money, and then John had twice as much money as Sam. How much money did each boy receive?

    This problem requires students to solve an equation with one unknown, in this case,
    2*(85+x) = 220 + x.

    Not having learned algebra yet, a student cannot just “intuit” the answer. He needs to diagram the problem, and then solve it, a process he has been taught and has practiced since his lower elementary years, and with which he is quite comfortable by the time he encounters such a question.

    It is important to note that when teaching problem solving skills, we start with simple computations first, because the focus is on teaching the method of diagramming problems, which the students can then apply generally. Students are expected to be able to multiply 7×5, for example, long before they are given the 3rd grade problem. The reason for involving a computation they have mastered is that it allows the child to isolate the problem solving skill being presented.

    In contrast, the Math Expressions program used in the Irvine public schools does not distinguish between teaching the computational facts, and teaching a problem solving approach involving the use of those facts. The program does try to push a conceptual perspective, for example by emphasizing diagrams and word problems. But it does so at the same time as teaching the basic facts. As a result, the word problems have to be very simple, which in turn means they don’t actually promote a conceptual approach. Instead, they risk teaching students to mechanistically apply memorized processes to solving math problems, leaving students stumped when they are expected to deal with more complex problems in the higher grades.

    Compare the Singapore Math 3rd grade problem, above, with this problem, from the IUSD’s Math Expressions in 3rd grade:

    Math Expressions, 3rd grade: The Fuzzy Friends pet store has 3 rabbit cages. There are 5 rabbits in each cage. How many rabbits does the store have in all?

    This problem, in essence, is the equation 3×5, with some words thrown in. The purpose here is unclear–is it to teach the computation 3×5, or to teach problem solving involving that computation? If the former, then the story problem does not add much of value; if the latter, then the problem is too simple to be effective. (In fact, it is probably the former.)

    Because multiplication is introduced to students so late, and with such simplified applications, public school students are essentially two full grade levels behind students participating in a well-executed Montessori program. Witness this example problem from Math Expressions in 5th grade (Activity Book 1, Unit 1, Lesson 5), which is, structurally, exactly the same problem that our 3rd graders solve:

    Math Expressions, 5th grade: There are 3 times as many deer as moose in the forest. If there are 5 moose, how many deer are there?

    Math is a challenging subject. But because it is challenging, it is also immensely satisfying to master. Our students, whether they come up through our own Montessori program, or join us from the outside, invariably come to like math, and develop a joyous confidence in their ability to solve quantitative programs. The reason is that we make it a point to ensure that students not only learn the skills they need to learn, but that they experience the pleasure, pride, and efficacy of applying those skills.
    The proof that our method works? You probably have seen it in your own children, if they have been with us for any length of time, and can share observations like these:

    My son, who loves math, gets to advance at his own pace. Last spring, when he was in 2nd grade, at “watch me work” day, he was using the Montessori Checkerboard to multiply a 4-digit number with a 3-digit number. He was moving all these bead bars around in this complicated operation, and I couldn’t even follow. But he had mastered it: his result matched the control sheet when he turned it around. It was crazy to see how such a complicated operation can be broken down into concrete materials. My son is now in the fall of 3rd grade, and he is multiplying and dividing fractions! He has already done addition, subtraction, multiplication and division for decimals.

    Jan S., parent of a 3rd grade student

    At her old school, my daughter worked really hard in math, and it just didn’t work. She told her math teacher that math is now one of her favorite subjects–and you have no idea what that means: this came as a total shock to me and her dad, because she used to cry doing math. It’s a total turn-around from what it was before. Two of her least-favorite subjects, math and science, are now her favorites!

    Lina S., parent of a 6th grade student

    We hope that this blog post helped you gain a better understanding of our math program. We believe that by combining Montessori math and Singapore Math into a thoughtfully-structured, conceptual approach to teaching mathematics from preschool through 8th grade, we have found the preventative medicine for math anxiety. We hope you will see the results in your child’s enjoyment of and confidence in his math abilities.

    We know that paying for a private education is a difficult investment to evaluate, especially when the difference to the public school system is not always evident. Whatever the important non-academic considerations you might be weighing, I hope that by seeing exactly what your child can gain in mathematics, and by contrasting LePort’s math curriculum with the public alternative, you will become better able to judge the ways in which the academic difference might add up for your child.

Five differences that enable Montessori elementary students to thrive

I remember setting foot in that Montessori classroom. I sat down on a chair … near the door. I had just stepped into someone’s living room. Or was it a science laboratory? Or maybe an office building. I couldn’t put my finger on exactly what was different at first, but this was unlike any classroom I had ever seen. It felt different too. Peaceful. Purposeful.

Trevor EisslerMontessori Madness

Montessori elementary classrooms are fundamentally different from traditional elementary school rooms. In fact, they are so different that it can be hard to understand how they work, and why they are so great at helping children thrive.

While it would be easy to write volumes about this topic (and some have: read Paula Polk Lillard’s book, Montessori Today, if you want a detailed description of the Montessori elementary classroom), here are five key differences, and how they matter to your child’s success.

montessori preschool palos verdesTeachers are guides, not lecturers. They individualize instruction to keep each child optimally challenged. In traditional elementary education, much instruction happens at an all-class level; students generally move through the same curriculum at the same pace. This is more true now then ever, as mandatory standardized testing forces teachers to ensure that all students meet common minimum standards. This approach by definition fails to optimally challenge most of the students, most of the time: a child who is advanced in a subject will be bored; one who is behind will quickly become anxious and concerned about his shortcomings. Montessori is different. Most instruction happens in small groups: teachers observe students and bring together children who are ready for a particular lesson. After a lesson, each child has time to practice a skill or further explore an area, either alone or with freely chosen partners. Writes Lillard: “Because the children are in a period when they have immense energy and curiosity, the secret to maintaining their interest is to keep them challenged.”In a Montessori classroom, an advanced student will be challenged to perform at his best: it’s not unusual for a 3rd grade Montessori student to tackle what would typically be considered 5th grade math, for example. At the same time, a child who struggles can get the extra support he needs, without suffering the negative effect on his self-esteem that comes from needing remedial work in a traditional elementary school setting.

montessori preschool palos verdesChildren have choices, there’s no one-size-fits all curriculum. Students are encouraged to be curious; they are engaged and love learning. When do you do your best work: when someone makes you do a task, or when you freely choose it? Autonomy is a huge factor in motivation, and Montessori elementary enables children to have a say in their learning. Of course, each child has to learn certain skills; mastering arithmetic isn’t optional. But instead of forcing each child to complete the same worksheet, the Montessori elementary classroom ensures repetition by offering a variety of materials for practicing a given skill: multiplication practice includes work with the Bead Chains, the Stamp Game, the Checkerboard, the Large Bead Frame, and the Flat Bead Frame. When we take our students on field trips, the people we encounter, from museum guides to park rangers, regularly comment that our students are the most curious and engaged group of children they have seen. This is a common refrain for Montessori elementary schools: the children love learning, because they have a chance to be actively engaged in the process.

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The classroom is full of materials instead of textbooks and worksheets. Children learn to solve problems and think, instead of repeat memorized jargon. Much traditional elementary school work is unfortunately focused on work with textbooks and worksheets. While there is nothing wrong with books (we love free reading time!), you will not find traditional textbooks and worksheets in the Montessori elementary class. Dr. Montessori viewed the early elementary years as a critical stage in the mind’s development, when the concrete thinking of the preschool years matures into abstract thinking. During the Primary years, children explored many materials, such as the Trinomial Cube or the Golden Beads, primarily for the sensorial interest. Now, in elementary, children use materials to understand how the world works. They are interested in the why and the how of things; they’ve become “reasoning explorers of the abstract”, in Lillard’s vivid description. The materials in Montessori are not mere instructional aids:  Just like in Primary, much of their learning happens as the children use the materials to explore topics from grammar to division, from the fundamental needs of man, to the role of water in erosion. With the materials, learning is focused on the world; children acquire a mindset of thinking about things and figuring them out, rather than memorizing words or processes on an adult’s say-so.

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The day has two 2 – 3 hour work periods, instead of a schedule where activities are constantly changed. Protecting children from interruptions when productively engaged is key to their development of concentration and interest in their work. Dr. Montessori commented that traditional schools have broken up the day in many short time periods, in an attempt to hold the children’s interest, and that they have failed miserably, as children remain mentally fatigued despite the alleged benefit of variety. In contrast, writes Montessori, Montessori schools have proven that children need a cycle of work for which they are mentally prepared; such intelligent work with interest is not fatiguing and they should not be cut off from it by a call to play. Interest is not immediately born, and if when it has been created, the work is withdrawn, it is like depriving a whetted appetite of the food that will satisfy it.
This is why there is no morning recess in your child’s class, and why we don’t provide you with an hour-by-hour schedule. It’s one of the often-overlooked benefits for Montessori elementary students: author Paula Polk Lillard notes upon observing in a Montessori elementary class that the children “have time to think. That is what impresses me most, I realize. These children are thinking.”

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Children learn with and from each other, in a mixed-age environment.  Instead of competing with each other, they grow into a community, and practice all-important social skills every day.  In traditional education, the emphasis in preschool is on “socializing” the child, and children are expected to do much together in groups. Come elementary schools, class time is largely focused on individual work, in strictly same-age classrooms, and social interactions are limited to recess and lunch.This approach—focus on group activities in preschool, and individual activities in elementary school—is fundamentally wrong, according to Montessori. Young children in preschool, left to their own devices, often choose to do things by themselves, and much activity in a Montessori Primary class is in fact individual work. As children near the end of Primary, they often start to work together in pairs. In fact, becoming interested in and able to work with a peer is one indication that a child is ready to move up to elementary!In Montessori elementary, children interact with each other, across age groups, all day. You’ll often see 2-4 children working together on projects, negotiating roles and learning social skills in a safe, supervised setting as they choose co-workers and figure out that they can work with a range of companions, not just with their closest friends.

A Montessori elementary classroom is very different from traditional schooling. These five highlights are just a start to understanding this unique learning environment. We encourage you to explore more: Read up on how we teach each of the subjects on our web site. Pick up Paula Polk Lillard’s book. And, most importantly, make time to observe in your child’s Montessori elementary classroom!

Transitioning to Montessori: The Prepared Environment (Part 5 of 5)

Every fall, children transition to our Montessori programs from other preschools or elementary schools. What can parents do to help with this transition? In this series of blog posts, we lay out a few Montessori principles that apply at the later preschool and early elementary school level. Our focus is on children who transition into Montessori during their kindergarten through 2nd grade years, but many of the ideas suggested here are helpful for preschool children, too.

“Education is a natural process carried out by the child and is not acquired by listening to words but by experiences in the environment.”

“The environment itself will teach the child, if every error he makes is manifest to him, without the intervention of a parent or teacher, who should remain a quiet observer of all that happens.”

–Dr. Maria Montessori

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A Montessori elementary classroom looks very different from traditional elementary school. Visit, and you’ll see children working alone or in small groups all around the room. They sit at small tables or work on mats: not a desk in sight. The teacher wanders between them, sitting with a child here and there for a few minutes, or bringing five children together around her desk now for a 10 minute small group lesson.

Parents often ask how the individualization of Montessori works: how can a teacher tailor his lessons to each child? How can there be order, when each child works on something different? How can children master the same fundamentals, if they have so much choice?

A key element to solving this apparent puzzle is what we call the prepared environment. Dr. Montessori observed that young children learn more from interacting with materials, then from listening to the words of teachers. That’s why the activity in a Montessori elementary classroom centers not on lectures and assignments, but on short lessons on how to use the activities spread out around the classroom on low shelves. These activities, plus the set of definite classroom rules that are essential to making freedom within limits work, are an essential part of the prepared environment.

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In his Montessori elementary school class, a child receives lessons on how to use different materials. Once a material has been shown to him, he is free to use it to master the skills embodied in the material. A 2nd grader, for example, may receive a lesson setting up a multiplication problem on the Montessori checkerboard. Thereafter, he can spend many productive hours practicing this new skill, self-checking his results without adult intervention, as the problem cards have solutions on their back. The children understand and accept that they are free to practice and explore any material in which they’ve been given a lesson—and the teacher performs the ongoing responsibility of nurturing them towards materials that optimally engage and challenge them. The whole system works beautifully—if you don’t believe it, you can get a glimpse of it here!

In preparation for your child’s entry into Montessori  elementary school this fall, you can implement some aspects of the prepared environment in your home. This will make it easier for him to feel at home, once he comes back to school in September. It will also enable him to share his experiences with you during the school year: while there is very little homework assigned in a Montessori lower elementary class, it’s not unusual for our enthusiastic students to want to share their work at home anyway!

  • Set up a work area in your home. Invest in a few low bookshelves (Ikea works just fine), a child-sized table (not a desk), some child-sized chairs, and a few work rugs. Equip them with materials your child can work with – a set of high-quality colored and regular pencils, pencil sharpeners, scissors, glue, blank and story writing paper. Put your child’s books on the shelves so he can access them. You may also want to put other activities your child enjoys there – such as puzzles, arts & crafts activities or building materials.  Finally, provide him with a place to put his completed work, such as a drawer or a file folder he can easily access.
  • Provide guidance on how to work in this space. In a Montessori environment, each child is only permitted to have one activity out at a time. He takes it from the shelf and carries it to his work space (table or rug on the floor.) Once he is done, he replaces it on the shelf, and tidies up his work space (sweeping pencil droppings, carefully rolling up the rug and replacing it in his bin.) He can then choose something else to explore. You can establish similar rules at your home, and guide your child to complete the process. A nice side benefit: there will be less clean-up needed at the end of each day!
  • Give him time and space to explore. Often, we over-schedule our children, taking them from one activity to another. 5- and 7-year-olds, just as younger children, benefit from some unstructured time. Now that you have set up his work space, you may suggest some ideas to get him started (see the follow the child post for details), then let him run with it!

The prepared environment in a Montessori elementary classroom is essential to helping a group of 20+ individual children work productively. Once your child is settled into his routine this fall, we invite you to come and observe him. We bet you’ll be surprised at what you see!

Read more in our Transitioning to Montessori blog series:

Transitioning to Montessori: The Follow the Child Principle (Part 4 of 5)

Every fall, children transition to our Montessori programs from other preschools or elementary schools. What can parents do to help with this transition? In this series of blog posts, we lay out a few Montessori principles that apply at the later preschool and early elementary school level. Our focus is on children who transition into Montessori during their kindergarten through 2nd grade years, but many of the ideas suggested here are helpful for preschool children, too.

“It is true that we cannot make a genius. We can only give to each child the chance to fulfill his potential.”

“Free choice is one of the highest of all the mental processes.”

“The prize and punishments are incentives are incentives toward unnatural or forced effort, and, therefore we certainly cannot speak of the natural development of the child in connection with them.”

“It is not in human nature for all men to tread the same path of development, as animals do of a single species.”
— Dr. Maria Montessori

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Visit many academically rigorous elementary school programs, and you’ll see ice cream party charts on the walls, treasure chests in the corner, and behavior points tallies next to the white board. Ask a teacher at such a school how she motivates a child, and these extrinsic rewards figure highly in her plan, as do punishments, such as loss of recess, notices to parents, poor grades, and visits to the principal’s office. To an observer, it may seem like rewards and punishments are indispensible to getting children engaged in learning.

Yet watch these same children—who, at school, have to be corralled into attention—outside of school, and you may find them focused intently on reading a book they have chosen for themselves, successfully playing a video game that even you can’t figure out, engrossed in making cookies with mom in the kitchen, or practicing for hours with their soccer ball.

If children can and will focus and work hard outside of school, without extrinsic motivators, why can’t they be similarly engaged at school?

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Our answer, it may not surprise you, is that they can!

In Montessori elementary school, we motivate children by their natural interest, not by stickers and rewards. We trust that they want to learn, if only we capture their attention by providing them with the right “points of interest” and offering work they find engaging.

We recognize that children are individuals. What motivates one may be dull for another; while one 6-year-old may be working on forming words, another one may be ready for writing stories; one child may need a quiet space to work alone, whereas another one thrives by working through math problems with a friend.

We aspire to help each child achieve the highest potential, and in fact, our academics are accelerated when compared to traditional elementary school (think 1st graders who write multi-story sentences in cursive; 2nd graders who do arithmetic into the millions!) What is different at our school is how each child meets these demanding academic standards. Rather than a one size fits all process, each finds his or her own path to success.

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For example, a Montessori elementary school teacher who observes a boy’s interest in cars may give such a boy a very different writing assignment than another one who happens to be fascinated by the tide pool animals he saw on a recent trip to the beach. The universal need to practice writing is true for every child—but there is no similar need for every child needs to complete the same standardized work sheets!

We call this the follow the child principle—help each child maximize his or her potential by first understanding his or her needs. As teachers, it is one of our most important responsibilities to observe each child, to get to know her as an individual, and to tailor our teaching to her interests, strengths, and weaknesses.

As your child prepares for the start of Montessori kindergarten or elementary this fall, you may want to try following his interests. As a parent, you’re probably doing a lot of this already (after all, you know your child!), but paying conscious attention to guiding your child by respecting and nurturing his uniqueness can pay huge dividends.

  • If you want to work on academics with your child over the summer, please don’t rely on workbooks. Instead, think about what your child loves, and tailor academic activities around that. Does he love art and animals, and can do some writing? Get him a digital camera (or let him borrow yours), and some story writing paper. Then set out to explore some of your local animal habitats and zoos. Armed with the camera and notebook, he’ll have plenty to write about on his return! We bet he’ll do more writing, more willingly, then if you had asked him to complete worksheets! Similar ideas can apply to math: engage your numbers-minded daughter in some cooking: have her figure out how to double or half a recipe; have her help you total up a rough estimate of the cost of the items in your shopping cart. For more ideas on supporting scientific exploration, read Encourage the Scientist in Your Preschooler.
  • Have your child make more meaningful choices, and own the process of learning. Let your child choose some of the outings you take. And then put him in charge of more of the process: what do we need to pack for the pool? (He packs. No towel? He’ll remember next time!) How do we get there? (A map reading lesson!) Have her pick the books she’d like to borrow from the library (you can have some discussions afterwards on which ones she liked and disliked, and how to make better choices next time.)
  • Go out and explore the world together! Much motivation to learn comes from “teachable moments”, and being out and about together on little adventures during summer time can offer plenty of these. Visit the tide pools (then read about them, research animals online, get books about ocean animals, write down the things you learn.) Do some theme-based reading: the Magic Tree House series provides a great jumping-off point for exploring different times and places. For example, if your son gets fascinated by the knights of the middle ages, follow his lead: Street Through Time is a great, child-friendly history book to explore. Then head out to Medieval Times to experience an (admittedly over-the-top) take on a medieval feast.

Following the child­—getting to know each child as an individual and allowing that individuality to guide his learning—is a great principle for tailoring instruction in such a way that ensures that every’s child potential is actualized. It’s a great way to get children to enthusiastically tackle tough work assignments, and to help them rise to their potential.

Read more in our Transitioning to Montessori blog series:


Transitioning to Montessori: Motor Skills and Indirect Preparation (Part 3 of 5)

Every fall, children transition to our Montessori programs from other preschools or elementary schools. What can parents do to help with this transition? In this series of blog posts, we lay out a few Montessori principles that apply at the later preschool and early elementary school level. Our focus is on children who transition into Montessori during their kindergarten through 2nd grade years, but many of the ideas suggested here are helpful for preschool children, too.

“Watching a child makes it obvious that the development of his mind comes through his movements.”

“Since it is through movement that the will realizes itself, we should assist a child in his attempts to put his will into act.”

— Dr. Maria Montessori

In a Montessori preschool program, we emphasize motor development as an essential component of education. The hand is the tool of the mind, said Dr. Montessori, so any activity that is to hold the child’s attention has to be one where his whole personality, mind and body, are engaged harmoniously. The child has a need to integrate thought with action, observation with movement, mind with body.

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Montessori preschool children have many opportunities to work on activities that make this integration possible. Indeed, the entire Montessori preschool class abounds with examples of “hand-mind” engagement—activities so deeply satisfying to students that they will do them quietly, focused, for up to an hour at a time.

Observe in a Montessori preschool class, and you may find a 3-year-old pouring water from one container to another for 20 minutes, or a 4-year-old carefully using the metal insets to create art work, or a 5-year-old writing elaborate stories with the moveable alphabet. The environment is a vista of different children engaged in different explorations, acquiring knowledge by acting purposefully in their environment.

These children are accomplishing something very important. They are extending their attention span. They are refining their gross and fine motor skills. They are following logical sequences of events. They are problem solving. This inner cognitive growth occurs in leaps and bounds because it is connected with the child’s need to move and engage in self-generated action. The opportunity to repeatedly use the mind to guide the hand is what prepares them to jump in and fully explore the exciting materials in the Montessori elementary classroom.

For children who join Montessori for kindergarten or elementary school, parents can help by providing similar mind-body integrated activities at home.

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  • Get your child involved in kitchen activities. Dicing vegetables fosters motor control and can easily take 20-30 minutes. Peeling eggs strengthen muscles. Scooping flour and measuring sugar to just a level table spoon require concentration and motor control. Now is a good time, too, to teach children how to make their own school lunches!
  • Provide him with crafts activities that help with fine motor skills. Mandela drawing tools or stencils can replicate some of the skills practiced with Metal Insets in a Montessori primary class. Stringing small beads can help with the three-finger grip and concentration skills. Tracing and coloring in figures (like animals in this book) are also wonderful activities, as are crafts tasks that require a child to use scissors carefully or glue small pieces of paper or other things to make art work.
  • Get outside and work on gross motor skills. Learning to ride a bike without training wheels fosters both self-confidence and balance (a balance bike is a great tool – read more here.) Find a balance beam. Join a gymnastics or dance class. Throw balls with each other. These may not sound like academic activities, but children who can’t confidently control their bodies are at a clear disadvantage in class!

These mind-body activities, rather than a focus on academic work, is a better use of the summer months leading up to your child’s start in the Montessori kindergarten or elementary class!

Read more in our Transitioning to Montessori blog series:

Transitioning to Montessori: Freedom within Limits (Part 2 of 5)

Every fall, children transition to our Montessori kindergarten or elementary program from other preschools or elementary schools. What can parents do to help with this transition? In this series of blog posts, we lay out a few Montessori principles that apply at the later preschool and early elementary school level. Our focus is on children who transition into Montessori during their kindergarten through 2nd grade years, but many of the ideas suggested here are helpful for preschool children, too.

“Respect all reasonable forms of activity in which the child engages and try to understand them.”

“To let the child do as he likes when he has not yet developed any powers of control is to betray the idea of freedom.”

— Dr. Maria Montessori

In a traditional elementary school, much activity is adult-led. There’s a schedule of subjects (40 minutes of writing, then 30 minutes of math, followed by 15 minutes of recess/snack, and 30 minutes of quiet reading time, and so on.) The teacher leads a lesson, often for the whole class or a sub-group of children. Children have little say on what they work on, where they work and when they work on certain things.

In contrast, in a Montessori preschool/kindergarten or elementary school, children have what we call freedom within limits. We like to give children space to work things out on their own, with the teacher acting as their guide, rather than telling them what to do.

montessori preschool

Throughout the day in the Montessori preschool, kindergarten or elementary schools, there are uninterrupted work periods of 2-3 hours each. During this time, the children receive individual or small-group lessons. But lessons typically take only 10-20 minutes each. Much of the time is not tightly scheduled by adults. Rather, it is an opportunity for a child to choose certain activities (guided, of course, by the teacher, who has observed the child and tailored his curriculum to his needs.) A child may choose to start with the challenging math problem while she’s fresh in the morning. Another one may ease into the day by doing some independent reading.

As long as children are engaged in purposeful activities, the teacher will not actively interrupt. Instead, he may step back and observe the child, and only get involved when an activity is complete, for example, to sit down with a child and provide guidance on a piece of writing. (In contrast to traditional elementary schools, where teachers do a lot of correcting of work, in Montessori, children often have access to control cards and eagerly correct their own work.)

This type of freedom, however, is not an unlimited free-for-all. It is the result of careful preparation, and of a profound invisible structure provided by the teacher and the materials. A child earns independence over time. For instance, a new child may be asked to check in with a teacher several time throughout the day, or be given a detailed daily work plan. A child who has a hard time focusing on work when seated next to a friend may be redirected to a separate table to work on alone. An experienced 3rd grader, on the other hand, may have whole days where he works largely independently, or may have the freedom to pursue joint projects with a classroom friend. Purposeful, self-managed work becomes the ideal to which all of the children aspire.

montessori preschool

Most students who come to Montessori kindergarten or elementary school from a play-based preschool or traditional elementary school program aren’t used to this level of freedom. We recognize that there’s some adjustment needed for such students, and so we slowly build up their capabilities so they can take on more responsibility.

As a parent, you can help by simultaneously ceding control at home, and handing more responsibility to your child.

For example, if you find yourself managing her morning routine, urging her to get dressed or to have breakfast or to brush teeth, you may want to consider transitioning that responsibility to your child. Do so in a careful, slow, step-by-step process, so she experience success:

  • Sit down and talk. Let her know that you trust her to become more independent, and that you’ll work with her.
  • Make a plan and write it down. Identify the tasks your child will do on her own (get dressed, make the bed, fix breakfast, prepare her lunch.) Make sure she can do the tasks (see the post on independence), and coach her where needed. Then create a routine chart together, listing each key step (add photos for younger children who still struggle with reading.)
  • Hand over responsibility. Put the chart somewhere accessible. Instead of reminding your child to do a task (‘it’s time to brush your teeth now’), point her to the task (‘we’re done with breakfast. What’s next on your chart?’)
  • Discuss progress. Rather than having the child get in trouble if she doesn’t meet expectations, ask her what went wrong? Does she not want to do it on her own anymore? Is there some other task she’d rather try first? Make it clear to your child that you are there to support her pursuit of independence—but also that you will hold her to her own commitments.

Other easy areas for handing over control could be getting ready for an outing (e.g., packing the things needed to go to the pool), or getting ready for bed.

Entrusting your child with more responsibility at home will help ease the transition into the freedom within limits environment of Montessori kindergarten and elementary school. And as a nice side benefit, it may also allow you to nag less and have more fun with your child!

Transitioning to Montessori: Independence (Part 1 of 5)

Every fall, children transition to our Montessori programs from other preschools or elementary schools. What can parents do to help with this transition? In this series of blog posts, we lay out a few Montessori principles that apply at the later preschool and early elementary school level. Our focus is on children who transition into Montessori during their kindergarten through 2nd grade years, but many of the ideas suggested here are helpful for preschool children, too.

“Little children, from the moment they are weaned, are making their way toward independence”

“Never help a child with a task at which he feels he can succeed.”

— Dr. Maria Montessori

If your child will be transitioning into a Montessori school late into the preschool/kindergarten program, or straight into Montessori elementary school, it is helpful for you as a parent to understand what your child would have experienced had he been in the program in earlier years.

montessori preschool

The goal of the Montessori preschool experience is to help children help themselves. “All by myself” is and ought to be the theme of a toddler’s life, and in the right environment, this motivation to be independent becomes the basis of tremendous learning. Montessori preschools, by satisfying the child’s need to be independent, help him acquire skills of daily living in a careful, step-by-step sequence that sets them up for success and earned self-esteem.

It starts with something as simple as enabling toddlers to manage their own snack routine. They start out by learning to lay out a napkin and a small cup. Before long, they are able to set the full table, serve themselves by scooping raisins and pouring water, and clean up the table, put away dishes and sweep up crumbs. Rather than being a passive recipient of snacks, a child learns to satisfy his own needs.

Preschool children in Montessori have the opportunity to do many tasks that other children are not entrusted with until much later. For example, they peel and cut fruits and vegetables, using real knives. They prepare and serve snack to their peers. They cut and arrange flowers and are in charge of taking care of classroom plants and pets.

As these preschoolers become more capable, they relish taking on more responsibility. At school, they take ownership of cleaning up classroom shelves, without being asked, and also teach these same skills and habits to younger friends. At home, they may be entrusted with preparing their own lunches, or being real contributors to family chores.

If a child transitions to Montessori as a 5-, 6- or 7-year-old (i.e., late in preschool or early in elementary school), he may not have had these same experiences. And, maybe more importantly, his parents may not have received coaching on how to foster this type of independence at home.

The best solution, if your child is in this situation, is to start now! Think about what things you may be doing for your child that he could do alone, if you made some slight adjustments to your routines and gave him some extra initial support.

Here are a few ideas to support independence for kindergarten age or early elementary school children (useful whether or not you enroll them in Montessori for elementary school!)

  • In the kitchen.
    1. Provide your child with a low shelf or drawer with his own utensils, so he can set his table. Make this a daily responsibility.
    2. Set up healthy food choices on low shelves in the pantry and refrigerator: jars with cereal, a basket of fruit, cut-up veggies in a bowl, a small pitcher with milk or juice. Invite your child to help himself to a healthy snack when he is hungry!
    3. Invite your child to help you with food prep. For Small Hands carries a great selection of child-sized implements, from vegetable peelers to cutting boards and aprons. 5- or 6-year-olds can do a lot of food prep, from peeling apples to cutting carrots, from measuring out flour to flipping pancakes!
    4. Enable your child to clean up after himself. Set up a child-sized broom & dust bin, a small bucket, a scrubber and a sponge, and ask your child to clean up around the table after eating.
  • In the bedroom, bathroom and laundry room.
    1. Ensure your child’s closet is child-friendly. Make sure he can access all his clothes easily. Limit choices to those appropriate for the season and day-to-day activities (put away special occasion clothes, unless you are ok if your child wears them every day!)
    2. Organize things so your child can do his own laundry. Get a two-compartment hamper for easy clothes sorting. Show your child how to manage the washer (including pre-treating stains!) Show him how to fold & put away laundry.

montessori preschool

In his Montessori elementary classroom, your child will have an increasing amount of responsibility. He’ll have the opportunity to keep his own work organized, take care of classroom plants and pets, and help keep the general classroom organized. He’ll learn how to be in charge of his own academic activities, planning out his daily and weekly tasks, and taking the initiative to reach out to teachers and friends for help when he needs it.

Giving your child more independence at home will help get him ready for this new environment of freedom within limits (more on that in the next blog post here.)

Read more in our Transitioning to Montessori blog series: