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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.

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.)
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.
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.

A Surprisingly Non-Academic Approach to Strong Academics

When parents tour our Montessori schools, we often hear questions about academics: when will my child read? How do you teach math? Will your program get my child ready for Kindergarten? In this competitive world, parents of toddlers are rightfully concerned with future academic success. And research supports this concern: children who start elementary school poorly prepared have a hard time catching up and diagnoses like ADHD have grown exponentially, even in the youngest students.

But does this mean you need to subject your toddler to programs like preschool prep or Baby Einstein, and enroll your preschooler in Kumon or similar preschool academics programs?

We think the questions and concerns about early academics are legitimate: a child’s experiences in his formative toddler and preschool years can have a significant impact on his future academic and life success. Poor preparation can, in fact, leave children behind, making it harder for them to achieve their full potential.

Montessori preschools do an exceptional job preparing children for academic success. Montessori children start their elementary career ready to flourish: most learn to read in our age 3-6 classroom, and solve arithmetic problems into the thousands. But the important point is how. Montessori children do not learn by drill-and-kill memorizing of flash cards, or repeatedly watching academic videos, or completing endless worksheets.

Montessori schools approach academics in a surprisingly non-academic way, laying strong foundations for self-motivated, successful learning as early as in the toddler program. Much of what we do is what Maria Montessori called indirect preparation: toddlers and younger preschool students engage joyfully in activities that impart a wide range of prerequisite skill which then, down the road at age 5 or 6, enable an almost explosive growth in academic achievement. Here are some examples of this indirect preparation for academics:

The ability to concentrate. ADHD diagnoses have grown by over 5% per year in the past years; about 12% of all boys ages 5-17 have at some point in time been diagnosed with ADHD, which can severely impact a child’s ability to function in life and in school. While there is no consensus on what causes the disorder, ADHD symptoms include an inability to sustain focus on a task for extended periods of time. Treatment often includes programs that help children learn better executive function skills. Learning to concentrate on an activity, to immerse oneself fully in a chosen task, is one of the most important goals for a child who enters a Montessori preschool or toddler class. In Dr. Montessori’s words, “The first essential for the child’s development is concentration. The child who concentrates is immensely happy.” When your child joins the Montessori toddler program, we offer him activities that appeal to him, and then give him the freedom to work with a chosen activity for as long as he likes. In this environment, even 18-month old children regularly focus for 10, 15, even 20 minutes on one task. As your child progresses through the Montessori preschool sequence of activities, he’ll tackle increasingly more challenging, longer tasks. It’s not at all unusual for a 5-year-old Montessori child to spend an entire 3-hour work period engaged in one chosen task, such as tracing, coloring and labeling a map of Africa, for example.
Developing executive function skills. A recent article in the New York Times explored the question of what really drives life success. One surprising discovery: being able to set goals, to self-motivate, to make mistakes, learn from them, and persevere in the face of challenges may well be more important than scores on academics or intelligence tests. Unfortunately, those are skills rarely taught, not in school and not in most preschool programs. Montessori is different. As early as the toddler program, Montessori children choose their own activities. However, there’s usually only on of each activity, so children learn to patiently wait their turn (no adult-enforced sharing happens in Montessori classrooms.) Children are free to make mistakes—indeed, Montessori encourages us to “become friendly with error.” Further, it’s usually the activity itself that shows them their mistake—water spills, a porcelain plate breaks, a tower doesn’t stand—and the children learn to pay attention to mistakes and learn from them (as against avoiding them for fear of being criticized by a teacher.) And as tasks get longer and more challenging, students learn to keep at it, often working on the same projects for several days at a time, not because a teacher instructed them to, but because they chose to do so. This internal discipline is precisely what life success requires, and what Montessori teaches so beautifully!

The discipline that we are looking for is active. We do not believe that one is disciplined only when he is artificially made as silent as a mute and as motionless as a paralytic. Such a one is not disciplined but annihilated. We claim that an individual is disciplined when he is the master of himself and when he can, as a consequence, control himself when he must follow a rule of life. Dr. Maria Montessori, in The Discovery of the Child

Strong motor skills. Handwriting is an important skill a child needs to master to succeed in elementary school and beyond. Children who cannot write well often under-achieve against their potential. Motor skills (and several other skills, such as visual-perceptual skills) are supremely important in learning to write. Montessori toddler and preschool purposefully develops these foundational gross and fine motor skills. Scrubbing a table or cleaning the blackboard strengthens shoulder and arm muscles. Peeling an egg, scooping beans, pouring water from a small pitcher, making orange juice, squeezing a sponge: these all strengthen wrist muscles and control. A series of activities, from the Knobbed Cylinders to the Metal Insets, from pinning activities to puzzle maps, help children strengthen their fingers and develop a proper pincer grip for later pencil use.
Oral language skills. A strong vocabulary and elaborate language is an important predictor of future success in literacy tasks. The Montessori toddler program builds these skills systematically. Children learn much vocabulary with matching object/card sets. Our highly educated Montessori teachers consistently use elaborate (age-appropriate) language. They may say things like “Sarah, I notice your pants are wet. They must feel very damp and uncomfortable on your skin. Shall we go and find you some dry, cozy pants to change into?” rather than “Oh, you had an accident. Time to change!” Of course, we read many stories, sing songs, and discuss daily events with each other. We also introduce toddlers beginning phonemic awareness skills: a teacher may hold up small objects, like a cat, a pan, and a mop, and have children identify the beginning sounds.

Earned self-confidence. In today’s age, many people talk about fostering children’s self-esteem. All too often, that means lavishing praise upon toddlers for every action they take. Unfortunately, research has shown that empty praise not only fails to foster real self-confidence, it in fact can inculcate an anti-effort mindset. In Montessori, we don’t play this game. We are convinced that self-confidence must be earned by real personal achievements, resulting from sustained effort. That’s why we present lessons step-by-step, and set our students up to explore, practice, and earn mastery. When they do succeed, we don’t offer empty praise. Instead, we help them appreciate their real-world achievement by offering up what Montessori calls a point of interest: “Notice how when you put the cup down slowly, without making a sound, the water stayed in it”, or “See how straight the mat stands in the basket when you roll it tightly?” When this is repeated frequently, over a child’s years in the Montessori toddler, preschool and elementary school programs, children learn that with effort, they can master tasks. They come to enjoy the struggle to master tasks, and don’t fear the natural failures that are part of the learning process.

Self-esteem doesn’t contribute much to success. But success contributes mightily to self-esteem. Kids have to “do” something, and do it well, to get a self-esteem boost. Madeline Levine, PhD, in Teach Your Children Well

Just imagine your child, at the end of his third year in Montessori preschool: he’ll be able to look around the class and all the materials in it. He’ll know that when he first entered the class, all these activities were strange, challenging, and maybe even a bit intimidating. But now, as a 6-year-old, he knows he has mastered them. Can you see the earned pride in his eyes—and the confidence that this real achievement will give him as he enters elementary school?

The Sensorial Area in Montessori Preschool: Where Young Scientists Are Born

A preschool child is fascinated by the world around him: eager to explore it, always asking questions, constantly getting his fingers into everything. As he does so, he acquires a tremendous amount of information – about animals, people, plants, common household objects, etc. He makes observations at home, in the park, at the store, on vacation.

In the Montessori preschool environment, we help him organize his wealth of information into an orderly store of knowledge. We guide him to observe carefully and provide him with a systematic way of conceptualizing the world around him.

The Sensorialareaof a Primary (preschool/kindergarten) classroom is where this training happens. Children work with a range of materials, each of which varies in a single attribute; for example, the length of the Red Rods, the shade of each Color Tablet, the texture of the Fabrics, or the pitch of the Montessori Bells. In using these materials, children learn to observe carefully and to order, match, or sort objects by their attributes.

Each Sensorial material presents to the preschool child one special key to the world. Dr. Montessori conceptualized the idea of keys as a way of introducing significant aspects of this vibrant world we live in to the young child. Keys serve as jumping-off points for learning more about the world.

Work with the Sensorial materials also broadens a child’s vocabulary. Once a child has experience with a material, the Montessori teacher introduces the appropriate words to fix the new idea in the child’s mind: “This rod is the longest”, “Feel how smooth this silk is”, or “Listen how these two bells have exactly the same pitch.”

Preschool children spontaneously apply what they learn from the Sensorial materials. For example, a child who has practiced matching and grading the Color Tablets will naturally begin to notice things about color in his surroundings that he previously didn’t. It is not uncommon for Montessori preschool teachers to hear a 4-year-old remark things like, “That’s dark blue”, “This green is lighter than that green”, or “This grey matches that grey.” A child who has explored shapes from the Geometric Cabinet and has learned their names will start to identify shapes in objects around him (“That stop sign is an octagon!”), buildings (“Those windows are squares!”), even food (“The yolk is a circle!”).

If a child is unsuccessful with a Sensorial material, we do not correct him directly. Rather, we observe and note any errors, and re-present a lesson from start to finish at another time. We might offer a point of interest, a detail that is important for the child to grasp in order to get full benefit from a material. E.g. “Watch how I line up the Red Rods neatly along the edge of the rug as I order them.” As always, we then invite him to continue working with the material independently. The preschool child eventually learns to correct himself, as the control of error is often a combination of his own developing discrimination and the materials themselves. For example, with the Brown Stair, the child will experience visual disharmony if he sees that the stair is out of order.

There are formal games and extensions that are connected with every Sensorial material. With the Botany Cabinet, for example, the child learns not only to trace and recognize a variety of leaf shapes, but also to connect these to actual leaves he might collect on a nature walk. Once he is writing, he might enjoy creating booklets about the different kinds of leaves or, more broadly, other parts of a plant. The Puzzle Maps are a great example of work that extends throughout the Primary (preschool/kindergarten) years. For instance, initially the child simply learns how to put the United States puzzle pieces back properly in the frame. By his second year, he learns the names and locations of each state. By his third year in Primary, he might begin to create his own beautiful map of the United States, carefully tracing and cutting out each state, pasting them accurately on a large poster-sized paper, and proudly labeling each of them. A child is also welcome to make his own discoveries and variations. Perhaps he might recognize the similarity between the Pink Tower and Brown Stair, and build them side by side!

Beyond all of this, the Sensorial materials are significant in that they indirectly prepare the preschool child for later work in language and math.

Early Sensorial work, such as the Cylinder Blocks, indirectly prepares the child for writing and reading. As he uses his pincer, or three-finger, grip to grasp the knob of each cylinder, he strengthens and prepares his hand for holding a pencil. Touching rough sandpaper on the Rough and Smooth Boards will feel familiar to him when he traces his first Sandpaper Letter, the key Montessori preschool material for introducing the sounds and letters of our alphabet. Tracing geometric shapes as well as puzzle map pieces increase his fine motor control and precision of movement.

The Sensorial materials also prepare the child for math work in a variety of ways. Many Sensorial materials (just a few examples are the Pink Tower, Brown Stair, and Knobless Cylinders) are designed in series of ten, which reflects our base 10 number system. Several others provide a thorough introduction to geometric shapes, solids, and the unique, constructive properties of triangles. The Binomial and Trinomial Cubes are three-dimensional puzzles based on the binomial and trinomial equations, respectively. The Red Rods, of course, are a prerequisite for the red and blue Number Rods, which solidify a child’s grasp of quantity and his ability to count to ten with one-to-one correspondence.

Through sight, touch, taste, smell, and sound, the Montessori Sensorial materials provide opportunities for the child to classify and clarify the world around him. If you are a LePort Montessori preschool parent, we invite you to enjoy getting a closer look at these materials and to see them in action during your next Watch Me Work Wednesday visit!

The Dual Purpose of Montessori Preschool Practical Life Activities

The first essential for the child’s development is concentration. The child who concentrates is immensely happy. Dr. Maria Montessori

Students new to Montessori preschool spend much time in the Practical Life area of the classroom, where shelves are filled with activities for dressing, food preparation, sweeping, polishing, and so on. In a variety of ways, Practical Life activities provide the preschool child with skills for self-care, caring for the classroom environment, and all-around independence.

This independence is a critical aspect of a Montessori preschool education. As Dr. Montessori wrote:

If teaching is to be effective with young children, it must assist them to advance on the way to independence. It must initiate them into those kinds of activities which they can perform themselves and which keep them from being a burden to others because of their inabilities. We must help them to learn how to walk without assistance, to run, to go up and down stairs, to pick up fallen objects, to dress and undress, to wash themselves, to express their needs in a way that is clearly understood, and to attempt to satisfy their desires through their own efforts. All this is part of an education for independence.

Dr. Maria Montessori

A 3-year-old preschooler, with proper instruction, is able to do many things for himself and can start to contribute meaningfully within the classroom or family community, too. It is in the Practical Life area of the Montessori preschool classroom that your child learns these skills – and you can help him by encouraging him to be independent and helpful at home as well:

Preparing food. 3-year-old preschool children love to do real work they see us do. In class, they often prepare snack for friends: peeling and cutting carrots, cutting and serving bananas, preparing apple and cheese trays.
At home, your preschool child can become a true helper in the kitchen and participate in real cooking activities. Invest in some good tools, like the ones available from For Small Hands, and you’ll be rewarded as your preschooler begins to peel vegetables, measure ingredients, and clean up small messes. By a child’s 3rd year (age 5 – 6) she might be capable of taking over much of the meal prep: My 5½ year old daughter recently prepared most of a taco dinner for us, cutting tomatoes, helping sauté the chicken, putting condiments into bowls, and setting the table for the family. She even surprised me by heating the tortillas in the oven, taking the oven mitt out of a drawer before she put the baking tray into the oven. I had never taught her that—I didn’t even realize she knew where the oven mitt was stored! If you welcome your children into the kitchen while you work and narrate what you do and why, you’ll be surprised by how much they pick up, and how eager to participate they become!

Cleaning up. Washing a table is a favorite Practical Life activity. It involves many steps and materials, and we build up to it slowly, teaching each component skill: students learn to squeeze sponges by transferring water between small containers; they learn to pour water by first pouring beans, then lentils, then rice, then water with small pitchers; they learn how to operate a faucet, making sure to turn off the water when done; they learn to put on an apron; they learn to fold a cloth; they learn to put materials away after completing their work. The table washing activity puts together all these skills: It’s amazing to see a 3½- or 4-year-old complete this rather complex, multi-step process.
At home, you can encourage your child to participate in cleanup after a meal—from bringing dishes into the kitchen, scraping food into the trash, and placing them in the dishwasher, to wiping down the table and sweeping up food crumbs from under it.

Taking care of plants. All of our Montessori preschool classrooms have plants, and taking care of them is a great Practical Life activity. Students learn to dust leaves, cut off and dispose of dead leaves, and water the plants. They also learn how to arrange flowers to help beautify their classrooms!
Your child can enjoy similar tasks at home by selecting a few small plants at a garden store with you and then being entrusted with their care. Observe her pride and attentiveness as she thinks to water her plants and keep them healthy. And, of course, if you have a garden, by all means invest in some child-sized tools so your preschooler can help you. Planting vegetables and fruits and harvesting them is not only a great Practical Life experience, it’s a great opportunity to awaken an interest in science, too.

Getting dressed and taking care clothes. The Dressing Frames are a set of Practical Life materials that enable children to learn how to manage common fasteners, such as zippers, buttons, snaps, belt buckles and shoelaces. Within his first year in the Montessori preschool class, your child will round out his dressing skill set. He’ll also refine other skills, such as folding cloths, sorting things by color, and placing things into their proper spots on shelves.
With these skills, your preschool child will soon be ready to take care of much of his daily clothing needs. A 3½ or 4-year-old is usually able to dress himself from head to toe—if he’s given enough time. He’s also able to place dirty clothes in a hamper, even sorting them by lights and darks, and can put folded clothes back into drawers and shelves. Older preschool children can contribute more to the family’s laundry: try teaching your 5-year-old to load the washing machine, measure pour detergent, and get the load started! She’ll also be able to fold many of her own clothes, and hang up dresses and pants on hangers in her closet.

As we wrote elsewhere, a child who feels capable because he can act in the world, without needing to rely on Mom or Dad for every little thing, is a child who is developing self-confidence. Writes psychologist Madeline Levine:“Self-esteem doesn’t contribute much to success. But success contributes mightily to self-esteem. Kids have to ‘do’ something, and do it well, to get a self-esteem boost.”

Helping the child learn to do things for himself, however important, is just one of the goals of Practical Life. Like all aspects of a Montessori preschool classroom, Practical Life has many learning objectives. Here are a few:

To facilitate a smooth transition to school by providing familiar activities. Practical life is the part of the classroom where new students feel comfortable because they reflect similar activities to what they see at home. Peeling a banana, pouring water, cutting with scissors, and cleaning spills are all familiar activities the young child finds comfort in.
To develop concentration. Practical Life is usually where a child first connects with a material and immerses himself fully in a chosen, repeated activity. A child who previously darted around the room, unable to pause long enough to connect with any particular material, might become fascinated with pouring water back and forth or with drying a table. In doing so he learns to focus his mind for the purpose of mastering a new skill. This is the start of a child’s attachment to the many Montessori materials, which build in complexity to help build concentration.
To develop fine- and gross-motor skills. Practical Life tasks are excellent motor skills activities. Carrying heavy objects such as classroom chairs or buckets of water builds gross motor strength; pouring from a small pitcher or scrubbing a table increases precision of movement; peeling an egg, using a dropper, or picking up dropped beans all strengthen the three fingers needed for writing with a pencil.
To develop problem-solving skills. Like most Montessori materials, Practical Life activities have a built-in control of error: They enable the child himself to judge whether an activity has been done satisfactorily or not (water has spilled; a button is left without a whole; the loosely rolled rug won’t stand up in the bin). With positive guidance from his teacher, the child learns to pay attention to these cues and acquires a habit of self-correction.
To develop logical work habits. Practical Life activities progress in complexity and, in doing so, increase a child’s ability to work through a series of steps in a logical way from beginning to end. This is vital for success with more abstract language or math work later on.

While many parents are eager to see their child progress to academic lessons in the preschool classroom, we hope you’ll see the hidden value in Practical Life, and wholeheartedly support your child as he explores the many fun and educational activities found in this unique part of the Montessori Primary class.

A Sense of History at LePort

Amid the safety and comfort of Orange County, it is hard for us to imagine that living in America once meant risking your life for an uncertain future. Yet this was exactly the challenge early British settlers faced in the untamed New World. Thousands of miles from family, friends, and king, settlers in Jamestown, Virginia, and in the colony at Massachusetts Bay, literally struggled for basic necessities while working to build a future for themselves and their descendants.

This school year, the students in LePort’s 7th-grade history class are studying early America, and last month they completed an assignment allowing them to vicariously experience the life of an early colonist. Writing as a fictional settler in one of the first American colonies, the 7th graders’ mission was to compose a letter to a friend or relative back in England and attempt to convince him or her to travel across the ocean to join the new colony. Within the bounds of what they learned from lectures, assignments and discussions, along with independent historical research, students were left free to determine the details of their letter – of their settler’s life, values, and voice. They completed their research, planning, and initial writing in history class, and received additional feedback on further drafts from their language arts teacher, Mrs. Longley. The results were impressive.

Below is one example student letter. Sidney Bowen – or Sir Terrance Francis Williams XVI – chose to write from the perspective of a settler who came to seek gold in Virginia, and found himself quite unprepared for the rugged life he now leads. In inviting his friend across the Atlantic to join him in America, “Sir Terrance” tries to put a good spin on the challenges he has faced, but does not quite succeed. I hope you enjoy reading Sidney’s letter as much as I did!

January 12th, 1622

Dear Sir Arnold Louis Bennet,

How are you, my old friend? How is your insuperable daughter, Mary? (I am only joking…) I am now living in the “New World” in Jamestown, Virginia. It is quite a lovely place, indeed! The reason I am suddenly speaking to you on such matters is because I wish for you to join the settlers and come to the new land. I know you were a wealthy man, just as I was, and I have heard that you are beginning to lose your fortune, as I had sixteen years ago in 1606. I was running low on gold, but I did not want to work, and why should I? Should a handsome, dashing gentleman be forced to plant crops and pick up foul cow manure? I think not! But before I went to weep in a corner, I heard that the London Company was going to send three ships out to Chesapeake Bay to search for gold. GOLD! In an instant I decided to invest in the London Company and board one of the ships to become a gold hunter, in order to gain back my fortune and possibly receive more. In late August of 1607, we all arrived in Jamestown, named after King James. We faced a few conflicts with illness, as any colony did, because of the lack of food and the swampy atmosphere. But a man named John Smith, whom I happened to abhor, saved some of the other gentleman settlers who were having a miniscule bit of trouble with local natives. The colonists and I were at the time living near the Algonquin Indians, whom John Smith befriended. This friendship allowed us to trade food and crops with the Indians.

After we settled briefly, all of the gentleman settlers, including me, went out to search for gold. After a few days of unenthusiastic rummaging, we all spotted yellow dirt deep in the ground! We brutally and viciously dug, and dug, and dug until we found immense pounds of gold! It was a precious sight…until we sent it back to England. We realized that our riches were not truly riches, but pyrite (fool’s gold). John Smith believed that we spent too much time searching for worthless gold. (But anyone could’ve mistaken it for gold, Smith!) Then—the nerve of the man!—he created a ludicrous law that we needed to plant our own crops or we would not receive food. “He that will not work shall not eat”, he snorted insolently.

In 1609, John Smith fortunately left our colony and went back to England, but then we had a little glitch in our lifestyle. People now call it the “Starving Time”, but that saying is quite exaggerated. We merely had a lower amount of food in our supply, which made us lightly gnaw on wild animals, and dead bodies…but it wasn’t as horrid as you might think. It could’ve happened to any colony without the proper tools for building homes. Luckily, England heard of our inconsequential troubles, and they instantaneously sent over supplies. We were saved…I mean, helped. In 1611, the London Company sent Sir Thomas Dale over to Jamestown to become governor of our little colony. He gave each person a three-acre amount of land, but we were forced to work in order to keep it. Soon after, we discovered that the Indians had found a plant, which they would smoke out of a clay pipe. The plant was named tobacco. After this incredible plant was discovered, everyone was planting tobacco in their land to sell to English merchants at exorbitant prices. And believe me, this plant that is formed into smoke is the most addicting material I have ever tasted.

1619 was one of the most exciting times in Jamestown because a ship of women arrived to enlarge the colony’s population. According to the colony’s laws, I am obligated to work most of the time in order to keep my land, which is a contemptible rule. The arrival of these women was principally exciting for me because I wouldn’t have to work nearly as much with a wife. My dear and charming wife, Jane, is not only beautiful, but labors day and night like a mule for her loving husband. Also, I do not have to pay my mule…I mean wife. Jane helps me through the horrendous pain by making our own clothes, planting crops for food, making soap, candles, and more! My favorite chore to watch is the process of candle making. There is a large iron kettle held on a crane over the fire, and when the fat and grease melt, she dips the cotton in the fat and allows it to dry.

From what I have explained about the colonies, you may not be entirely convinced to join me, considering all I have spoken about is work. If and when you arrive in Virginia, you will recognize that life is not only work, but there are families living in the colony, whose young children are receiving a glorious amount of education. I, for one, despise children, so I do not have any because they whine and cry, run around in dirt, and more things that I don’t wish to share with you. Since you always wanted to raise a family, you might consider having a child here. Although, I’m sure introspection will bring you to a firm decision to NOT have children, since they damage your life greatly.

Well, my dear friend, I have had a longing desire to see you again, for it has been sixteen years, and that is too long, Arnold. I anticipate that you find my letter influential enough that you will perhaps consider joining the colony. It is unlike anything I have experienced my entire life, and I believe you will concur with me. I hope to see you in the new land, Arnie!

Sincerely,
Sir Terrance Francis Williams XVI

One of our goals in the LePort history program is that students do not just study history, but are immersed in it — that the past is understood not as a series of names, dates, and events to be memorized, but as flesh and blood. Taking on the role of a historical character is one of the most rewarding ways to immerse oneself in history, but also one of the most demanding, because making such writing realistic and compelling requires a student to integrate a wealth of information. For assignments like the settler letter, students need to know more than the 5 Ws of history (the who, what, where, when, and why); they must have a full-blown sense of the past — of the goals, manners, and values of historical cultures and people. Sidney clearly achieved that in her letter, as did her peers in theirs, and the result is a meaningful understanding of early America that will not be forgotten.

Matt Ballin, History Teacher

Just not good enough: why your child deserves a better curriculum

If you attended Elementary Curriculum Night, you had a sneak-peek into LePort’s unique approach to education. [See the videos at the bottom if you weren’t able to attend.]

In this newsletter, I’d like to offer you further insight into what makes LePort’s curriculum different. How does LePort’s approach, which we call “Knowledge for Life”, compare with the California Standards?

Almost everyone agrees that there’s something wrong with “teaching to the test”, the practice of focusing in school on memorizing and drilling for standardized tests. But this practice is based on the California Standards—the textbooks, lessons and outcome measures approved by State education committees.

Why Do We Study Science

Science education is a staple of modern schooling. One rarely hears anyone question the value or necessity of teaching our children science. But what is the reason behind this view? Why should a child study science?

Despite today’s focus on standardized test and national content standards, it’s clear that the purpose of science education cannot merely be to ensure that children score well on standardized tests of science. (Why have those tests?) The same is true of any answer of the form that science education is necessary to ensure that a child will succeed in high school science, or be ready for college many years down the road. (Why should science be taught at those levels?)

Few question what students are being taught or how.

Memorizing and drilling students, once thought out of fashion, is now back in vogue in schools across the country. In the wake of the “No Child Left Behind” act, the emphasis of teaching has shifted to basic skills, and to increasing performance on state-wide standardized multiple choice tests. And while many children, especially at middle class public schools, are scoring better on standardized tests, some educators are starting to wonder if these results might not be telling the whole story.

In his book The Global Achievement Gap: Why Even Our Best Schools Don’t Teach the New Survival Skills Our Children Need – and What We Can Do About It, Dr. Tony Wagner questions the wisdom of the traditional teaching approach and the apparent excellence of suburban elementary, middle and high schools. It is an important book to read for parents and educators alike.

Dr. Wagner believes that even the best public schools spend too much class time on memorizing content and drilling on basic skills, and he suggests that this leaves students without the thinking skills and real, meaningful knowledge they need to succeed in life. He writes of his decades of experience as a teacher, researcher and education policy advisor:

What I have seen in some of our best public schools over the past decade is that while Johnny and Juan and Leticia are learning how to read, at least at a basic level, they are not learning how to think or care about what they read; nor are they learning to clearly communicate ideas orally and in writing. They memorize names and dates in history, but they cannot explain the larger significance of historical events. And they may be learning how to add, subtract, and multiply, but they have no understanding of how to think about numbers. Not knowing how to interpret statistics or gauge probability, many students cannot make sense of the graphs and charts they see every day in the newspaper. They are required to memorize (and usually quickly forget) a wide range of scientific facts, but very few know how to apply the scientific method—how to formulate a hypothesis, test it, and analyze the results. Finally, I have observed that the longer our children are in school, the less curious they become.

Dr. Tony Wagner

He quotes a scientist from MIT, who describes his two sons’ experience in science class in 4^th grade at one of the most acclaimed public schools in the country:

They went to the same school and had the same teacher. … My eldest son had a great experience. His class went over to the pond at Mount Auburn Cemetery and took samples from the muck. They brought them back to school and studied what they found. They discovered all kinds of creatures there –ones that even I hadn’t seen! It was great, ‘hands-on’ science, and it really motivated my son.

But my second son’s experience was totally different. Now all the kids had to take the MCAS test [annual standardized test required of all Massachusetts schools], and the teachers felt they couldn’t take the time for the ‘fun stuff.’ They felt they couldn’t take the time to collect and study the muck. They had to prepare fall the kids for the tests.

I worry about the future of science in this country… For kids to get passionate about science, they have to get their hands dirty—literally. They have to have labs where they study things in depth and learn to observe, instead of just memorizing facts from a textbook. The kids who take my intro lab courses today have gotten top scores on all the Advanced Placement science courses in their high schools, but they don’t know how to observe. I ask them to describe what they see in the microscopes, and they want to know what they should be looking for—what the right answer is.

Dr. Tony Wagner

In our view, this is one of the best summaries of what is wrong in education today: children memorize words, but don’t learn about the world.

Mr. Wagner continues with an even more alarming observation, namely, that the public education establishment—from educators to policy makers, from researchers to concerned business men—is not even asking the right questions to address the problem: “The only debate taking place about education in America today is simply whether to modify certain provisions of NCLB [the No Child Left Behind education act.] Few question what students are being taught or how.”

Yet these are exactly the questions an intelligent parent ought to ask of potential schools: Why are you teaching—what is the goal of your education? What are you teaching my child? And how are you teaching it? If you share our belief that children need to be engaged at school, that they need to care about what they learn, that the content of education matters (=what children learn), as does the pedagogy (=how children learn), then come and observe in our Montessori elementary school and Montessori middle school programs. You’ll discover an education like no other, and may just decide that it is time to question your own child’s educational options and explore Montessori for your child.

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