Tag Archive for: Motivation

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.










“The Red Coats Are Coming”: Visualizing and Feeling in Teaching

At LePort, we are always looking to improve ourselves as educators. And that means documenting and learning from each other’s ideas about great teaching practices. Over the years we’ve come to see that a major facet of great teachers is their ability to cultivate strong imaginations in their students and elicit even stronger emotions. Below is an internal paper written for our teachers on a related pedagogical tactic we employ daily. It is called visualization, and it is just one element of our experiential approach to education.

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Internal Paper: Experiential Teaching

Everybody has heard the line "The Red Coats are coming", usually at some point in elementary school. But how many of us can see and feel it? How many have a rich visual scene in their heads, with a real emotional connection to go with it?

Too often in school all we hear is words. Disconnected, uninteresting, non-visualized words. At LePort we know that words matter, and we revere them, because they are the means by which we grasp and communicate knowledge. But we also know that for words to actually represent knowledge students must understand them.

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An important method by which we ensure that words are understood, that our students connect what we’re talking about with their own personal context, is visualization – the eliciting of images in a individual’s mind. This tactic allows students to see what we’re teaching and to feel the emotional connection that comes only from experiential learning, ultimately making knowledge a student’s own.

To illustrate this idea, let’s travel back in time to our own elementary school, to our 5th-grade History (or Social Studies) class, when most of us first heard the "Red Coats" phrase. But on this occasion, let’s give the presentation the visuals and feeling it deserves, let’s make it a LePort style lesson:

Transport yourself to a cabin in early Colonial times (you know, homespun clothes, dirty hands, farm life). You’re ten, and you’re sitting in the living room around a fireplace reading. Above the fireplace, as in most homes of the time, sits a musket. Your dad is there, maybe a brother or sister if you have one. Mom’s out somewhere, don’t know where. Each of you are enjoying a book, you an exciting novel, though you’re a little tense because you’ve heard that British troops – Red Coats – have landed in your town and are abusing locals, some of whom are your friends’ parents. But the presence of the troops is still not fully real. It is still merely a news story to you.

You’re just reaching the climax of your novel, and your mind is now completely absorbed in your book. All of a sudden you hear shouting from outside the door. The voices are garbled at first, but then you make out the words. "The Red Coats are coming! The Red Coats are coming!!" Your eyes immediately shoot to the fireplace, and then to just a few feet up, where your dad’s musket sits. You see the musket as if it’s for the first time. Everything is quiet, motionless; life itself seems to have stopped. Then you remember that your dad is with you, in the living room. You look over to him. He is completely still, so still that his stillness belies what’s occurring within. In his eyes you see the deepest, most serious agitation you have ever seen in a man. One question then immediately comes to your mind: What is dad going to do?

At this point in the lesson, there is not one boy or girl who is really "in" the classroom. Each is in his own mind, living out his own visual story. And each wants to talk about it, to share his feelings. Hell, I want to share my feelings! This is when the teacher would transition to a class discussion – and boy what a discussion it would become.

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As teachers, all of us have experienced those special moments when every child, seemingly without exception, is engaged. In this case, the engagement is accomplished through storytelling. But why is this particular story so compelling? I think it’s because it offers the children a visual and emotional experience. When dramatizing this story in class, there are a few actual visuals a teacher would use – a picture of a British troop (a Red Coat) and a video of a musket being shot – but the real visuals come from within the child’s mind, from his capacity and willingness to use his imagination, to turn the teacher’s words into images … to paint his own unique picture of the story.

Our students have such a capacity in them, if we can provide the spark. Through visual and emotional teaching, we gain huge in our efforts to impart knowledge. And that is why I believe whenever we are speaking in class, our intent should be to help kids see and feel what we’re saying. We’ll succeed if we go in with this underlying objective to make words visual, to transform sounds coming from our mouths into the equivalent of experiential knowledge. This applies throughout subject areas, whether we’re teaching a novel, some math formulas, a grammatical concept, or a species of tree. (No doubt this tactic is most challenging in math, but maybe all the more reason to make it a stretch goal!)

So the takeaway here is simple. Whenever we are prepping what we will teach our kids, or whenever we are up in front of the class ready to say a few words, let’s ask ourselves: Will my students be able to see this, will they be able to feel this? The more we can answer "Yes", the better our classrooms, the better our teaching will be.

The Fundamental Choice

It is the child who makes the man, and no man exists who was not made by the child he once was. Dr. Maria Montessori

Last May, I had the opportunity to observe a kindergarten and first grade class at the local elementary school my then 5-year-old daughter would have attended in fall, if we went the public school route.

The school I observed is about as good as it gets in public education. It’s a “Blue Ribbon”, “California Distinguished” school, with standardized test scores in the top 5% of the state. It has families all over the city vying for spots. The principal, whom I had the pleasure to talk to at length, is a kind man and a good listener; he struck me as the type of educator deeply dedicated to providing the students in his charge with a quality education.

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Generally, public schools are reluctant to allow observations by prospective parents. After I shared that my daughter attended Montessori school, and that I was concerned how she would transition to the public school environment, the principal made an exception to his usual policy and invited me to observe some of his best classes.

I saw a lot in the time I spent in each of two classrooms. The kindergarten students were working on individual letter sounds q, v, and z. The 1st graders were writing 3-4 sentence paragraphs and working with numbers up to 100. The contrast with a Montessori classroom was dramatic. Kindergarten-aged children in a Montessori environment are reading real books and writing multi-sentence stories in cursive, and elementary 1st year students are writing page-long stories, reading chapter books and doing arithmetic into the thousands.

But while the contrast was dramatic, it wasn’t surprising to me. I went in expecting this difference in academic progress. What really took me by surprise was just how deep the difference between the programs went. The traditional classrooms I observed were, in a thousand ways large and small, training students to conform passively to adult rules and expectations—a completely opposite behavioral mindset than the active-minded independence we encourage in Montessori preschool and elementary programs.

Let me share just two small observations among many, one from each class.

First grade: Teachers as guides or as servants? Children as independent actors, or passive observers?

In the first grade class, the children were studying how seeds grow into plants. Each child was asked to observe how a few lima beans and sunflower seeds germinated, and to record their observations in a science journal—a project that you might well find in a Montessori lower elementary classroom.

But here is how the project was implemented in this classroom: the teacher walked around the tables in the room, stopping by each child. She tore off a paper towel, put it on a plate, and sprayed it with water. She then had the child put the lima beans and seeds on the paper towel. After that, the teacher folded the towel, and inserted it into a zip lock bag, upon which the child had written his or her name. Over the entire 15 minutes I observed, the teacher was occupied making these kits for the children, while children were apparently supposed to be working independently on other tasks, but in fact spent much time chatting and mingling without a clear purpose, as the minutes ticked by. The teacher completed the kits of approximately 6 out of the 30 students in the room, suggesting that she was going to be occupied by kit making for well over an hour that afternoon.

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As someone familiar with Montessori rooms, I could not believe that the children had such a passive role! This was a class of 6 ½ to 7 ½-year olds, fully capable (one hopes!) of tearing off paper towels, of wetting them by using a sprayer, of counting out beans and seeds and placing them on a towel, and so on. These children could have and should have made these science kits by themselves! Instead, the teacher did it for them. The teacher was in charge, the students, outside observers of their own education.

I couldn’t help but contrast this with how the same experiment would happen in a Montessori classroom. The teacher might take 10 minutes in the morning, collect a group of students ready for this experiment, and give them a brief introduction, describing the purpose of the work and demonstrating how to assemble the experiment. She would then set up a table with all the materials, and invite the children to make their own kit. The children would autonomously make their own bags, taking turns at the table. They would have ownership of their work, and reinforce many practical skills in the process. They would help each other if one got stuck, with the teacher monitoring from afar to ensure that the peer interaction was to mutual benefit. The teacher would gain over an hour to dedicate to her actual job, helping students learn, rather than spending her time in essentially the role of an unwanted nanny or servant, doing things to children perfectly capable, and almost certainly eager, to do them for themselves.

Kindergarten: Respect for intellectual independence, or conformity and obedience?

In the kindergarten class, I arrived during a silent work period. I was pleasantly surprised at first: after all, independent, engaging, self-initiated work is the core means to develop concentration skills in children!

But when I observed more carefully, here’s what I saw: these 6-year-old children were totally silent. Not one word was spoken. They were glued to their desks, upon which were found things like play dough, simple coloring pages and other very basic activities typically undertaken by 3- or 4-year-olds in a Montessori class. Some children were engaged, but many more seemed bored and disengaged.

And then the work period ended. The teacher turned on the light, and started counting, loudly: “Five, four, three, two, one. All eyes on me!” Without giving children time to process her expectations, she immediately started directing her students: “Sara, put that down. Ian, stop. Look at me, now. Come on class, remember our agreement: when I count, you stop working. Let’s try that again. Put your fingers on your noses, all eyes on me!”

I stood, stunned, as I saw these twenty-odd six-year-olds touch their noses, line up, and stare at the teacher. I cringed as they were ordered to clean up, pronto (“you have three minutes to clean up, then please find your spot on the carpet” and “Peter, you are late, pick up your pace.”)

Compare this scene with the work periods I observe regularly in Montessori classrooms. There, children have 2-3 hours of uninterrupted work time, twice a day. During this time, the classroom is calm, but not eerily silent, as children are free to move about, talk in appropriate volumes as they work with friends, and select from a wide range of stimulating activities much more engaging than play dough or coloring pages.

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In such a Montessori room, here’s how the work period might end: the Montessori teacher would ring a small bell, and speak gently in a quiet voice, “Children, I invite you to finish up your work and put it away if you are interested in coming together in circle.” After this request, children are free to complete their activity, and to put it away on their terms. A child immersed in an advanced task might continue with it, even as the other children join the circle and the teacher starts reading a book or singing a song. Another child might leave his work out, with his name badge on it, so he can continue and finish it in the next work period.
Consider the difference. In the public school class I visited, the implicit theme is obedience to adult rules. In practice, students learn to conform habitually and unthinkingly to cues and prompts and commands. In a Montessori class, in contrast, the theme is respect for each individual, and the result is that a child develops the ability to responsibly take care of his own work, learning how to act freely while also considering the needs of others.

I cannot be sure how representative my observations are of public schools in general. As a parent, if you’re considering public school, you should definitely make the time to observe the school and classroom your child would be joining. What I know is that this was a highly-rated school, and the two classrooms I observed were chosen by the principal as examples of what a good public school education can look like.

If what I saw is indeed indicative of a pervasive characteristic of public education (and sadly, I suspect it is), then the implication is that in choosing between a public school and an authentic Montessori school, you are making a choice that goes far deeper than just the difference in academics. You are choosing the type of implicit values that will be emphasized to your child: respect vs. obedience, creativity vs. conformity, active-mindedness vs. passivity.

As Dr. Montessori put it, it is the child who makes the man. I’d encourage you, in judging your child’s future classroom, to ask yourself what kind of man or woman you want your son or daughter to become.

This blog post was originally featured on the Maria Montessori website.

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

montessori preschool private school huntington beach irvine

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?

montessori preschool private school huntington beach irvine

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.

montessori preschool private school huntington beach irvine

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:

 

At LePort, the “passion for learning” is kept alive

montessori preschool

What does medieval history have to do with a juicy steak from a modern, upscale restaurant? Read on, watch the video and find out!

In a recent LA Times article, education reporter Karin Klein reflects on her experience at her children’s back-to-school nights:

Read more

Creative Play and Montessori Principles

Several recent articles in major newspapers discussed the demise of creativity in kids, and linked it to a lack of “unstructured, messy play.” For example, The New York Times reports:

For several years, studies and statistics have been mounting that suggest the culture of play in the United States is vanishing. Children spend far too much time in front of a screen, educators and parents lament — 7 hours 38 minutes a day on average, according to a survey by the Kaiser Family Foundation last year. And only one in five children live within walking distance (a half-mile) of a park or playground, according to a 2010 report by the federal Centers for Disease Control, making them even less inclined to frolic outdoors.

Behind the numbers is adult behavior as well as children’s: Parents furiously tapping on their BlackBerrys in the living room, too stressed by work demands to tolerate noisy games in the background. Weekends consumed by soccer, lacrosse and other sports leagues, all organized and directed by parents. The full slate of lessons (chess, tae kwon do, Chinese, you name it) and homework beginning in the earliest grades.

We’d agree with many of the issues these articles highlight, such as the deplorable amount of time US kids spend in front of TVs and computer screens each day, or the creativity-stifling impact of teaching that focuses on improving standardized, multiple-choice test scores.

At the same time, we don’t agree with the view of creative development underlying these articles. They pieces intermix valid criticisms of forced parental structure or too much computer time with a lot of talk about encouraging messiness, putting up with chaos, clutter and uncertainty, and fostering the child’s imagination by letting fantasy run wild. The implicit assumption, which we dispute, is that creativity is borne out of disorder and impulsivity. Polemics against too much forced structure are important and valuable. But more important is the answer to the question of why play is so important to children, of how, fundamentally, creativity comes about—and what the connection is to a child’s intellectual development.

Notice that descriptors such as “clutter” and “noisiness” evoke a picture of an environment quite different from a Montessori classroom, which seems to suggest that the structure of Montessori—the sequential materials, the orderliness, the purposefulness, the calm—are in some way undercutting a child’s creative development.  If this were true, then why are Montessori educated children renowned for their curiosity, their creative problem solving, their ability to think outside of the box? Put differently, does a Montessori education stifle imagination and rob children of the essential play of childhood, as these articles suggest?

In our view, nothing could be further from the truth. The superficial messiness of play, the focus on imagination and chaos, obscures a more fundamental difference between play and many other activities. The New York Times authors get close to this essential attribute when they discuss a need for “unstructured, child-led and child-created” activities, such as building a fort out of sofa cushions, making up elaborate pretend stories to act out, or drawing creative pictures, and contrast them with adult-led, pre-structured pursuits, such as organized soccer leagues, step-by-step adult-led crafts sessions, or foreign language classes.

In our view, what is really missing from many children’s experiences is not a license to engage in impulsivity per se, but rather an environment which enables children to independently choose to develop and pursue their own interests, and which equips them with the skills and knowledge to do so competently and successfully. Let’s look at these three elements in turn: choice, pursuit of interests, and knowledge and skills.

First, to engage in creativity, a person’s mind has to be voluntarily engaged in an activity. Whether it is drawing a painting, writing an article, or solving a challenging puzzle, a mind works best when it wants to do something, not for external rewards (stickers, grades, trophies, praise), but for the satisfaction of the activity itself. When children play, they by definition do so by their own choice: no-one forces a child to pretend to sail off to adventures on the living room sofa, and no stars are handed out for arriving at the pretend destination.

Second, creative people actively pursue a goal. While you can passively default to sitting in front of the TV, you cannot passively play, or passively achieve any worthwhile goal in life, whether it is building friendships, achieving success in a career, or mastering a hobby. Play is goal-directed activity, even though it might appear unstructured from the outside. It also typically involves problem-solving in the broadest sense. When 3-year-olds builds a sofa-cushion fort, they have to figure out how to place the cushions, where to get that sheet they need for the roof, how to gain an adults’ help if they can’t get up to the shelf where the sheet is hiding. It’s their goal—and they solve whatever problems arise in their pursuit of that goal.

Third, creative people have to have skills and knowledge to actually achieve their ends. No matter how inspired a writer may be, how creative his story idea may sound, he needs to have mastered grammar, acquired a strong vocabulary, and have learned the personal skills, such as organization and time management, which will enable him to successfully pursue such a long-range, challenging goal. Especially in today’s advanced civilization, ignorance makes creativity impossible. Worthwhile achievements of any type require a plan, and the ability to execute on it. Play, at its best, is skill and knowledge building, in a wide variety of forms. The toddler who stacks Legos is working on fine motor skills; the 4-year-olds who pretend-play at shopping are practicing language skills and daily processes they’ll need to master to become successful adults. Even video games derive a lot of their appeal from building skills—albeit often very limited skills only applicable in the video game’s own world.

Montessori education fully embraces these three principles. In Montessori classrooms, children have 2-3 hour periods of unstructured work time, each morning and afternoon. Each child chooses what activity to take from the shelves and work with. He actively engages with the material, he keeps at it until he masters it. It is his choice, his goal, his effort that will bring him the satisfaction of mastering a new material. Every activity offered to children in a Montessori classroom is carefully designed to help the child develop a critical skill, whether it is learning to pour without spilling, or learning the letter sounds. In fact, Dr. Montessori was convinced that a child has to know about reality first, before he can be truly creative, so she created a well-rounded collection of materials, one that gives children a balanced exposure to the basic elements of the world and human knowledge. This balanced education ranges from basic life skills to simple arts activities; from training the senses to observe carefully, to categorizing observations systematically so they can be easily retrieved later; from math and language, to geography, science and music. Dr. Montessori saw this rounded education as the foundation from which an individual can develop true creativity, in the sense of doing new things with real materials and ideas. Every item in the Montessori classroom is carefully chosen to give each child the “keys” to the world that may serve to spark his interest in discovery and creativity.

Montessori students, from the earliest age, learn that they are in charge—they choose, they pursue, they build skills and learn how to use their time and resources effectively. (And, by the way, they also learn to clean up their own messes, and acquire the habits of mental and physical order that are, in fact, another prerequisite of real creativity!) By daily experience, they become active explorers who enjoy tackling and mastering new challenges, rather than passive consumers reluctant to move off the couch, or to open any book beyond required homework.

The crucial difference is that Montessori education develops the capacity for creative effort, rather than mere impulsivity. It is this, the ability to apply oneself joyously to the task of pursuing or creating something personally meaningful, that is the hallmark of creativity. This is why the child who is allowed to uncritically “do what he wants,” without developing a capacity for discipline in pursuing what he really wants, inevitably ends up passive. Buy your child a new toy every time he gets bored, without giving him the opportunity to use his mind to find something interesting to do with the toys he has, and the result will be that he simply becomes less willing to do the work of escaping his own boredom.

So if your children want to build castles in the yard and have a princess picnic with a friend, or engage in messy arts projects, as Montessorians we say that by all means you should encourage them to do so. We just encourage you to keep in mind that creativity is the ability to apply effort in uniquely interesting ways. And because of this, we hold that a pro-effort, child-led classroom environment such as is found in a well-run Montessori school, helps rather than hinders the development of creativity. And as the icing on the cake, it will also help your youngsters learn to clean up the messes they make in their daily play!

– Heike Larson

Tiger Mom vs. Enjoying Childhood: A Choice you Don’t Have to Make

A recent article excerpting a chapter of Amy Chua’s book, Battle Hymn of the Tiger Mother, has sparked quite a debate on parenting and educational choices.

Ms. Chua and her supporters argue that it takes an authoritarian approach to parenting to prepare children for successful adulthood in today’s competitive world. For instance, Ms. Chua writes “My Western friends who consider themselves strict make their children practice their instruments 30 minutes every day. An hour at most. For a Chinese mother, the first hour is the easy part. It’s hours two and three that get tough.” Read more

Praise Effort, not Smarts

With the New Year upon us, it is the time for New Years Resolutions. Here’s one that may strike you as odd, but that you may want to consider for your family: praise your children less.

Odd as it sounds, this is a key insight by researcher Carol Dweck, as reported in the recent book “NurtureShock: New Thinking About Children”, by Po Bronson & Ashley Merryman.

While many parents and teachers believe they can strengthen children’s confidence and help them achieve more by praising them for their intelligence and achievements, Dr. Dweck’s team of researchers has discovered that praising smarts can lead to an avoidance of challenges. Read more

Igniting a Passion to Learn

Take a moment to think back over the different experiences you’ve had during the past year.  What do you remember? When you do a quick survey of the significant events of your recent life, what type of things come to mind?

If you’re like most people, the events you tend to remember are more emotionally charged than those you’ve forgotten. Your mind goes to the gripping movie you watched, the novel that you couldn’t put down–but not that dry lecture at the long work conference. You have a vivid memory of the exuberant bike ride where you finally made it up that hill in target time, or the morning when you pedaled up over a fog bank to see a beautiful sunrise—but not the everyday training slog you conducted much more frequently. It’s hard to recall the daily routine of cleaning around the house and washing dirty laundry, but easy to invoke an image of the moment when your son took his first step right before your eyes, or the time you and your daughter had that wonderfully silly pillow fight, the one that left both of you out of breath from giggling so hard.

It’s not surprising that your lasting memories tend to involve events in which you are emotionally engaged. To the contrary, it intuitively makes sense: the reason you’re emotionally affected is that you care about what’s happening—and since you care, you’re more likely to remember it.

But why? What is it about being emotionally invested that enables greater retention?

In his recently published book, The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How, author Daniel Coyle offers us a fascinating answer.

Coyle argues first that learning of skills and memory occur as a result of particular way of being voluntarily engaged in a task—what he calls “deep practice”. Deep practice is a type of sustained focus in which a person is intently focused on completing a task superlatively. Coyle suggests that such deep practice results, neurologically, in the accelerated growth of myelin, an insulating substance that wraps around brain cells carrying signals from location to location the brain, and thereby strengthens those neural pathways.

The connection to emotions is this: only when learners are emotionally connected to the skill or knowledge they are pursuing are they sincerely motivated to put forth the effort that deep practice demands. Coyle argues that the will to engage in deep practice is ignited by emotional passion.

In his research, Coyle studied what he called talent hotbeds, places around the world where a certain talent–for music, baseball, learning–abounds, and observed that they all shared passion for what they do:

When I visited the talent hotbeds, I saw a lot of passion. It showed in the way people carried their violins, cradled their soccer balls, and sharpened their pencils. It showed in the way they treated bare-bones practice areas as if they were cathedrals; in the alert, respectful gazes that followed a coach. The feeling wasn’t always shiny and happy—sometimes it was dark and obsessive, and sometimes it was like the quiet, abiding love you see in old married couples. But the passion was always there, providing the emotional rocket fuel that kept them firing their circuits, honing skills, getting better.

Coyle’s argument fits with what we’ve observed in our classrooms at LePort Schools. The best teaching is teaching that makes a values-based, emotional connection between students and the rigorous academic content they need to learn. Only if students connect what they are studying to their own values, only if they are sincerely interested and engaged with what they learn, will they consistently remember and be able to apply their knowledge to situations in their own lives. Engaging students emotionally in what they study is a fundamental principle of correct pedagogy, and a necessary component of ensuring that students develop a meaningful, deep, integrated knowledge base.

So how can material be made emotionally engaging? There are countless ways, large and small. Take a Montessori classroom. It’s not an exaggeration to say that the entire Montessori approach is geared towards the goal of ensuring learning is properly motivated—students are provided an environment in which their internally driven interests are what fuels their cognitive inquiries.

Or consider LePort’s middle school history curriculum. We interest students in the study of a given historical period in a number of ways, one of which is by dramatizing that period through the inclusion of rich, moving historical fiction—novels and plays that invest the students in the times they are learning about. For instance, after reading The Lantern Bearers (a book that tells the story of a young Roman boy’s life in a once-civilized Rome now ruled by Saxon barbarians) our students become much more engaged in learning about the Fall of Rome: the literary dramatization of the period makes it emotionally real and important. Our history program also invests students emotionally by tying what they learn to their own values and life experiences—i.e. to that which already matters emotionally. See a vivid example here.

The underlying principle here is age-old: when something matters to you, you pay attention much more closely. Or more simply, when you care, you focus more. What Daniel Coyle offers in The Talent Code is a fascinating new perspective on this principle: not only do you focus more, but you actually focus differently. This point, along with the rest of Coyle’s uniquely rich analysis of the mental and neurological processes underlying the retention of knowledge and skills, makes The Talent Code a book that all educators should take the time to read and reflect on.

Ray Girn