The Mysterious Trinomial Cube

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Today, we’re going to highlight on one of our students’ favorite works; the trinomial cube. There’s real beauty behind the intricate details of this mathematical work, details that are hard to notice at first glance.

The direct aim of this work is rather obvious; to build a puzzle in a box. The indirect aim, an introduction to algebra and preparation for the formula a+b+c³. DSC_0349 (1)

The child approaches the box with curiosity. It’s elegant details can spark the interest of anyone. Children are inherently captivated by mathematical materials. The colors, the difference is sizes and heights…”Why these specific colors?”, “Why do they fit together like that?”…DSC_0343

While there are many hidden lessons in this puzzle, the child is actively working towards building a concrete foundation for the abstract nature of the formulation, which they will later expand upon. The puzzle helps the child grasp the concept of a+b+c³ at such a young age, rather than simply memorizing the formula.

Through the child’s discovery, they come to unlock the intricate layers of the trinomial cube.DSC_0356 (1)

To begin, the guide carefully opens the box, and lays out all of the pieces, organizing them in different manners. With little, to no words, she places the cubes upon the lid, pairing the colors to one another. Each layer is placed in the box upon completion. The child is then invited to do the work on their own. There are many variations of the trinomial cube that call upon the child’s creativity, imagination and critical thinking.

“These small objects fascinate a child. He must first of all group them according to their color, then arrange them in various ways, making up a kind of little story, in which the three cubes are three kings, each one having a retinue identical to that of the other two, the guards being dressed in black. Many effects can be obtained through the use of this material…when playing with this material, a child forms a visual image of the arrangement of the objects and can thus remember their quantity and order. The sense impressions received from these objects furnish material for the mind. No object is so attractive for four-year-old children. Later on, by calling the kinds a, b, c, and writing the names of the separate pieces according to their dependence upon their own king, five-year-old children, and certainly six-year-olds, can store up in their minds the algebraic formula for the cube of a trinomial without looking at the material, since they have fixed in their visual memory the disposition of the various objects. This gives some idea of the possibilities that can be attained in practice.” (Montessori, The Discovery of the Child)

To see the lesson in full, click on the link below:

https://www.youtube.com/watch?v=ZEZnNFxsnS8#t=13

Back to Basics: Preliminary Lessons

“It is interesting to see how little by little, these children become aware of forming a community which behaves as such…Once they have reached this level, the children no longer act thoughtlessly, but put the group first and try to succeed for its benefit.” (Dr. Maria Montessori)

In Montessori, our main goal is to help the child succeed in whatever way possible. When they first enter the community, there is a certain level of expectation for how they are to act. Children are treated with respect, and treat one another as such. This is called Grace & Courtesy. To help orient them to the environment, they are taught basic, or preliminary lessons on how to function in the classroom. They’re given lessons on which works are to be used at the table, or which ones can be used on the floor, where to locate table/floor rugs, the Guide models how to gently close/open doors, how to walk quietly and control ones body while moving about the community, how to ask for help, how to push in a chair, how we walk around our friends’ work, saying “please” and “thank you”, covering one’s mouth when coughing, or saying “excuse me”, and just generally how to act in the classroom. Exercises in Practical Life are also introduced to help the child refine skills necessary to carry out more complex works, such as dish washing, sweeping, dusting, window washing, and so forth.DSC_0230 (2)

I get asked quite frequently by newly enrolled families, “Why is my child receiving lessons on how to push in a chair”, or “Why did they spend the afternoon practicing walking on the line? Shouldn’t they be reading, or doing the art works”, or something along that line. These preliminary lessons, are just as important as any other lesson, and build the foundation for how the child will act and work in the classroom for years to come. These lessons are extremely significant to the child’s orientation to the environment. We cannot expect a new child to enter the community, and immediately focus all of their attention and concentration on one work at a time. Especially if they’ve never been in a school setting before. Take “learning to write” as an example. The child will never learn to properly write without first mastering the pre-writing lessons, such as strengthening their large muscles, developing strong hand-eye coordination, then refining their pincer grasp, and then working with pre-writing materials, such as tracing the metal insets, or tracing sand paper letters with their fingers, and so forth. In time, the child learns to master these complex works through muscle memory. Montessori children are patient. Their young minds are extremely absorbent. They have a deep appreciation towards caring for their environment, and those around them, above all else. 

12822325_361454707358585_1076512372_nDr. Montessori introduced the exercises in Grace and Courtesy as she observed a young child’s need for order.  “Montessori education includes explicit instruction on social behavior in a part of the curriculum called Grace and Courtesy, which are on par with lessons in math, music, and language” (Lillard, Montessori: The Science Behind the Genius). Grace and courtesy lessons help the child to have the language required to build confidence and awareness of those around them. They also help the child become a productive member of the classroom community.helping handsDSC_0238 (1) (2)Our goal is to model these fundamental lessons for the child, and have them repeat the activity in their own successful way. The child needs to participate in these core activities to prepare them for their environment; to learn how to grow into problem-solving, independent, young thinkers.

To initiate perfection at this time of life is an immensely productive piece of educational work: the teacher reaps a wonderful harvest after a minimum of trouble given to sowing the seed. (Montessori, The Discovery of the Child)

The New Preschool Is Crushing Kids, Erika Christakis, the Atlantic

Step into an American preschool classroom today and you are likely to be bombarded with what we educators call a print-rich environment, every surface festooned with alphabet charts, bar graphs, word walls, instructional posters, classroom rules, calendars, schedules, and motivational platitudes—few of which a 4-year-old can “decode,” the contemporary word for what used to be known as reading.

Because so few adults can remember the pertinent details of their own preschool or kindergarten years, it can be hard to appreciate just how much the early-education landscape has been transformed over the past two decades. The changes are not restricted to the confusing pastiche on classroom walls. Pedagogy and curricula have changed too, most recently in response to the Common Core State Standards Initiative’s kindergarten guidelines. Much greater portions of the day are now spent on what’s called “seat work” (a term that probably doesn’t need any exposition) and a form of tightly scripted teaching known as direct instruction, formerly used mainly in the older grades, in which a teacher carefully controls the content and pacing of what a child is supposed to learn.

Continue reading

Transition Techniques and Tips

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Imagine that you’re back in preschool. You arrive at school for the day, hang up your coat and back pack, and get settled into the morning routine. You decide to paint this morning, and begin gathering your supplies, which takes roughly 15 minutes or so. Before your brush touches the piece of paper, you’re interrupted by loud clapping. “Okay, everyone! Put your things away, it’s circle time!”. You’re frustrated. You barely had time to even start painting, and now you must put your things away. All that time put into the preparation, only to be interrupted and forced to do something else. Circle time begins, filled with sing-along songs and a few stories. After that, it’s music lessons, then outdoor time, lunch, nap, and then it’s on to afternoon extra curricular activities. Your day is filled with transition after transition, leaving little to no time to adjust to each new activity.

This rarely happens in a Montessori community. The children are given the freedom to work, uninterrupted for long periods at a time, with calm, comfortable transitions throughout their day. The Montessori Guide observes and understands when the appropriate time is to transition from the morning work cycle to outdoor playtime, or to lunch, and so forth. We observe the children to find out their needs. We look for signs of readiness for what comes next; signs that the child is ready for a new lesson, or for greater responsibility. We make the expectations for each transition very clear. We demonstrate and model how to carry oneself during a transition, and let the older students help the younger students practice.IMG_6431

If you’ve ever been in a Montessori classroom, and truly know the philosophy, you understand the necessary role that transitions play in the students’ daily routine. Transitioning from one period of the day to the next, can be quite challenging, for any age group. Guiding an entire group of children during a transition takes practice; both for the Guide, and for the children. Keep in mind that you need to have realistic, age-appropriate expectations for the children in your care, and expect them to struggle or make mistakes during the learning process.

The patterns and daily routines that we establish for our children help build the foundation for their ability to adapt. This, like many other skills, is something that has to be taught, and learned through repetition and consistency. A new student does not often come to school knowing how to transition, so we have to help them.

Whatever your technique may be, do so with the utmost respect for your children’s needs, and make sure their work is not interrupted abruptly, or unnecessarily. Over the years, I’ve witnessed many different transition techniques. A popular technique is to simply sit on the rug and sing, ever so softly, as to get the attention of the entire group. Another, has a small bell to ring when the work cycle is complete. This is usually done by a senior student. Lining up is also a lesson that needs to be taught. You cannot just expect a child to know how to stand quietly, or where to stand, what to do with their hands, or feet, can they talk to their neighbor in front or behind them, are they to remain quiet…there are lots of skills to be refined!
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Give your students advance warnings of an upcoming transition. Walk quietly from one child to then next, reminding them that “you have a few more minutes”, or play a quiet, familiar song. Give a set amount of time for actual clean-up. A child who’s been working on the world map all morning, and has lots of different materials, may want to leave their work out. Put it aside, with their name on it, for them to return to at a later time. Practice this “clean up” routine every day, be consistent, and encourage students to help one another. And as always, safety is of the utmost importance. Always make sure students respect one another’s space. One Guide can help clean up, while the other watch the students to make sure they are safe at all times.
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Most importantly, follow the child. The dynamics of your room will tell you how to conduct each transition, in a way that is beneficial for you, and your students.

Here are a few teacher resources, to help reference when planning transitions/daily routines:

Parent Resource: Managing Daily Transitions at Home:

Superwoman Was Already Here! – Daniel Lipstein

“According to a recent Newsweek article, preschool children on average ask their parents about 100 questions per day. Sometimes, parents just wish it would stop. Tragically, it does stop. By middle school, children have pretty much stopped asking, and student motivation and engagement plummets. Kids don’t stop asking questions because they lose interest. They lose interest because they stop asking questions. In a Montessori classroom, this does not happen, because questions matter more than answers; a child’s natural curiosity is welcomed, not shunned. In fact, a child’s curiosity is also what drives the lesson forward.

…Preparing children for the future demands that we encourage and inspire them to ask questions, and teach them how to explore those questions for themselves.”

Really interesting video created by a Montessori father, talking about the positive impact Montessori education has on our young children. Definitely worth 6 minutes of your time!

A Helping Friend

Parent Discovery Session: “Third Year Montessori”

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“At the end of the day, the most overwhelming key to a child’s success is the positive involvement of parents.” – Jane D Hull

We had a great turn out for last night’s Discovery Session, “See. Experience. Believe. Third-Year Montessori.” Families from all our classrooms came to witness our senior primary students presenting lessons in the classroom. Our friends were very excited to display works that they’ve been practicing for many months now! This was truly an enlightening, informative night!

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One of our friends showing the short chain of 1-5 to her parents. The beads allow the child to visually see number quantities, and skip count (3…6…9…and so forth). This is an important step in learning enumeration; a lesson that is taught all throughout their three-year primary cycle. It was so neat to witness our young friend teach her mom and dad this special lesson!

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Everything the child learns as a young infant, prepares them for works such as this. When they first enter the primary community at age 3, they’re given the opportunity to explore and discover their new community. The second year is a time of solidification, further refining these new-found skills. And the third year (5-6 years old) is a time for application. Each lesson builds upon itself, ultimately preparing the child for the last year in our primary community.

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I practiced for such a long time on the Map of Europe. My muscle memory allowed me to do the entire puzzle off the board, and without a control chart. I was so happy to include my mom and dad in this work!

Thank you, parents, for supporting your young ones, and being a big part of their educational development!

Summer Camp at HBMH – 2016

Summer Camp at HBMH – 2016

PEN, Third Year Montesssori

Join us tomorrow for a special Primary Discovery Session…

“See. Experience. Believe. Third-Year Montessori”

5:00pm in the library

Hosted by Ms. Geetha and Ms. Patti

(lessons presented by children 5 years and older)

This parent workshop is applicable to ALL our HBMH Families! We encourage everyone to join us!

Our Primary program is structured in a way that the 3 year old child, or “first year” is a time for discovery. The “second year” is a time of solidification. The 5/6 year old, or “third year” is a time for application for all the child has learned since early infancy. Our goal is simply to enlighten you and help you experience what your 5 or 6 year old child will be doing during their “third primary year” in Montessori. You’ll have the opportunity to witness lessons being given by some of our older, third-year students. We don’t always offer an opportunity like this, so now is your chance!

**Not all children will be presenting lessons. Classes will combine in Apple for those not participating in the workshop. Please RSVP if you plan to attend.

“Montessori children are encouraged to observe, explore, question, and investigate everything. They are allotted the freedom and time for the conception of a problem or situation and the discovery of its solution. This gives them the opportunity to produce ideas through flexibility which allows for the ability to switch from one perspective to another.” – Tami Kinna, Owner/Director HBMH

Hope to see you all there!

Throwback Thursday – 6 years strong