3 - 6, 6 - 12, Math and Geometry, Montessori Materials, Uncategorized

Long Live the Short Chains

The Montessori Short Chains and Arrows pack a big learning punch and are often under-utilized.IMG_4716  They’re great for a homeschool environment because they don’t take up any shelf space.  Their initial purpose is to help the child first count linearly and then skip-count.  But when your child is comfortable with these two concepts, you can use the chains for much more!  Here are four ideas…

IMG_4657Find the number: Ask the child to set out the hundred chain with the corresponding arrows, while you cut up a few blank paper arrows (cut little rectangles and trim the corners to make arrows).  Write a number on the arrow (any number between 1 and 99) and have the child place the arrow on the corresponding bead.  If you notice mistakes, you can either let it be for now (and encourage more practice) or invite the child to count from the nearest tens-arrow (e.g. if the paper arrow says “26” and it’s in the wrong spot, invite the child to count linearly from the “20” arrow).

When they get comfortable with this activity, you can place blank arrows on random beads along the chain and ask the child to write down the numbers on the arrows. Later the child can do the same activities but without the tens arrows as guides.  You can ask questions like, “What number would you reach if you added 10 beads to 26?” or “What number would you reach if you counted backwards 8 beads from 45?”  You can do all these activities from around the age of 5 if counting skills are solid.

Find the missing number in a sequence: When a child knows how to skip-count, youIMG_4500 can present a new challenge by having them find the missing number in a number sequence.  The first few times you do this, you can use the regular arrows for any chain and hide one behind your back.  Ask the child to lay out the arrows and tell you which one is missing. (e.g. The child lays out 5, 10, 20, 25 and tells you that 15 is missing.)

Later, with the ten-chain, you write sequence numbers on paper arrows and the child has to use addition and subtraction to figure out the sequence and which numbers are missing. (e.g. Make arrows for the numbers 2, 19, 36, and 70 and the child has to lay them out and then figure out the pattern in the sequence and what number arrows are missing).  Help the child verbalize the process he’s using in order to solidify the concept and extend it to any number sequence without the material.  The first part of this work is great from the age of five, and the sequence activity is great from six onwards, increasing in complexity.

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Rounding to the nearest ten: The concept of rounding is not presented in isolation in the Montessori elementary, but is instead part of an ongoing conversation when working with money, estimating, etc.  However, if a child isn’t understanding the concept, you can use the hundred chain to support their comprehension.  Have the child match the tens arrows to the bead chain, and then talk about how the tens are numbers that we can work with easily. Give examples of when we might want to work with numbers rounded to ten instead of exact numbers.

Write the number 62 on a paper arrow and ask the child to place it on the corresponding bead on the chain.  Then ask him what “ten” the arrow is closest to, and explain that 62 can be rounded down to 60 (or is closest to 60).  Do the same with a couple of numbers with the units under 5.  Then make an arrow with a number that has the units higher than 5 (e.g. 68).  Ask the child what “ten” that number is closest to and point out that 68 rounds up to 70.  Then write a number with 5 in the units (e.g. 65) and tell the child that our rule is that if a number has a 5 or above in the units, you round UP to the nearest ten.  Give a couple of examples for the child and then encourage him to make his own examples.  The book “Sir Cumference and the Roundabout Battle” has a lovely story that fits well with this activity.

IMG_4719Polygons: The chains provide a fun exploration of shapes, from triangle to decagon.  Have the child carry all the chains on a tray to a large rug and ask her to make a closed shape with each chain imagining that the center was pressing out evenly on all sides.  Then ask her how many sides each shape has.  If you have a Geometry Cabinet, ask her to find the corresponding shape from the cabinet and put it inside or next to the bead shapes.  The child can write on a slip of paper the number of sides each shape has, and then you can give the names.  You can do a three-period lesson with a Primary child, and you can make an etymology chart with an Elementary child.  The child can also build the shapes around each other, with the square surrounding the triangle, the pentagon surrounding the square, etc.

I hope these fun chain activities bring new life to your bead cabinet!

This post contains affiliate links.

6 - 12, Cosmic Education, Theory and Practice

The Un-Checklist

If you’re a teacher or homeschooling parent who uses checklists to encourage a child’s organization and accountability, then you already know just how quickly checklists can turn into a battle of wills between adult and child.  You also probably sense that checklists hinder freedom of choice.  And you’ve surely noticed that checklists shift the focus of the child’s work away from self-development and flow, and towards task completion and industrial efficiency.

While checklists can work beautifully for a pilot safety-checking an airplane or a hospital staff preparing for a surgery, they wreak havoc on a child’s innate ability to follow his interests in the quest for true mastery and understanding.  There’s nothing wrong with wanting children to develop organization skills and hold themselves accountable.  So, how can we reach these well-intentioned goals without the drawbacks associated with checklists?

In our house, my son and I had a conversation about the reasons for practicing each of the disciplines that are currently a part of his homeschooling journey.  I made a large watercolor circle for each subject and wrote our combined thoughts.

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Then, on one sheet of paper, I started a mind map with the six subjects he’s currently exploring written in the same colors as the individual watercolor circles.  We re-read the reasons for exploring each subject area, and I asked him to think of some interesting topics he might want to learn about.  I connected those interests to the relevant subject areas.  We talked about some topics that I wanted to share with him and I wrote those down as well.

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This became our learning map, and we turn to it daily throughout the month.  Some days I choose what to present and other days he takes the lead.  We add topics to the month’s map as he discovers new interests, and I direct his attention towards the areas of the map that we haven’t visited yet.  Next month, I’ll start a new map and together we’ll discuss what he’s explored to his satisfaction and what he’d like to transfer over, in addition to the new topics we’ll be adding.

I love seeing him stand in front of the learning map, taking in the depth and breadth of explorations and learning opportunities he’s had in just one month.  This map doesn’t begin to capture the richness of his homeschooling experience, with daily adventures in nature, countless opportunities for social interaction, and freedom to play and daydream.  But I think it sends a message that’s developmentally appropriate for his age: Learning is a journey across a vast and varied landscape.  You may spend more time exploring some lands than others, but every stop along the way will enrich you and change you forever.

Montessori Theory, On Parenting, Social and Emotional Learning, Theory and Practice

The Puzzle-Child

Over the years of working in Montessori classrooms I’ve met many children who are eager to attend lessons, engage in follow-up work, and share their new knowledge.  And then there are the occasional “puzzles” (as my son’s Primary guide once referred to him).  How do you know if you live or work with a puzzle-child?

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Puzzle-children are those for whom learning comes easily but who see most teaching as a hindrance to their own learning agenda. On a good day, they grumpily humor your agenda for a short while and then stealthily slink away to pursue their own interests.  But most days, your invitation will send them into fight/flight/freeze mode: they either become argumentative (fight), run away from you (flight), or shut down (freeze), refusing to speak or make eye contact.

I used to think puzzle-children felt intimidated by the work or lacked the desire to learn.  But these children aren’t insecure or apathetic – quite the contrary!  I started taking the time to connect with puzzle-children to understand why they rejected lessons, and the phrase they said again and again was: “I already know that.”  Upon gentle prodding, it became clear that indeed, they did understand the concepts I was trying to present.

Puzzle children don’t care about your ego. In fact, in a battle of egos, theirs will always win.  They don’t care about sitting politely through your carefully planned presentation or showing you what they know.  They don’t care about your album sequence, the state standards, or your lesson plan.  They know what they want to learn, and they know they can use you as a resource to overcome any gaps in knowledge that pop up as they pursue their own explorations.

And that right there is the key to engaging successfully with a puzzle-child.  You have to be like a floor lamp: present but unobtrusive, and willing to shed light on whatever topic the puzzle-child approaches you about.  The puzzle-child will often be found with his nose in a book; tinkering with random objects; or using Montessori materials in ways that might seem sacrilegious at first but that, upon closer inspection, constitute legitimate intellectual explorations.

Conversations are essential for connecting with the puzzle-child.  But you have to watch your tone of voice: puzzle-children detect the moment you switch to a “teacher” voice, and in that instant you’ve lost them.  They also detect when you’re trying to quiz them.  You’re better off assuming they’re already experts. Use precise terminology when chatting with them; rest assured they’ll pepper you with questions if they don’t know what you’re talking about!

Puzzle-children love stories and experiments, and they are cosmic thinkers (meaning they’re able to effortlessly make connections among seemingly unrelated topics).  They’re autodidacts who focus on a topic until they have filled their cup. And then, just as quickly as the interest blossomed, it seems to disappear (but rest assured that the knowledge remains).

For puzzle-children and their adults, the most difficult times are those when the puzzle-child is between interests.  They’re often restless and irritable, flitting from one activity to another.  This is an important time for puzzle-children, and one should not jump in to fill the void with busy work or adult teaching agendas.  For it is precisely the space and boredom of their aimless roaming that will help them find their next “big thing”.

Puzzle-children don’t need to be taught how to learn.  If anything, they need to be protected from well-meaning adults who want to impose their teaching methods at the expense of the puzzle-child’s creativity and resourcefulness.  It’s a blow to the adult’s ego not to be needed, especially when your entire identity rests on being a transmitter of knowledge.

For teachers and parents of puzzle-children, it’s time to change that identity and protect these powerful and eccentric learners.  Help the puzzle-child learn how to communicate their needs and let them know you’re there as a resource.  Prepare their environment with quality books and essential Montessori materials. Provide open-ended tinkering, building, crafting and drafting materials.  Go outside together and explore nature through their eyes.  Listen, observe, document, trust, and wait.  Be flexible, creative, and honest, and above all, be genuine.  Follow the child.

“Our care of the children should be governed, not by the desire to make him learn things, but by the endeavor always to keep burning within him that light which is called intelligence.” – Dr. Maria Montessori

 

6 - 12, Cosmic Education, Favorite Books, Montessori Materials, Montessori Theory, Science, Theory and Practice

Moon-tessori (haha, couldn’t resist)

“You’re great at this homeschooling thing because you’re a teacher… I don’t think I could do it because I don’t know much about anything.”

I can’t tell you how many times I’ve heard this phrase since we started homeschooling two months ago, coming from the most capable and well-prepared mothers in my circle of friends.  So here’s a little secret… I don’t know everything.  Heck, I don’t know most things!  But I don’t let that hold me back from learning and sharing with my children.  Here’s an example of how I facilitate learning, and how you can, too!

The moon is a topic that seems to keep coming up in the Full Montessori household.  Over the past few months we’ve read several fiction and non-fiction books about the moon (links at the bottom of this post) and we play games trying to find different shapes (a rabbit, and old man) on its surface.  Seven-year-old Zachary had been asking why the moon changes through the month, so I knew it was prime time for a moon lesson.

Truth be told, even after 12 years as a Montessori guide, I could never quite grasp HOW the moon moved in relationship with the Earth, why the lighted part changed throughout the month, or how to tell when the lighted part was growing or shrinking.  But the beauty of being a guide is that you don’t have to know everything, you just have to “learn ahead of your children” (I love that Charlotte Mason phrase).

So, I found these two extremely helpful videos and FINALLY understood how it all works (thank you, Google)!

Then I dragged my kids to the craft store to buy a foam sphere (without telling them what it would be for); printed, cut, and laminated these free Moon Phases cards; and practiced the Moon/Earth/Sun demonstration when my kids weren’t around.  Yes, sometimes it takes That. Much. Work.

But, you know what?  It was so worth it!  I invited my son to sit down and told him his head was the Earth (my three-year-old daughter wasn’t interested, because, hello concrete thinker!).  I then began slowly moving the moon around his head, and he saw how the lighted part of the white sphere grew from waxing crescent to first quarter.  His eyes widened and his mouth stretched into a knowing smile.  I continued moving the moon around his head and I could tell he was enjoying the discovery process as much as I had.  When we were done and I had casually sprinkled the terms for the moon phases into the demonstration, he got up and went downstairs to play with his sister.

I waited for a lull in their play and pulled out the moon phases cards.  I told him we were going to play a moon game and put the “New Moon” card on the rug.  I lined up the other cards randomly on the edge of the rug and said, “Hmm, which card might go next?”  Eager to apply his knowledge, he quickly fished out the Waxing Crescent card and completed the entire cycle on his own.  He mixed up Waning Crescent and Waning Gibbous, but I didn’t say anything.  I just offered the control chart and he caught his mistake on his own.

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If you’re a Montessorian, you might be wondering why I used the control cards for the lesson (heresy!!).  If you must know, my son has little tolerance for three-part cards.  They just don’t resonate with how he learns.  If he knows the information, he isn’t the type of child who will humor you with busy work just to show you what he knows.  And if he doesn’t know something, he wants to get straight to the knowledge and understanding part right away – and three-part cards just don’t give him that.  I knew (from experience) that if I went through the whole rigamarole of having him lay out the picture cards, finding the corresponding labels, and then using the control cards to check, I’d lose him for sure.

There are about a thousand different ways to help your child solidify their knowledge of the moon phases, or any other concept they’re curious about.  My intention here was to illustrate how I go about preparing myself to facilitate my children’s learning – and often, my own!

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Favorite moon books:

Fiction: Luna and the Moon Rabbit, Kitten’s First Full Moon

Non-fiction: Jump Into Science: Moon, The Moon Book

The books mentioned above are affiliate links.  Purchasing through these links helps support the quality work you enjoy on this blog, at no cost to you.  Thank you!

Montessori Theory

The “Annoying” Seven-Year-Old

Seven-year-old Zachary learned how to build a popscicle-stick catapult at a free library workshop last week.  Over dinner that night, I “casually” asked my engineer husband if he knew the difference between a catapult and a trebuchet.  A brief but interesting discussion ensued, and my son hung on to every word.

Sitting around the kitchen table after breakfast Monday morning, I asked Zachary: “What would you like to explore today?”

He pouted and crossed his arms.  “Nothing.”

I tried again.  “Your pen pal is waiting to hear back from you.  Or I could give you ideas for that letter you’ve been meaning to write to Papa.  You could also practice the ukulele.”

“That’s dumb.” He walked upstairs and threw his lanky body on the floor of his LEGO-strewn room.  I followed him.  He mumbled, “I’m not doing anything today.”

Then I casually pointed out, “I’m going to be building a trebuchet downstairs.” (Because all moms need a trebuchet.)  “I would love your help.”

His head popped up.  He tried to look nonchalant as he followed me downstairs.  Five minutes later, he was reading instructions, gathering materials, and pondering physics.  He worked with joy and determination for almost two hours, through fingers scalded by hot glue and countless design adjustments. IMG_1008

We discussed potential and kinetic energy; used fractions and measuring; identified angles and defined new words.  He beamed with satisfaction when his creation was complete.  He then spent thirty minutes flinging projectiles onto a cardboard castle with his catapult and trebuchet, comparing the tactical advantages and destructive power of both weapons. IMG_1016

Second plane children want need to think for themselves.  For many children (and their parents) it can be a time of massive struggle.  Dr. Montessori wrote that the seven-year-old “starts to express judgements” and observed that “the adult finds [the seven-year-old] a bit annoying.”

“Without a new pedagogic directive, a new battle between the adult and this new child arises… [The adult] must be sure of what he ought to do, of what he ought to say, and of the extent to which he must reply to questions… It is indispensable to the child to feel the security the adult can and must give.”

Dr. Montessori observed that, “his thoughts could… have the tendency to lose themselves in abstraction by reasonings without end.” Pushing away or shutting down are the second-plane child’s ways of saying:  I’m feeling overwhelmed by the enormity of the world and I need a concrete activity to ground my imagination. 

She reminds us to connect the child to “an external activity to which he will give all his potential.”  You can start anywhere, with any activity that requires the use of the hands and the imagination.  But the art of Montessori in the second plane is to help the child connect that one detail to the whole of the Universe.  “Each detail holds the child’s interest by reason of its strict relation to the others,” Dr. Montessori wrote.  Therefore, “it is sufficient to choose any one detail which will then become a point of departure in the study of the whole.” IMG_1015

You don’t need to have a vast depth of knowledge to engage a second plane child.  You  just need to know enough to get an activity going, and subtly point out a few connections through simple stories.  Spend some time today noticing how everything connects to everything else, and think about the little stories you can tell to bring those connections to life.  Learning will never look the same again to you or your child.

 

 

Montessori Theory, On Parenting

What Montessori is Not

Montessori is not a curriculum – not a series of boxes to check off.  It’s a guide for understanding how humans grow. It’s a way of supporting how humans learn.  It’s a means for finding joy and purpose in life.

Montessori is not dogma – not a script to follow blindly.  It’s a conversation about priorities.  It’s a toolbox for navigating parenthood with grace.  It’s a dance with the imperfect realities of life.

Montessori is not just for the wealthy – not a ticket to career success.  It’s for the homeschooling family.  It’s for the public school family.  It’s for the refugee, the migrant, the orphan, the elderly.

Montessori is a way of seeing and being.  It’s a new understanding of the adult’s role and a window into the child’s soul.  It’s a path that leads to trust; a path that leads to peace; a path that leads to life.

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Uncategorized

BOTW: The Story of Money

Is your child afraid of math?  I know many who are.  I also know that one of the most effective ways to help them overcome their fear of math is to give them an allowance.  In addition to teaching your child patience, opportunity cost, and the value of things, money is a hands-on way to work through many math skills!

My son got hooked on math through his allowance.  At the age of four, he wanted to save up for a LEGO kit. On a piece of graph paper, I marked one square for each dollar he would have to save.  Whenever he got his allowance, he would color in the associated squares and we would count how many more squares – or dollars – he needed to reach his goal.  By the age of five, he was using addition to calculate his goals, and by six he was multiplying.  Now that he’s seven, he has a money journal, where he writes down his debits, credits, and current balance.

His interest in money, and his age, led to the question: “Why do we use paper money?  Why don’t we use gold or computers?”

I’m glad we had The Story of Money in our home library!  This lovely book, written by an elementary teacher, traces the fascinating history of world currencies from the time of the very earliest humans. The engaging illustrations and clear text will take you and your child on a journey through ancient civilizations like Sumer and China.  You’ll then make your way to colonial America and discover how the dollar came to be. storymoney

The Story of Money is written in the style of Montessori’s Cosmic Stories, which helps children stay engaged from start to finish.  My son loved looking at all the different ancient coins, all carefully illustrated to actual size.  This book can inspire many avenues of research for elementary students, from timelines to coin collections.

So, the next time your child feels scared of math, connect math to money, and money to human history with The Story of Money, and watch their fear turn to enthusiasm!

(This post contains an affiliate link.  Purchasing through this link helps support the quality work you enjoy, at no cost to you. Thanks!)

Montessori Materials, Montessori Theory

When Help Is A Hindrance

Few clean-ups seem as overwhelming as that of the Montessori fractions.  The halves through sevenths are easy enough for most children, but the 27 hard-to-distinguish red wedges that make up the eighths, ninths, and tenths can leave even Elementary children feeling stuck and discouraged. Screen Shot 2019-02-16 at 7.03.31 AMI’ve inherited Montessori fractions in several of my classrooms, and I’ve often found that a well-meaning predecessor had written the corresponding value on the underside of each fraction piece.  At first glance, this might seem helpful.  It sure makes cleaning up those pesky fractions a lot quicker!

So, why did Dr. Montessori design the fraction pieces without labels?  Did she harbor some evil desire to torment children and their over-worked adult guides?  Or did she observe that leaving the fractions unlabeled led to the development of problem-solving skills through creative use of the child’s knowledge?

The answer becomes clear when we consider Dr. Montessori’s advice: “Every unnecessary help is a hindrance to the child’s development.”

Is writing the values on the underside of the fraction pieces really necessary?  Or, by doing so, are we preventing the child from developing essential skills?  If we don’t want to be a hindrance to their development, but we need them to eventually clean up, what can we do to guide a child who’s feeling discouraged by this overwhelming task? IMG_0573

When a child is faced with sorting a pile of unlabeled slim red wedges, it’s enough to help him recall that two eighths are equivalent to – or take up the same space as – one fourth.  Depending on the child’s prior knowledge, you can ask, “What do you know about equivalences?” or “What do you know about the relationship between fourths and eighths?”

If the child is younger and doesn’t know this information, simply guide him in a sensorial exploration.  Invite the child to bring out the fourths inset, ask him to remove one fourth, and show how the space within the inset serves as an objective control of error.  When fractions other than two eighths are placed within the space vacated by the fourth, you will see a gap.  Only two eighths will fit perfectly within the space of the missing fourth.

The monumental clean-up now becomes a fun puzzle that satisfies the child’s love of precision and bolsters his self-confidence.  You can back away, returning only if he needs guidance to find the relationship between fifths and tenths, or thirds and ninths (children familiar with equivalences will likely make the connections on their own).IMG_0577Take a moment to observe the child’s concentration, enjoy his smile of accomplishment, and know that you helped him move one step closer towards reaching his full potential as a creative problem-solver.

 

 

 

Uncategorized

The Valentine’s Day Story

Zachary, age 7, asked me how Valentine’s Day started.  I told him we could research that at the library, but later that night I got curious and went online.  I found conflicting information, so I decided to put together a Cosmic Education story to tell him the tale of the origins of Valentine’s day.  I shared it with him and it inspired us to make care packages for the people experiencing homelessness in our area.  I hope it can inspire acts of kindness, or at least get some conversations started, among the children in your life.

Note: I don’t follow any religion, and I’ve tried to make the story as secular as possible so it can be used widely.  I use the lower-case “g” in all instances of the word “god”, but if that bothers you, feel free to copy/paste and edit at will.  This story is meant to be told orally, as are all Cosmic Education stories, so you can adapt it to fit your audience and/or beliefs.

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The Story of the Origin of Valentine’s Day

Have you ever wondered where people got the idea to celebrate Valentine’s day?  Historians don’t have much information to go on, so I’m going to tell you one of their theories.  For this story, we’re going to go back in time, almost 2,000 years ago, to a country in Europe called Italy.

Italy was the home of the Ancient Romans.  The Roman Empire was very powerful, with a large army and a series of emperors that controlled land from Northern Africa to Western Asia and a large part of Europe.  The Ancient Romans believed in many gods. You’ve probably heard of Saturn, Jupiter and Neptune… Before they were the names of planets, they were just three of the hundreds of gods the Romans worshipped! Keeping the gods happy was of utmost importance to the Ancient Romans, and the Emperor would throw in jail anyone who didn’t believe in these gods or who refused to make sacrifices to them.

One of the groups of people at risk of being jailed were the Christians.  This small group believed in only one god – a god very different from the Roman gods – and felt their mission in life was to help people who were poor, sick or hurt.  After receiving help from the Christians, these people would often convert – they’d stop believing in the Roman gods and start worshipping the Christian god.  As you can imagine, this made the Roman Emperor very, very angry!

One of these Christians was a priest named Valentinus.  He helped the poor and the sick, and many of those he helped were so grateful that they decided to convert.  When the Emperor heard what Valentinus was doing, he locked him in jail to stop him from helping and converting any more Romans to Christianity.  However, Valentinus did not forget about those he’d helped.  He wrote letters to them from jail and signed them “From your Valentinus.”

Valentinus died in jail on February 14th, which was around the time of the Ancient Roman feast of Lupercalia.  This rowdy party celebrated love, and when the Christians became more powerful than the Romans, they replaced this raucous festival with a day to remember the work of St. Valentinus.  And thus, Valentine’s day was born! You can research how the holiday evolved to include chocolates and love poems; it’s quite an interesting story that will take you to Medieval England.

I look forward to hearing what you discover.  But for now, when we celebrate Valentine’s day, let’s take a moment to think about how we – like Valentinus – can make the world a better place by helping those who are poor, sick or hurt.  Because that’s the true spirit of Valentine’s day!

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