Sunday, July 20, 2014

The Crow and the Pebbles - An Extension Lesson for Sink and Float

The story of the crow and the pebbles is a well known Aesop's fable. A thirsty crow comes across a pitcher of water and seeks to quench his thirst. However, there is only a small amount of water in the pitcher and its opening is quite narrow. The crow examines the situation and then uses its beak to drop one stone after the other into the pitcher to raise the water level until it is accessible to him.

I am very familiar with Aesop's fables and find them to have many scientific and mathematical elements to them, as well as social, political and economic ones. I had not thought of the crow and pebbles fable for years and then, a few months back, I came across an interesting article in the New York Times Science Section regarding it. You can view the video that was linked to the article here:

There had already been several sink and float extensions done in my classroom during the Spring months, but this narrative appealed to me and I wanted to include with it dialog about weight, volume, distribution and redistribution of mass, as well as a continuation of our on-going conversation regarding the two actions: going down and going up. Here the stones would go down and the water would go up, that is the obvious answer. However, air bubbles might be formed and those would also rise. That had happened in an earlier, outdoor sink and float work. Those bubbles were a great and satisfying surprise to all.


Photo below - The bubbles are difficult to see. They are rising on the right side of the rock that was used to secure a piece of tape and yarn. The tape and yarn were being used as part of an anchor for a student constructed boat that is not included in the photo. Wonderment is the only word I can use to describe the look on the students' faces when they noted the rising bubbles. "Air got trapped under the rock, Miss Susan, and we didn't even see it happen," one of my students told me. Ahhh...I love my role as a guide.


OK, enough digression, back to the crow and the pebble work. I also wanted to include in this work the question, "Does shape matter?" The rocks I chose for this work were pretty uniform in that they were black and somewhat flat and oval. The flexible or unstable variable was their weight, as their size varied from small to medium. I also had a box of small, smooth, colorful u-curved-shaped pieces of glass that I thought could serve to answer the question noted above, "Does shape matter?" Too, I thought they provided a little eye-candy for my students. They would therefore serve as a point of interest.

Lastly, I didn't want the water to rise with the dropping of the pebbles without something else rising with it. I wanted to include a sink and float element to the lesson. I knew I had the sink variable covered with the pebbles. I wanted the objects that were used to float upward as the water level rose to be duplicate items from the introductory sink or float work that was still on the shelf. I decided on a cork and a chestnut. The student doing the work would chose one of those items and place it at the bottom of the canning jar and then add a small amount of water to the jar to initiate the floating action. So the purpose of the work was no longer to just have the water level rise, but to bring the object to the top of the jar within the reach of the student's grasp - or, more specifically, the grasp of their held pair of tongs.

I put together a tray - actually, a small wire basket - and placed in it a blue-glass, medium sized canning jar, tongs, a sponge for clean-up, a lidded container that held within it two objects that would float (cork and chestnut), a small pitcher for water and a jar containing the colored, u-shaped glass pieces.

Next to the wire basket, when placed on the shelf, was a jar of similar  looking pebbles.  These items were placed on the shelf above the introductory sink and float work. To the left of that work is the introductory magnetic and non-magnetic work.

And then I made a goof, yup, but I went with it as I had recently read an altered version of this fable that replaced the crow with a wolf. Having recently moved from Juneau, Alaska to Madison, Wisconsin, I wrote the raven and the pebbles on the label for the stones and didn't even realize it until I placed the jar on the table in front of my students. Ravens are very common in Juneau. I explained to my students that a raven and a crow are quite similar and that both birds could use their beaks to drop the pebbles. The lesson was intact and we simply went forward.

Below - the wire basket with the items needed for the lesson and the jar of pebbles.

I removed all the items and placed them on the work mat. I returned the empty wire basket to the shelf, reserving the space for this work. One of my students filled the small pitcher with water and poured it into the jar.  I removed the cork and the chestnut from their container and placed them on the work mat, also.

I asked my students to carefully observe the water line and the fact that the chestnut was floating at that line.

I then asked another student to carefully drop a few of the pebbles into the jar. They did so.

They were completely captivated and silent as they observed that the pebbles had caused the water to rise and with it the nut.

Each student took a turn adding pebbles. 

The water level rose higher and higher.

A student then used the tongs to remove the chestnut.

All immediately asked to repeat the work and we did. 

After the second time doing the work with the pebbles, I opened the jar with the u-shaped glass pieces and asked the question, "Does shape matter?" They asked back, "Does a pebble weigh the same as one of the glass pieces?" And, "If the glass doesn't weigh as much, will it take more of them to make the water rise?" I invited them to compare one of each and discover any weight variances.

The photo below illustrates that comparison work. Here one of the students holds one of each object on the very edge of her fingertips and compares the weight of both. This is exactly the way students hold the baric tablets to compare variances in weight and to find those that match. The glass pieces did weigh noticeable less.

They repeated the lesson exactly as they had done with the pebbles.

We sat back from the table after the work was completed and talked about water displacement, about how the locks work on the Erie Canal and about how weight has force and that force can be used as leverage.

Each of my students contributed ideas and insights. Then one of my five year olds looked at me and said excitedly, "Miss Susan, I know. It's like when you take a bath. The water rises when you sit down in it. The water has to go somewhere, so it goes up. Well, if there was a hose attached to the tub to let the water out when it rose, then it would go out the hose." Another student jumped in the conversation and said, "I think that has something to do with water pressure. The water has weight and it forces itself to find a way to get out of something when it doesn't have room." A third student stood up and said, "If you bring your foot down hard in a puddle, the water splashes." He then demonstrated the act of stomping in water. Right then, the head of my school walked in and said parents were waiting and that my students needed to pack up quick to go home. Ahhhh...but it was wonderful.

I repeated the above lesson only with the label on the stones amended to correctly read, "The Crow and the Pebbles," during the first week of summer camp here at Toad Hill. Again it was amazingly successful. This time several of my younger students engaged the work. They had not when it was first presented in the classroom. Here are a few photos of the work being done outside:

With pebbles...

With u-shaped, glass pieces...

Interestingly, when we came in to get out of the sun for a little bit, my youngest students immediately took the introductory sink and float tray off the shelf, they had already had a lesson or two on it, and went to work. All good - so very good!

There is still something tugging at me about this work, though...beaks and their size and shape. What is the span of an opened crow's beak compared to a robin's? What is the the geometry of a bird's beak? Triangular when opened, cone shaped when closed? How much weight can a crow lift with it's beak and how can a child visualize a beak as a tool? What tools are they familiar with that resemble and are used similarly as a bird's beak? I have a hundred more inquisitive questions. In the classroom, the children ask the questions after I have provided materials and lessons that provoke curious ideas and insights within them. Here, is where I ask questions. More just popped into my head...better call it a night. Hey, it's raining out. Maybe I will go and stomp in some puddles and try to measure the arc of the spray of water. Wonderment. I have it too!

Sunday, May 11, 2014

"Nothing goes into the mind that does not first go through the hands."

I was told this quote when I was taking my AMI training at the Montessori Training Center of Minnesota almost 20 years ago. I was told it was a modified version of the Aristotle quote,“There is nothing in the intellect that was not first developed in the senses." I have repeated it more times than I can count to assistants, parents, heads of schools and non-Montessorians as a means of explaining a component of the method referred to as sensorial education.

Watching a child do a work with a blindfold on has always served as visual evidence of the hand-mind connection. Too, this notion of the mind gaining access to knowledge through the hand reinforced my educated belief in the value of muscular memory.

I often speak of having a greater understanding of both the direct and indirect purposes of the Montessori materials via my own touching of said materials and the muscular memory that is stored within me due to that touching over a period of fifteen plus years. My cultivated hand-mind relationship has provided me the opportunity to speculate on the harmonic interplay between all of the materials in the classroom. It is those speculations which serve my own leaps towards abstraction in the form of extensions.

Recently, I have been turning the phrase, "Nothing goes into the mind that does not first go through the hands," over and over again in my mind, asking myself if I truly understand what it means for something to "go through the hands." It seems a concrete, and even obvious, statement. Simply explained, the hands are the instruments of the mind. You touch something and immediately information regarding its texture, temperature, color and, possibly, weight is gathered and recorded. That is easy enough to comprehend. Yet, I have been asking myself whether or not I really get the more abstract qualities of grasping something.

I have been captivated by the gesturing my older students make with their hands when they are formulating an opinion or leaping towards a greater understanding of a complex concept. It appears as if they are wrestling out an idea they have in their minds and that they are using their hands to give shape or form to that otherwise invisible and newly born notion.

When I am authoring a blog post or an article and I have to describe in detail elements of lessons I have given, I hold one of my hands up in the air so as to mold it in various ways so that I may re-imagine the geometric forms my students create or the cursive letters they form. As my fingers shift and light spills through the gaps between them, my thoughts synthesize and are then manifested onto the page or screen via my hands and the tools needed, i.e., pencil, keyboard, etc.

I am now recalling one of the fundamental laws in physics which states for every motion there is an equal and opposite motion. Therefore,  the statement, "Nothing goes into the mind that does not go first through the hands," should be couple with the following, "Nothing goes into the hands that does not first go through the mind." This duality may also be viewed as an infinite loop; an infinite dialog of input and output / output and input.

Here, again, I pose the question, "What is implied by the statement to go through the hands?" Does form have to have a physicality to it or can it simply be the shape of an idea expressed through the hands? And once that shape is formed, is it then measured and valued by the very hands that first gave it form? The sequence would then be: mental idea, wrestling of idea into an invisible form via the hands, qualities of that form assessed by the hands and recorded in the mind, mind expresses form via hands into a physical, i.e., concrete object - an infinite looping of sequential actions.

Why is this important for a lead guide to acknowledge within the Montessori classroom? Every child should be provided the opportunity and the freedom to give expression to their gathered and reflected upon ideas. Every child should be provided enough non-lesson time to engage in an inner dialogue with themselves. This inner dialog maintains the input / output loop as it processes new information, synthesizes it with old and provides opportunity for the two to merge into an abstract revelation. This is the developing and advancing of the child as a unique individual who's singular insights serve to both define himself/herself and to support the collective community of the entire classroom. Those children who actualizes this are the active citizens of their current arena, the classroom, and of the future: entrepreneurs, politicians, humanitarians and more.

Next time you sit down to write observations in your classroom, dedicate time to noting the origami of hand movements your older students make. Then, after several moments of observing, approach a couple of them with large sheets of white paper and ask them to illustrate all that they are thinking. Make sure the paper is large enough to give expression to their ideas and that, too, they have sharp pencils available to them.  After you have provided them with these tools and a place to work, go and work with a few younger children and serve their needs.

Twenty minutes later, or so, casually find a seat near those students sketching out their ideas and, with calm, centered energy, ask them to tell you all about what they are working on, to add more details to their work, to think one more thought along with all the other thoughts they have had and prompt this thought-seeking with open-ended questions such as, "What opens in the morning and closes in the evening?" "What's the shape of that thing?"

Finally, lean back in your chair, lift up your own hands and let them dance through the air for just a moment and then place them back on your lap. Now get ready to watch and to listen to the great genius of young children's minds and view them wrestle out into the open air their ideas regarding physics, geometry, math, art and all that defines humanity. Lastly, do not weep at the wonder of it all. Rejoice in the gift of your role as a guide.

Later, at home, when sitting amongst friends and family, re-tell the story of Helen Keller and her great accomplishments, of Einstein's frequent walks with Madame Curie and their vivid conversations, of children gesturing profound thoughts through their small cupped hands, each etched with map lines before their own birth. And as you tell all these stories, let your hands take flight and see before you the shape of all that occupies your own thoughts.

Tuesday, May 6, 2014

"All I heard were the deer and the deer told me they were watching over me."

Next week, when I am feeling better, (I was in a bike accident and I am home from school recovering) I am going to approach the administrator at the senior center right next door to Toad Hill Montessori School, where I am the lead teacher, and ask them if I can teach either science, art or creative writing there once a week. I really miss the elderly and their good, good stories.


If you work with elders you work with individuals who hold within themselves a historical record of the world at large. In some cases these historians are the last living witnesses to the most noteworthy events of the past one hundred years. Too, here in Alaska, native elders remember a life not often recorded in textbooks, but instead shared within their own villages or communities. This is the same for most indigenous people around the world.

A volunteer from the Alzheimer's Association comes to the Bridge to lead an art activity with the seniors twice a month. The activity she prepared for today was centered around the theme of "Our Childhood Homes." After each of the participating seniors were seated, she invited them to think about their place of birth and to began sketching that place on the sheets of paper that had been handed out to them.

I entered the room halfway through the activity and noticed one of the Tlingit seniors drawing a small house on her paper. Then she wrote across the paper where this and that was. It was a fascinating image that had map-like qualities. I knew from a previous drawing of her's that she was born inside a smoke house. The piece she was working on now was her "childhood home" and the place where she entered the world.  Close-up of her picture below:

I sat down next to her and began asking her a few questions about her drawing. Slowly but willingly, she told me stories of thirteen families living in this small house at the same time, of fishing for salmon, of netting and drying seaweed. She also told me a story about running-away from home, from the smoke house, when she was a child. Here is all that she told me:

"I am thinking of them poor days in the 1950's. We all slept inside around the bonfire in the middle of the smoke house. There were thirteen families living there together. I am proud of my family. We learned a lot from them. They told us how to can the fish. We did a lot of fishing ourselves. We pulled the fish in with nets and we cut them up.

For the seaweed we had to go far out into the ocean to get it. They told us not to take any seaweed where dead people were or near where people went to the bathroom. That's why we had to go real far out into the ocean to get the seaweed. Then we dried the seaweed in the smoke house on one side and then we turned it the next day onto the other side. The next day we turned it again and then we left it there for a week until it gets real dry and then we canned it or we ate that. Person got to learn to go way out to get beyond the dead people to get the seaweed.

I was away from home for a whole week when I was a kid.  I left a stick in a tree pointing to the smoke house so I would know how to get back. Someone told me how to do that. I ran away from home and I slept out in the woods. I woke up in the morning and did feel scared the first day, but then I told myself I don't need nobody, so I just kept moving. All I heard were the deer and the deer told me they were watching over me. I came back after a week. I found my stick and it showed me where to go. It's a real good past I got."

Here is a final close-up of the drawing she did today:

The above three paragraphs are part of this woman's autobiography, the narrative of the self. The questions stirring within me are how to assist her in adding more details, to create a timeline, to start a list of family names, on and on. She has drawn this map of a smoke house, a vegetable garden and the beach. She has noted at the bottom of the page - 13 familys home (Klawock). She has outlined much and she is right, she has a real good past.

Documenting oral histories told by elders attending or residing in senior facilities is on-going work around the world. Much has been unrecorded, and that is lost testimony to the collective history at large. What Montessori lessons are there to assist in this documentation? My initial answer came to me via a visual memory of children in Elementary II doing timelines in their classroom. That is a starting point. I have much reading to do this weekend on that work.

Tonight, though, I just want to close my eyes and imagine a deer talking to me; telling me that it's watching over me. I want to breathe in the smell of salmon and seaweed hanging inside the smoke house. Finally, I want to bend down onto my knees and pull weeds in the vegetable garden alongside all those whose hands planted what grew there. This is what good stories do. They make history come alive. Can you hear the deer talking to you?

Sunday, April 27, 2014


This post is simply going to be a photo collage of much of the work done in my classroom during the month of April, 2014. It is also a celebration of the amazing community here at Toad Hill Montessori School.

Tulips with their heads bowed down in prayer.

A four year old student doing flower arranging work using one of the tulips above.

Math work is a constant in my classroom.

Multiplication with the stamp game.

Division with the stamp game.

She is checking her Dot Game answer (the paper in front of her) by doing the same equation with the large bead frame (someone else was using the small bead frame).

The student below was so excited that I gave her an addition problem that included numbers in the millions.

She went to work and had the correct answer just a few minutes later.


Introduction to addition via the cards and bead material.

Sometimes, if I can find what I am looking for, I create pictorial math problems via magazine clippings. It helps me identify those children who are more/or less visual learners.  I find it interesting that those students of mine who can quickly use the small bead frame to add  something like 4,354 + 2,311 -  have to slow down to do this work as it requires that they translate the visual information into a mathematical equation. I am also presenting this work as a component to the preliminary lessons that will ultimately serve to introduce word problems to my older students.


The Money Exchange Game

 Blindfolded work

Doing the binomial cube with a blindfold on.

The mystery bag with objects.

The mystery bag with coins.

 Identifying coins while wearing a blindfold.

Blindfold work with the fabrics.

 Shoe polishing work.

Metal polishing work.

Learning to use an eyedropper work.

My youngest student carefully dissecting a tulip.

Fetching and pairing chopsticks, which were purchased during the head of our school's recent trip to China.

Such focused work with the knobless cylinders.
 Expression / Art / Visual Literacy

I cut out images from magazines and then simply used a small piece of each image for this project. I glued the small pieces onto large white paper. I then invited my students to pick one of those and to complete the picture. I did this work with seniors at The Bridge and had the same wonderful results. This work is about bringing work to a conclusion, completing a composition and it is an introductory to visual literacy - narrative construction via pictorial compositions. 

The above picture was done by a six year old. The one below was done by a four year old.

The student that completed the eagle image is a frequent user of the bird watching basket.

The last example (below) of this work was done by a three year old.

Land form work / illustrations.

Introduction to the layers/ strata of the Earth

Expression and response to multiple lessons on land forms and the geometric solids.

 A three year old's lake / island work (below).

 Understanding wind / breath as a force via catamaran constructions and races.


The moveable alphabet and phonetic word / sentence construction.

Her first lesson with the moveable alphabet. We are replacing the print moveable alphabet with the cursive one for the next school year. Cursive sandpaper letters are already out and on the shelf next to the print ones. Both will remain until I give lessons which will reveal that each set represents the same sounds and are in fact the same letters - such as the lessons one gives to show the relationship between the continent map and the globe.

I love his Jackson Pollock-like movements around the canvas/work rug on which he is piecing together his composition of words. 

 The geometry of birds.


Snack outdoors on the front playground.

He was describing to me how narrow he wanted the tip of his sand mountain to be.

Sitting next to these two, I heard the girl in the green coat and yellow boots say, "Hello worm." Then the other, older child, came and scooped up the worm, turned and placed it in the soil behind her.

Yoga / Walking on the line with the bell / Games -
Indoor Recess
Yoga - Meditation

 Walking on the line with the bell.

Indoor recess. 
Musical chairs.

Of course, I played too.

 Beauty - Wonderment

Geometry - Fractions - The Cosmic Universe

"And so..." he explained to me.

Below - Clay hemispheres.

Fractions inverted to create a dome.

Where fractions, geometry and the metal insets meet.

"You do know that the top of this is a sphere?" she asked me.


The children preparing Friday's community lunch.

The children serving their fellow students. 

 It's was all very good!


The Upstairs Classroom.

Toad Hill Montessori School

The month of April was a busy month. So much more work was done then shown above, but this is a good sampling of that work. May will be an exciting time here at Toad Hill, as will June.


Me on the front stoop giving one of my students a little hug time.