Tuesday, April 22, 2014

Birds




 A Post About Birds
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My last post included photos of a rocket constructed by one of my students after careful study and frequent use of the geometric solids. Cone + Cylinder = Basic Rocket Shape.


He added a parachute and referred to it's slightly inflated shape as a dome. It was an amazing, independently motivated and actualized project that illustrated his keen understanding of geometry outside the cabinet and solids.

When I first viewed him working on another project, the illustration of a jet, I remember noting in my observation journal - bird beaks. I had noticed that the cone of his jet had a slightly bent tip. This immediately made me wonder how I could interest him and his fellow work mates in the variations of bird beaks and how these variations serve each, particular bird. I have asked a parent that works at the local Nature Society to assist me and she is piecing together some handouts for me.

My students had already had two art projects focused on birds. One I gave and it was a simple, illustrate the cut out shape of a bird, project.



The second was a project I selected due to its geometry, but it was my assistant Sarah who did all the cutting work for it and so I invited her to present it to the class (she is taking her AMI Primary training in the fall, making her the fifth assistant I have had working with me to become a Primary teacher). It was wonderfully successful.

Let me note that I added one preliminary work / practice which was then done by each student just before they did this work and while they also waited their turn to do it. I was concerned that some of the children would not understand the word spiral or have muscular memory of constructing a spiral, so I asked Sarah to include this dish (photo below) I had purchased which has a raised and very tactile spiral constructed on its surface. I clarified my request by stating that I want the students to use the tips of their fingers to trace the spiral so they could understand it as a concept and a movement. I believe it truly aided in the success of the project, as each of the paper birds were constructed with circles and spirals. This dish remains on the Practical Life shelf and is often used simply by itself.


 Here is one of the paper, geometry birds made by a student. 

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Returning to thoughts about bird beaks - anticipating the bird information from my parent, I put together a bird watching tray which includes binoculars, a local bird identification book and both a journal and small sheets of sketch paper. I gave a lesson on how to use the binoculars and, too, how to note or sketch what was observed with them. It remains a popular work.



Early one morning, after the work had been on the shelf for several days, I caught this lovely scene.


Below is a photo of a student who had just used the binoculars, had returned them to the tray and then next made a drawing of what he had seen in the bird watching journal included in the tray/basket.


(I thought I had a photo of the tray/basket - but I don't, so I will add one later this week. Too, I will add photos of some of the more recent bird-watching drawings - look for the post "Birds - Updated.")

Bird imagery started showing up here and there. The drawing below was a gift to me from one of my students who arrived to school one morning with it, along with some other drawings.


A "finish the picture" art project resulted in a magnificently illustrated eagle's body and wings with incredible details. The boy, that did the work below, often uses the binoculars. 


Bird beaks - ok...so, I was sitting with a five year old and we started talking about the rocket that had been made a few days earlier and I interjected a comment about bird beaks - that they had a cone-like shape to them similar to the nose cone on the jet that was drawn. Immediately, he started to tell me about all types of bird beaks and how some are curved downward, etc.

I asked him to bring me the cone from the geometry solids. I also asked him to see if there was one that resembled a bird's body. He returned with the cone and the ellipsoid - they still have the tape on them that I used to bisect them in order to illustrate other lessons.

He lifted each in his hands and, with complete seriousness, began telling me how birds are designed in such a way as to facilitate flight. 


I listened carefully and then encouraged him to trace them. I then suggested he use the ellipsoid from the geometry cabinet and, perhaps, a triangle that he felt would represent the cone 2-dimensionally. These, I told him, would be easier to trace then the solids. He placed the solids on the table and fetched the two insets. I got paper large enough to truly allow him the freedom to document his ideas.

First, he traced the ellipsoid and the triangle in a manner that would look like a bird's head and beak.


I asked him to draw the base line of the triangle and to carefully draw a much smaller ellipsoid for an eye. Next, we talked about a lesson my co-op student had recently given on joints. "Does a bird have joints?" I asked. He answered, "Yes." I assisted in placing the ellipsoid in such a way as to illustrate the curvature of a bird's neck, such as a duck's. He then took over, asking me now and then if he should perhaps stop or add one more, and then another, ellipsoid outline.


I encouraged him to continue. When he had pretty much composed the bird's body, I asked him how he thought he might make a tail. "Easy, Miss Susan. That's just a triangle." A minute later, he said it was done. I agreed.


He got up, briefly left the table and then returned with a pair of scissors. He cut out his bird drawing and then placed it near the geometry bird he had constructed weeks earlier. I snapped a photo or two and then out the door he went. I could see his ellipsoid bird drawing folded and sticking out of his coat pocket as he grabbed his lunch box and left for the day. When he opened the school's front door, I could hear birds chirping and hoped that he could, also. 


A second child, who had occasionally swung by the table where I was working with the above student, walked up to me, smiled and handed me his own interpretation of the work above.


He said he wanted to do the work, but wanted to try and do it on his own. He did a great job. He was out the door moments later, also. I sat and thought how some days I can almost see their wings - my students' wings that is - they seem to be taking flight, or to use the classic Montessori phrase - leaping to abstraction, all around me.


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A little note about the geometric solids - I have seen this beautiful material hidden underneath exquisite pieces of blue cloth in so many Primary classrooms simply waiting to be used for the next three period lesson with two and three year olds. It is neglected most of the time. I think it is so interesting that many of us yarn on and on about the binomial and trinomial cubes as actually being complex mathematical equations, which are only discovered by the students years later in upper elementary, but rarely speak of the solids in such a way.

Ok...hmmm...let me put this out there as perhaps it will get the solids off the shelf more. The geometric solids are complex mathematical equations, too. They are mind blowing! Perhaps it is because after so many years of touching them myself, I have my own muscular memory regarding their use and this memory is activated and built upon every time I use them. This insight into my own hand/mind relationship allows me to imagine the relationship my students may have with the solids, and all of the other Montessori materials, after working with them for 3-4 years. So, I have included the image below as an invitation to begin or re-begin a relationship with this truly magnificent, mathematical material called the geometric solids.










Sunday, April 20, 2014

Lake and Island and so much more. Landforms as Polygons...so much to share.



Island

In my classroom, children create landforms with their hands. They do not use plastic molds. This work allows them to carefully craft "land" into specific forms and to then place on these landforms various models of animals. Included in the lesson, is a reference to an earlier work in which models of animals are placed on a map. This placing is specific to the habitats of each animal. Ex. Zebras are placed in Africa. (Note - Children frequently note that they have seen zebras in zoos. I clarify for them that the zoo is not their natural habitat.)



Below - A child uses careful hand movements to do the work. She continued to mold the clay after she had poured water into the basin. Her intention was to create a narrow peaked mountain. She did.


Discovery

An unexpected outcome of this work was the discovery of footprints left in the clay by the polar bear. They were discovered when the bear was carefully removed from the island as the child doing the work began the clean-up process. It was an exciting discovery that lead to an in-depth discussion on identifying animals via their footprints. That work, matching animals to their footprints, will arrive on a shelf this upcoming week.


 Sink and Float

Just before I gave the lesson on lake and island (lake not shown), I re-presented sink and float. I included this here as I will refer to this work much later in this post.


 (Above - she is carefully using tongs to place a sink or float object into the bowl of water she has prepared.)

 Okay - I need to interject here a thought, or two, that is distracting me slightly - yet, it is still on topic in regards to land forms. Here it is:

When I was just now reviewing some of my many photos of the work done in my classroom over the last several months, I stopped to look at a few of the Practical Life area and work done there. I asked myself if this work is not also a preparation for identifying landforms and the vegetation that might grow there? Too, is this work (ex. care of plants) an introduction to ecology or environmentalism? Also, the use of work mats are, themselves, a reference to bounded areas. One may make a "leap to abstraction" and even view these as work islands.


 Yet, that is not much of a leap after all.  Let me also pose a question here regarding the the basin used to hold the water in which the stems of the flowers are cut via flower arranging work. Is that not a body of water?


Of course all of what is noted in the above paragraph is not shared with the child as it is for their discovery, or not. As a Montessori theorist, these overlapping elements of the work allow me opportunities to view the entire room as a composition in which each work is independent and interrelated. I can almost hear a sound - a vibration in my mind - which gives me insight as to how to better prepare my classroom and what lessons to give next / what extensions to present that will ultimately result in the child rediscovering a material they believe they already know.

Extensions - Landforms / Polygons / Domes


The geometry cabinet is used everyday in my classroom, as are the solids. We bisected three with tape to understand them as one understands the number rods. They are both one thing and more at the same time. The number rod of seven is, in itself, a representation of the number seven as a whole. It is also an introduction to multiplication - one taken seven times = 7. Although, addition is the more frequently referred to mathematical act. It is also a linear line and a reference to the broad stair and...well, I will stop here. But wait, one more - it reminds one of bamboo, a botanical reference, in that bamboo's bark is segmented in such a way that one is left wondering if, while in India, Maria Montessori ran her fingers along its bark with her eyes closed and silently did the same work that the children now do with number rods - one plus one, plus one... This is the same with the solids, it is a multifaceted material, as are most Montessori materials.

The ellipsoid segmented provided opportunity to discuss and display spherical caps. When a sphere is bisected into two equal spherical caps, those caps are referred to as hemispheres. The bisecting of the solids was a preliminary work for understanding that the globe of the earth and the hemisphere map represent the same information. One is three dimensional. The other is two.

Sphere - Globe


 The globe cut in half and flattened.


The continents being drawn onto the clay hemispheres.

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After much work with the globes, the hemisphere map and regarding spherical caps, I noticed a student had made a very interesting discovery with the fraction work. He inverted each segment and created a dome. He traced his discovery onto white paper.



He traced it again on a small sheet of yellow paper. He cut out the yellow paper outline and folded it so that it had more of a 3-D structure to it.


A wonderful curiosity about domes began spreading amongst the four and five year olds. Our classroom became a lab in which they used their keen observation skills to identify several dome shapes or curved lines which arched in such a way as to be identified as having dome elements.


(The above is the shadow cast by the arched and spindled back of our classroom rocking chair)

Spherical caps, domes, cones.

A day or so later, the same boy who initially inverted the fractions, did so again and, as before, traced their outline onto paper. He pulled from his work file the yellow paper model he had made using the same set of fractions earlier. Two other boys gathered around him and soon, a soft, industrious buzz could be heard amongst them. One of these two boys brought with him the sandpaper globe. He had separated the globe into two hemispheres and held one in each hand. I walked by and casually offered to their think tank a couple of diagrams that I thought might stimulate even more conversation while simultaneously anchor it to the Montessori materials.




A cone and a cylinder = A rocket - with a hidden geometrical surprise.

Yes, a rocket was constructed by one of the boys above. He did come to me and ask first. I told him it was fine.  Let me state here for those of you who may be asking yourself - "What, she let him make a rocket in school. What Montessori lesson is that?" My reply, "Of course it's Montessori work." I clearly remember my trainer frequently reciting a quote by Aristotle, "Nothing goes into the mind that does not first go through the hands." If you truly want your students to understand geometry, provide the freedom, the opportunity and the materials to do so after they have received many, many lessons in all areas of the classroom. He had.

This independently motivated work had a hidden geometrical surprise...



A parachute... 




which he pulled out from the interior of the hollow cylinder (paper towel tube), allowing some air to fill it, and then said to me in a voice of absolute mastery over all that we had recently done with spherical caps and such, "It's geometry, Miss Susan. The parachute is a dome."

And yet, how does this good work fit into the category of land forms and polygons? First, let me state that a reference to a jellyfish was made by an onlooker in regards to the parachute's shape and the material it was constructed from. Additionally, I asked the constructor of all these things - rocket, parachute - whether he saw items in nature that either modeled these shapes or influenced their construction. What opens and closes? What sways in the wind? What takes flight via wind, and the shifts in its greater construction by both age and the elements? 

I verbally reminded him of earlier work we had done that included the tracing of plant leaves and the piecing of them together to create orbs. (Photos below.)



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A second and then a third child joined the discussion and started articulating spontaneous responses. "A flower opens and closes and, too, it sways in the wind," stated one. "Pollen takes flight and travels when petals part. Wind lifts the pollen and carries it somewhere else," a second student stated. "Flowers and plants are different in different parts of the world. The land and the weather is different, so what grows there is different." Here we go. I have put out the invitation to imagine the answers to so many whats and they have responded with the knowledge gained via so many lessons. This stored knowledge and experience was being funneled into their own hypothesizes and insights regarding the diversity of species and their habitats. Yes, this has to do with land forms, if, that is, we populate those masses with flora and fauna. 





I viewed these plates / ceramic polygons sitting taped together at a local thrift store and immediately knew that I must have them to use with my land form work. I paid $1.60 for them and happily separated them and placed them on top of the geometry cabinet. My placement allowed onlookers to see the curvilinear triangle of the metal insets simultaneously and therefore link the ceramic objects to geometry mentally and easily. Luckily, the head of our school loved them, also.

I asked a student to bring me all of the circles from the tray in the geometry cabinet that held them. We do not have superimposed geometric figures in my classroom, yet, so we made the circle ones by tracing these onto brown, earth colored paper and then cutting them out. We carefully scattered the geometry insets and the paper circles across the table.


Below - In a flash of certainty and insight, exactly what I had hoped would happen did. A student I was working with held one over the other and said, "Look, Miss Susan, a mountain." This was the beginning of our work on topography.


We layered a few and then repositioned the insets so as to simulate an archipelago of geometric circles.


We then included the remnants of  paper from our cutting work. Soon, the words bay, cape, isthmus and others were heard spoken.


The next day, I brought in a container much larger than the one we currently use for landform work and invited the student who had done the above work with me the day before to construct a landscape occupied with multiple landforms - which is more true to nature than the isolation of specific and singular ones.  I also placed the ceramic polygons on a work mat so that they could visually see the multiple forms as landforms and, too, view the spaces in-between. He eagerly began creating a diverse landscape with the clay, added water and models of various animals. It was truly amazing to watch.


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The Earth's Strata

The boy who had done much work with the dome and then discussed with me its form in nature, looked at me a few days later and said, "I'm bored." I said, "Oh, good. I was hoping to give you this piece of yarn to work with sometime today. Now is the perfect time." He looked a me as if he thought maybe he could simply and quietly walk away and find a good book in the library. What was so interesting about a piece of yarn?! So much! He stayed and listened to what I had to say. An hour and a half later he finished his work it. He was amazed, as was I.

I stretched the piece of yarn out and told him it was one of the, if not the most, important elements of math and art - a line. I reminded him of work he had independently done just the day before - he stood a metal inset on paper and traced its base line. Then, with a smile on my face, I also reminded him that I see all things.


Too, I referred to an all class lesson I had given a day before on how to use a paintbrush to paint a singular line. Next, I showed him how to stretch the yarn/ line across a piece of paper and to hold one end with one finger of one hand while using the other hand to hold a pencil and trace said line. But, I asked that he trace the line without stretching it so as to capture more wave-like elements of the line.

He went to work with clear focus and deep concentration.


Soon, a second child was drawn to the line work and did the "how to use a paintbrush to create lines" work at the same table. It was so cool to watch them silently work across from each other - each doing unique work that simultaneously echoed that of their peer's.


The more one added details, the other did, too. 


I stopped and spoke with the student tracing the yarn lines. I asked him to now illustrate each section with earth colors. He asked me to explain. I sat down and explained to him that this work was actually about illustrating Earth's strata. It was to help understand the layering of sediment and to see the segmentation of the Earth into these various layers. I asked him to look at his drawing and to find the surface where trees and mountains might occupy. I asked him to find the waterway at the base of the page, to illustrate it blue and to create lines so that it was obvious that the water was moving in one direction or another. He worked eagerly and almost effortlessly. He asked me to show him some images of what strata actually looked like. I did. He then drew stones within a segment of one of the layers. He had pointed out this detail in one of the photos I had shown him.

I showed him another image that included Native rock drawings of  horses and cows. He added his own "rock art" to his drawing. 


And too, a canoe was drawn in the water to highlight that it was in fact a waterway.  It was such good work.

So what's next? An Aesop's fable will be played out in a new sink and float work, as well as...yes...a new landform work.

Here is a quick overview of the story: A thirsty crow drops pebbles into a pitcher to raise the level of water enough so that it can get a drink. I have modified this, after reading a recent NYTimes article, narrative/ problem. I have put together a tray with a wide mouth canning jar, a pair of tongs,  a pair of tweezers, a small dish of stones, a pitcher for water and a very small object which floats. The task will be to add water to the jar up to a marked point. Next, the small float-able object will be placed in the water. After the object is placed, the child will use the tongs to carefully drop the pebbles into the water so as to make the water level rise and to retrieve the object with the tweezers.



A small dish of wooden pieces will also be placed on the tray so that children will identify which items sink or float and which cause the water to rise. Older students will note the number of stones needed and more.

I will present this work early next week and will post photos and a description soon afterwards. The land form component involves floating bog islands and is just too much to write about tonight! I must write more frequently so that I do not have to write so much.