Tag Archives: learning

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“Organic” Math

This year many of our youngest children (primarily 3 year olds) showed strong interests in math, and an opportunity to collaborate on a big mathematical problem came up on our last day of school.

We have been using a rolling calendar all year, marking the number of days we’ve shared at school, and watching the roll of paper get bigger and bigger. Our plan was to unroll the paper on the last day so that we could see how long our school year was. We also planned to cut the paper up afterwards, so that each child could take a part of their school year home.

Rather than lead this process completely, a teacher asked an “I wonder” question once the children marked day number 163 on the calendar:

“I wonder how we could figure out how many days each child can bring home today. We have 163 days and we have 15 children here.”

Many children spontaneously began to share their estimations – (“we’ll each get 2… I think 8…I think 4…. I think more than that…”)

Someone pointed out that we could figure it out if we had something to count. A teacher thought out loud about what we had 163 of in the classroom and remembered that we have many periwinkles, and the children thought we should count out 163 of them. When the teacher pointed out that this would be a very big job, and asked if they really wanted to do all that counting, many children enthusiastically said yes.

At this point, the children needed a bit of guidance, so a teacher suggested that we could count the 163 shells and then make a pile of shells for each child from those 163. Then, if we counted each pile, we’d know how many days could travel home with each child.

Again, teachers asked children to think about how big the job would be. We’d have to find a big enough space for 15 piles, and make sure no one combined piles, or moved them until we had counted out all the shells. About half the group decided they would get the job done.

It took a long time, but we did manage to count out the shells and create 15 piles. And children discovered that some would take home 11 numbers, and some only 10, but that was ok because we only had 163 days.

Before cutting our days, we worked together to unroll the calendar to see how long it was. Too long for the hallway! By this time everyone was working together, since it took all 15 children to hold “our year” in place.

The level of interest and enthusiasm for taking on this counting challenge was quite impressive, as was the children’s capacity to stay on task for the extended time it took for all this counting to happen. Although the children weren’t ready to figure out on their own how to divide 163 into parts, once that suggestion was made, they helped each other stay on track, count accurately, make sure there was a pile for everyone, check their work, and then call on others to help manage the long length of paper representing our year.

Every child was involved in the project – each at his or her own level, each with his or her own approach, some counting by tens, some by ones, listening to and learning from each other. Contrast the learning that comes out of an experience like this to the learning that comes out of drill or worksheets.

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Map Project

This year many of our youngest children have been traveling and there has been lots of conversation about vacations and trips to visit family. We often talk about how children traveled: Was it so far away that you took an airplane? Could you drive? Did you need to sleep away from home? Where did you sleep? Did you go over the ocean or over land? As we talk together, our classroom globe is featured and we help children find where we are now as well as where they traveled, so that we can show how far the trip was on the map. This informal and often spontaneous conversation also leads to questions about the globe itself, and we often talk about the symbols children notice, whether they show land forms, water, continents, animals that live nearby, etc.

Teachers decided to see if a more formal project might develop from this interest. We decided to start by asking families to help by sharing places around the world that are important to each child’s family identities. We posted this information in each location on 2 huge hallway maps – one of the United States and one of the world. And as information came in, we began our project by taking children out into the hallway to find their names and notice all the places associated with their families.

What a powerful beginning this turned out to be! For some children, finding their names and the names of countries important to family members has been the primary focus. For others, the interest has been in the maps themselves: Why is a globe round and this world map flat? Why does the United States look so big on this map and so small on this one? We live in Massachusetts – where is it on this map? Why can’t I find my house on the map? Why are there dots or lines or bumps? Blue is the water – there is land and water. What makes this place an island?

Our next step was to invite children to work together on a map of our classroom. Because so few children are representational in their drawings now, we used shapes as symbols for our table surfaces, hoping that would help children visualize our classroom activity centers and other features. Children looked around the room as we decided the best shape for each area and how to place it. We noticed the shape of our whole room – where the shorter and longer walls are. We found doorways together and noticed that only one wall has windows. When children weren’t sure, we walked over to the room area in question with our map, comparing what we placed with what we saw in our classroom space.

Many children chose to continue this process by making their own maps and with a focus on both family identities and our immediate shared environment (the classroom) we found the maps that children made also held personal meaning. Many maps of children’s houses were made, along with maps of the route children take to school. Details included our neighboring mountain, the Great Blue Hill, and children have added the road that passes Houghton’s Pond, another neighborhood landmark. Other children drew themselves in the car on family errands to the store, or on the way to a favorite gymnastics class. Some drew maps they could use, like a map of the zoo that shows the way to see monkeys, elephants and giraffes.
When families supported this project by allowing children to bring in family photos or artifacts that represent important places and people, our conversations were deeply enriched and children made new connections to each other. Some families have brought in books featuring places important to their cultural identities too, and we hope that this will continue.

Right now children are finding maps around the classroom, asking for details, and finding places relevant to their family experiences and identities. The book “Me On the Map” by Joan Sweeny has stimulated many conversations as children clarify the scales of different kinds of maps, and we’ve found children drawing themselves on classroom maps as well. Books featuring global families or houses often have maps in the back, and now children find them on their own and ask for more details about where the stories or people they’ve read about come from.

And we’ve seen children begin to represent land areas in their art. One child, when she mixed a beautiful shade of brown new to her, decided to surround it with blues so she could make “an island” We find children using lines to connect shapes, and are hearing more and more children label their work as a representation of a “house” or “mountain” as they develop their capacity for symbolic thinking.

We are taking the time to observe and collect information on what’s most important to the children so that we can offer meaningful extensions to this project. We know we want to find ways to think more deeply about land forms. We know we want to extend our classroom mapping experience to other parts of our school environment. As the weather gets warmer, we may be moving outdoors for more experiences relating to our mapping experiences – thinking about the outside of our building and our playground, and thinking more about the landmarks and features of our neighborhood.

And we’ll continue to look for ways to include families in this shared experience. Our annual multicultural family lunch is coming up, and we are hopeful that at least a few of the foods we share will represent some of the rich diversity of family experiences and identities that are present in our community.

 

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Exploring Early Literacy at a Family “Open Door” Day

We recently invited families to join us for a family “Open Door Day” when we could talk together, share perspectives about how children learn and why we approach curriculum development the way we do, and focus on one important area of development that we are all thinking about. Our area of focus was early literacy and beginning reading.

We teachers know that many family members wonder about the best ways to support their children’s literacy skills. An “Open Door Day” format offers a perfect opportunity to meet with teachers and other parents, collect information, and ask questions. After a discussion, the classrooms are set with activities that are engaging at school and that can be easily replicated at home. There’s no better way to get a feel for how developmentally appropriate, engaging, playful activities and interactions support learning than spending an hour or so playing with the children in the classroom!

We talked about many things, including:
• The importance of conversation – listening, talking about topics or experiences that are personally meaningful to children, sharing feelings and ideas about shared experiences
• The values of reading to children, even as they begin to read on their own
• The importance of developing a rich and expanding vocabulary
• The continuum of developing reading, from infancy on
• How children develop an understanding of symbol, and the importance of pretend play in that process
• The development of writing from drawing
• Using sensory materials like shaving cream, finger paint, or sand to support fine motor development, alphabet knowledge and writing
• Helping children develop an understanding of why reading and writing have value – reading and writing as communication
• Joining children as they discover print in their environment
• Developing language and an awareness of how lines come together through descriptive conversations about children’s artwork
• Beginning stories and storytelling
• The values of puppetry in developing a sense of story and character
• The relationship of musical experiences to early literacy
• Breaking down skills that children need to read, with an understanding that skill development without a meaningful context is insufficient
• Choosing good books for beginning readers

Here are photos of children, families, and teachers together:

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Connections and Curriculum

As we start our school year together in a classroom of very young children that we don’t know well yet, we are looking for interests everyone shares that can give shape to our developing curriculum and can help children make connections across many experiences. We want to encourage children to engage with materials and learn more about how to use classroom tools and media and we hope that children will begin to connect socially at the same time – talking together, helping each other find what’s needed, sharing ideas and experiences, and beginning to notice the things children have in common as well as the differences in approach or experience that we can all learn from and appreciate.

Teachers often think about very open-ended themes or projects to get his process started – looking at the environment, thinking about color, making a mark, telling stories all offer beginnings that can unfold in multiple ways over time.

An example this year has been color as an organizing idea around the classroom. We began by encouraging children to use primary colors at the easel and at collage as we introduced these classroom spaces to the children. When we used glue at collage with a variety of colorful circles, would children notice colors? Sort colors? When children created their first paintings, would they keep primary colors “clean” or would they begin mixing experiments right away? Would line or filling a whole page be the primary interest or would color be an organizer? When we introduced children to classroom puzzles or color cubes what could we observe about the children’s understanding of and thinking about color as they constructed? Our observations inform decisions about experiences to offer next, and help us understand how children are thinking about the experiences we share, even when they might not be ready to tell us much about their ideas yet.

Right from the beginning of our year, we’ve had children very interested in using color as an organizer as they sort, create patterns and construct. We’ve had children interested in naming (labeling) colors And we’ve had many children mixing, experimenting, and investigating the multiple shades that can be created when colors are combined. With these approaches and interests in mind, we could offer a wider variety of classroom experiences that we knew would be engaging and offer rich opportunities for the children to connect.

At the easels, we’ve encouraged children to focus their interest in shades of color by changing the color combinations offered. One week might focus on yellows and blues so that a variety of greens could be easily created. Another week might focus on yellows and reds, or reds and blues. When the primary colors returned, we observed a more purposeful investigation of color mixing, and the conversations about shades of color have engaged more and more children. At our weekly paper day, when children share work with classmates before it travels home, many children describe the ways they thought about color to create as they painted.

We offered a variety of books that feature color, so that conversations could continue in a new way. Books featuring fall leaves, and books like Mouse Paint by Ellen Stoll Walsh or Mix It Up by Herve Tullet have been read and re-read often. Mouse Paint became so important to the children that we decided to extend its themes into our first fingertip and hand painting experiences and for collaborative retelling and drama experiences.

When we were ready to cook our first recipe using tomatoes, we made sure that we investigated many kinds of tomatoes – with different colors as well as sizes. We used these investigations to introduce documentation to the children, encouraging them to talk about, observe carefully, and then draw the varieties they were interested in.

At the science table, we’ve been mixing colors in muffin tins filled with water. Primary watercolors are in 3 of the tins, and children used a pipette to move colors in and out of the water, so that they can create a variety of shades and colors. Including transparent color viewers, mixing tools, and seasonal vegetables at the table enriches the conversation about shades of color, mixing color, and seasonal changes. A favorite activity is to take a viewer and look at the classroom and classmates through yellow, or blue, or red.

And now that the leaves are changing, we are well prepared to look for color in nature. We’ve offered a bed of leaves for pretend woodland animals to shelter in on one of our side tables, encourage children to look up and out of our classroom window often to notice the changes outdoors, and are beginning to investigate changes outdoors as well.

This is one example of how in a busy classroom informed by child interest one thing leads naturally to another. The same process is unfolding in storytelling, making a mark, looking at the environment, thinking about letters and words, and in many other rich investigations that are on-going every day.

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Blocks and Construction Play

Whenever family members ask about good toys for children, one of the first that comes to mind is blocks.

Unit blocks – blocks that come in several sizes and shapes that are proportional – offer tremendous learning opportunities. As they play, children solve problems and develop motor skills. They measure, sort, compare, think about shapes, and develop spatial skills. In order to successfully realize their ideas, children develop the capacity to plan and to use their past experiences to inform their building designs. Children learn to practice and persist as they cope with design challenges. They explore scientific principles and physics as they experience the challenges building their structures pose, whether it’s making a long bridge, creating a window opening, or building higher.

Even taking blocks off the shelf and cleaning up offers opportunities for learning. When children match a picture of a block to the block itself at cleanup, they are “reading the blocks” – using an abstract representation of the block to know where to put it. This is an important prerequisite to reading words.

Many children are also developing stories and pretend skills as they build. The buildings may be part of a city, or may represent a neighborhood where children live. There may be people who live and work in the buildings that are constructed. Children may explore jobs people do, road or pipe works, and relate their block play to their life experiences.

There are many opportunities to develop social skills as children build as well. A bigger structure or thematic plan is possible when children work together, but to do so requires talking together, planning, sharing ideas, negotiating, taking turns, and generally learning to take the perspective of others.

Many different kinds of construction toys, including unit blocks, encourage children to create and solve problems. Because open-ended materials like blocks can be used and combined in so many ways, children are invited to expand their capacity for divergent thinking.

Free exploratory play with blocks and construction toys is important, but is not the only way that these materials can be used. More experienced children may benefit from following a plan to build, or by solving a problem with blocks posed by a teacher.

Constructing with blocks gives children opportunities to learn as young children learn best – through physical activity with concrete materials in their environment, on themes that are personally meaningful, and in an integrated way.

Enjoy the collection of constructions shown by these photos!

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