A Cow Says "Moo"

This has been an extremely interesting week...the children have proven to me through their actions that learning is recursive, free-flowing, and dynamic. Participating in a child's development continues to be a joy and really a gift....getting to see the "aha" moments, as well as the furrowed brows and the frustration that often come with learning. Mix that with my own expectations and assumptions, and one gets a really inspiring, awesome experience! Take these three examples....

LEARNING IS MESSY
Earlier in the week I presented a child in one my Constructing Number Concepts workshops with a really messy, ill-structured problem. Ill-structured simply means that there are multiple paths to solve the problem, and often, multiple "correct" answers. There are no simple algorithms or processes...the learning comes from the construction of knowledge.

Here was the problem:

"You are a walnut farmer (I thusly presented the boy with a basket of walnuts.) You are going to sell these walnuts, but first, you must organize them into wooden bowls to sell them to your customers."

[Under my breath I counted out 27 walnuts, so that the child would not know the quantity, and placed them on our activity table. Then, I set out 6 wooden bowls.]

"Okay, your task is to put the SAME amount of walnuts in EACH bowl. How will you do it?"

Oh boy! This really stumped the child. He grappled with it for a long time. He got frustrated and wanted to move to another activity. His brow was furrowed. It was really, really messy learning. So then I said to him, "If I put 1 walnut in this bowl, what should I put in the others?" In learning theory, this is called a scaffold. Basically, I was providing a bridge for him to connect to.

Aha...a brief moment passed and he got it! He placed 1 walnut in the other 5 bowls. But this is where conceptual understandings are so complex, because in the next instant he was placing unequal quantities of walnuts in the other bowls. So I reminded him that each bowl must have the same amount. What he did next surprised me greatly...

He took two of the bowls, one containing two walnuts the other containing seven, and turned them upside-down, keeping the contents in each bowl. Next, he pushed the bowls around each other a couple of times and then finally, lifted each bowl up and then looked at me perplexed.

"How come they're still the same?" He asked me. It took me a second to absorb what he was thinking, and then it came to me. He had turned the bowls, like a magician does with cups and the objects beneath them. He really believed that by doing so the quantity of each bowl would change to a more desirable arrangement.

"Well," I said to him, "I guess magic doesn't work very well with walnuts. I guess we'll have to count out the walnuts and put them into groups. Shall we turn the bowls over again?"

"Oh man!" the boy exclaimed, but he turned over the bowls nonetheless and we began the arduous task of counting out the walnuts so each bowl had the same amount. At last, he finished his task. But if you remember, we had 27 walnuts and 6 bowls, so of course, there were 3 walnuts remaining!

"So what shall we do with the remaining walnuts?" I asked the boy. His response....

"One customer will get 3 extra. Lucky for him!"

That's what I love about ill-structured problems...there is no WRONG answer. And the learning is not embedded in facts or knowledge (procedural or declarative knowledge); rather, the learning is conceptual and requires higher order thinking. One does not need to know that 6 X 4 = 24; rather, one must create that understanding through manipulation. This is at the heart of what we do in the playroom....we create understandings and meaning to lay foundations for lifetime learning.

LEARNING IS EXCEPTIONAL
So this leads me to my second exciting experience...my Earth Explorations workshop. We have been talking a lot about how our actions affect the world, and how if we do something that disturbs our environment, we hurt the animals and plants in that particular biome. Now how many 5-year olds get to learn about biomes? Well, we do! Anyhow, we had worked our way through talking and drawing pictures of food webs and food chains. And parents, do you know that your children already have a solid foundation in understanding hierarchical structures? It was fabulous to help them craft graphic organizers to display the relationship between plants and animals in a food web and in a linear food chain. They really have a great foundational understanding!

In all honesty, I was a little nervous about this particular Tuesday because we were doing something that most kids do in junior high school, but I felt I had prepared them adequately and of course, they astounded me. We culminated the workshop in a dissection of an owl pellet (owl throw-up, to be exact).

Before we even touched the owl pellet, we talked about safety (wear gloves) and how to pull the pellets apart (tweezers & toothpicks). We also put on safety glasses, like true scientists do. Then, I displayed a chart of bones from small animals like rodents, shrews, and birds. We then started to pull apart the fur from the bones and piled up the bones in the middle of the table (on newspaper, of course!) I shouldn't have even doubted what 5-year olds are capable of, as they carefully, with hands as sure as surgeons, separated tiny, tiny bones from the fur and placed them in the middle of the table. "What's this Miss Cheryl?" they exclaimed each time they found something. For the first 15 minutes I helped them identify their treasure by comparing the bone shape to those on the chart. Then, something amazing started to happen; they started to identify the bones on their own!

"Look, Miss Cheryl, I think I found a leg bone!"

"Wow, look how big this skull is...and what are those tiny things...could those be teeth?"

"Hmmm...this looks kind of like that hip bone we found earlier, but it is a bit bigger, do you think it is a hip bone Miss Cheryl?"

And the icing on the cake? We found a vertebra of a bird!

If you think about what your child is capable of doing; rather, what you BELIEVE you're child is capable of doing, you are often dead wrong. And that is the beauty of learning...we each have our own place and time for connecting with our learning. When we can connect as a group, that is an exceptional experience!

So what did the children beg to take home? You guessed it, another owl pellet to dissect at home!

Now perhaps some of the parents were a bit concerned about what to do with an OWL pellet, but no worries...you've got junior scientists on your hands!

LEARNING IS LITERAL
And lastly, a reminder that early learners are quite literal in their understanding of the world....

The other day I was working on a phonemic awareness activity with my 3-5 year old Whirl group. Each child had a picture card and one child had a ball. The object of the game was to roll the ball to the child who had a picture card with the same beginning sound as the child with the ball. So, the child with the picture of the "snake" would roll the ball to the child with the picture of the "seal" because they both contain the /s/ sound, and so on.

So, to model the activity, I first went around and asked each child what picture card they had. One boy said, "I have a duck."

"Yes, you do have a duck!" I responded. "What does a duck say?" The entire group said "Quack."

"Yes, a duck says quack, I confirmed, and then added, "Duck has the /d/ sound." The children repeated the /d/ sound after me.

We proceeded in this fashion until we reached a little girl with a picture of a cow. "What does the cow say?" I asked.

"Moooooo" the little girl said. I was stumped! We have been working on initial consonant sounds, so why was she saying "moooo" instead of "/k/"? Well duh, it suddenly occurred to me. I was not asking the right question, and therefore, she was responding literally.

"Yes, a cow says 'moo'" I responded. "Can you tell me the beginning sound of the word 'cow'?”

"/k/" she said. "/k/...../k/....../k/" the little girl repeated.

It was at that moment that I had a little reminder about how children learn - how literal they are, and how my adult assumptions could easily cloud their understandings. Quite literally, the children were responding correctly...a duck does say ‘quack’ and a cow does say ‘moo,’ but my questioning was not precise enough for them to understand the task, so I had to make modifications.

We completed the activity with each child identifying a sound and finding a matching picture. And, I was left with an excellent reminder, that often as teachers we have to remember to put ourselves in our students' shoes and to reflect on how a child might be interpreting what we are asking, because after all, a cow does say "moo"!

Counting & Numerosity

We find great joy when we see our children counting things. We applaud them when they say, "Look, there are 1...2...3 balls!" Or when they count the days on a calendar, touching each numeral with a fingertip. But do they really understand what they are counting? And what does it mean to count? A child who can count, as in the examples above, does not necessarily understand the numerosity, or "how many-ness" of what she is counting.

To help her develop a strong "number sense" we must provide her with a variety of opportunities to explore numbers through hands-on explorations with objects, such as mathematics manipulatives and things used in her everyday world. She must be given tasks that encourage her to think, reflect, and consider, so that she may construct her own understanding of mathematical ideas, as true learning occurs only when we create it for ourselves.

Think about growing a tomato plant....surely, you can read about how to do it and explain it to others based on what you have read, but when you actually plant the seeds, transfer the sprouts into the soil, determine how to steak the drooping vines, keep the bugs off the leaves and fruit...it is then, and only then, that you construct an understanding of how to grow a tomato. Prior to doing it yourself, it was just knowledge.

In the WRC Educational Playroom, children participate in a wide variety of activities, designed to help them develop, over time, the following (just to name a few):

• the notion of relative magnitudes - a child can discern one set as more or less than another without counting the objects in each set
• the one-to-one principle of counting - each item to be counted is counted once and only once
• the stable order principle - number words must be recited in the same order
• the cardinal principle - the last word counted represents the "how many-ness" of a set
• the principle of increasing magnitudes - the later number words refer to greater quantities
• the one-to-one principle of numerosity - two sets are equal if the items in each set can be matched one-to-one with no items remaining

We often talk about learning in terms such as "building blocks," "stepping stones," or even "a good foundation," which is really quite inaccurate. Cognitive development occurs in more of a give-and-take way where children move forward and backward in a recursive manner as concepts and ideas begin to take shape in their minds, over a long period of time--usually years.

And while it is true that we want our children to have a "strong foundation" in math, their development will not happen in a linear, static way; rather, it will be much like an Impressionist painting--when you stand very close to the painting, you see lots of dots that appear to simply be dots, and the dots may seem rather disconnected, which is similar to the seemingly random bits of concepts, skills, and knowledge we may see in our children. But, when you stand back a bit farther, the painting begins to take on a more recognizable shape, and the relationship between all the dots becomes evident, just as we start to see our children making connections as they construct their own understanding of mathematical ideas.

So what do we do in the playroom to help children develop their own mathematical ideas?

• We visualize quantities using dot patterns independent of and within ten-frames for quantities 1-10. The patterns are ordered and predictable, to help children develop strong mental images.
• We count using base-10 language, in which the words we say actually mean the quantity. So your child may say "10-two" for "12" or "2-ten-7" for 27. Have you ever considered how confusing it is for a child to say "ten... eleven...twelve....thirteen..."? The words after ten have no relationship to the quantities they represent. In contrast, ask a child to count to "2-ten" (20) and he will be able to do so, with relative ease, AND will be able to match objects to the count.
• We solve problems that are difficult and messy, but situated in their own world. How do we share markers equally? In what order do we place the numerals on the calendar? Are there more purple kinds of flowers in the garden or yellow ones?

So how can you support your child's learnings in the playroom? Play games that require your child to build and decompose sets, count objects, assign quantities, and solve problems. Situate them always with number patterns, and help her see those patterns in her everyday world. And have fun while doing it together!

And while you're mathematizing with your child, check out the National Council of Teachers of Mathematics website activities that use the same ten-frames and counters we do in the playroom! It's a great way to weave developmentally appropriate technology activities into their play, too.

What do we DO in the playroom?

When people ask me what I do and I tell them, "I run an educational playroom," they often ask me to elaborate. I tell them that the playroom is a unique place to learn and grow, not only because the curriculum and learning environment are "green," but also because my pedagogic stance is also very progressive.

The playroom is a place where children can play and discover the joy of learning through hands-on, kinesthetic experiences. All of the instructional strategies are scientifically research-based and have been proven effective with children of varying abilities. And my teaching reflects an eclectic pedagogy—one that supports problem-based learning opportunities, allows children to develop a strong conceptual foundation, and tailors learning experiences to each child’s individual needs.

Ultimately, my goal is to help children develop into thoughtful, well-rounded citizens of the world who have the ability to think creatively, solve problems analytically, and work collaboratively—skills necessary for our children to be successful in the 21st century.

For some folks, this is enough explanation, but for others, they ask, "Yeah, but what do you DO in the playroom." This is the question I love to answer! I tell people that we wrestle with, contemplate, and explore ideas. We listen, look, touch, and feel. And we also do a lot of considering...how our actions affect others and the environment, how we feel about the work that we do, why we make the decisions that we do, and how we can solve problems presented to us.

This means that children will dig a little deeper in everything they do. For example, in my Constructing Number Concepts workshops, instead of rote counting, children participate in activities where they visualize number patterns, sort and group objects, organize and compare, and slowly over time, they begin to construct their own understanding about the concept of number, e.g., what exactly 5 means. To most kids, 5 is 5 and nothing more. Well, some may be able to tell you it is before 6 and after 4, but even then they don't really have an understanding of the relationship 5 has with 4 and 6.

But to a child in The Well-Rounded Child Educational Playroom, 5 is 2 and 3, it is 4 and 1, it is even half of ten! A child could tell you that 6 contains 5 with an extra 1. Or, that there are only two sets of "partners" in 5 and one left over. She can draw patterns of 5 that show different ways in which to organize the quantity graphically. The patterns help her "see" a number inside another number. And soon, the child begins to see the patterns in her own environment...the tiles on her bathroom floor, the dots on the back of a ladybug in her garden, and even the eggs in an egg carton.

Experiential learning happens all around us, in the things we do daily. Today, a group of children in my Earth Explorations workshop made an oil slick. We talked about what it looked like and how the oil and water didn't seem to mix. Then, we pondered what might happen if oil was spilled in the ocean. The children asked one another if the oil would sink or float, and where the oil would go. So I encouraged them to consider what might happen to a bird that decided to land in the water and do a little fishing. What would happen to the bird? One little girl looked at me quizzically and then said, "Well, it [the oil] would get all over the bird."

"How do you know?" I asked. She didn't know, so I left her to ponder the question for awhile.

Next, I asked each child to choose an object and attempt to "clean up" our oil spill. One tried a plastic spoon. Another tried using long strips of newspaper. Still another tried a napkin. The little girl who had thought about a bird landing in the oil said, "Oh, this is sticky....the oil would stick to the bird!" And then all the children wondered if the oil would hurt the bird and if it might die.


This is a weighty problem for a small child to consider, but an important one because it led us to discuss our personal habits and what we do with our trash. We then read a book, All the Way to the Ocean and learned about how trash that ends up in the street often flows through storm drains when it rains, and out into the ocean. And this led us to another conversation about what we consider "trash."

Now this all may seem very haphazard to anyone observing our little group...I mean how can we weave so many topics into one 50-minute class? And what connections are the children making to the concepts and among one another?

The short answer is that I anticipate as many possible ways that a conversation may go, or an activity may shape, so that I am prepared for what will pique the children's interest next. And because we work in small groups of 2-6 children, we can on a dime, switch gears and move down a path that supports the children's curiosities. However, learning in this natural, Constructivist environment is often organic and comes from the children, so I watch for key points to facilitate, nudge, or gently encourage a new path, a different line of thinking, or another option.

So what did we do after reading the book? We went through the trash, of course! Okay, so the children just pointed and discussed while I sorted through the trash. On their own, the children came up with two groups that we could sort the objects into: trash and recycling. I placed a comp0st bowl in front of them and asked them to tell me about what they saw in it. Should the contents go in the trash bin or recycling can?

They noticed some ends of green beans, lettuce leaves, some egg shells, and even a banana peel. I asked them, "What should we do with all of these fruits and vegetable parts that we don't eat?" None of them new, except one little girl who had an inkling of an idea.

"We could put the egg shells in the ground!" she exclaimed. So I asked her why would we do that and she pointed out our seeds, now sprouts, that we had started in old egg shells a couple of weeks ago. Aha...a light bulb went on! And so, another opportunity presented itself...a conversation about composting. We talked about one little piece that was stuck to the banana that would not be good for the soil....a bit of plastic.

"What do we do with that?" a little boy asked me.

"I don't know....what do you think?" I responded. The children all thought it could go into the recycling, because of course, it was plastic. I noted that not all plastics are recyclable, so then in horror, all of them said, "Oh no, we'd have to throw it in the trash, and that might get into the ocean and hurt the fish!"

Connections....just when I thought our brains had enough work for the day, one of the boys in the group said, "Miss Cheryl, if trash goes in the ocean, it won't look like that anymore!" He pointed to a photo of a pristine ocean we have hanging in the playroom...so clear it looks like a swimming pool.

And then in a blink of an eye, our class was over. I encouraged the children to tell their families about their experiences today as they hurried out the door. Recounting the day's events is a good way to make the learning their own and extend it into other avenues of their everyday world.

Sometimes it is hard to grasp what we do in the playroom because giving a short explanation about it does not do justice to the children who bring their bright shiny minds into our place of contemplation to question, probe, and wonder. It is my intention though, that families are drawn to the playroom because of how their children feel when they arrive--happy to be there!--and the state in which their children leave--peaceful, contemplative, and yes, still happy!