“I think that wolf should go in this row, with the pigs,” protests five-year-old Harper. 

“What? Why? He’s a wolf, not a pig!” insists Harrison.

“And he’s not pink!” chimes in three-year-old Evelyn. 

“The wolf will go with the pigs in this row for ‘Stories,'” explains Harper. “You know, like in that book, The Three Little Pigs!”

I wander over to see what this deep discussion is all about. Wow! The older preschoolers are lining up and labeling groups of animals from the basket. This is child-led learning at its finest!

“Oh yeah! That makes sense!” Miguel agrees.

But Evelyn seems puzzled by their reasoning. Math skills such as sorting and patterning are developed in a sequential order—and Evelyn’s early math skills are not as developed as those of her older friends.

At all ages, children classify objects intuitively to make sense of the world. Two-week-old infants can already distinguish objects that they suck on from other objects.

By the age of two, toddlers can form sets of similar objects. By preschool, children can sort and categorize objects according to a given attribute.

When children engage in classification, they are sorting objects according to some established criteria. For Harper, it makes sense to classify the wolf with the pigs. It also makes sense to Miguel when Harper explains his reasoning. 

I look at the list that Harper has created. I chuckle at his phonetic spelling as I read the three categories that he has printed across the top of a sheet of green paper: “Jungle, Farm and Stories.”

When learning how to classify objects, children first learn how to identify and name the attributes that the items in a group will have in common. Then they move on to identifying the attributes that will exclude items from a group.

See Harper’s list in the bottom right corner?  It reads, “Not in a group.”

Wow! This is math! This is early literacy! All while playing and having fun!

Remember back in first grade when we were learning about sets and we had to circle the apples, but not the oranges, on our math worksheets? Our morning of animal sorting is a similar exercise, but the children are establishing the rules.

Hands-on play will beat a worksheet any day of the week. What sticks to the hands, sticks to the brain. 

When children sort objects in their environment, they are using their analytical thinking skills, which are the lifeblood of mathematics. When children engage in organizing activities, it helps them make sense of their world.

Sorting allows children to determine where they think an object belongs and why they think it belongs there. Often, objects will be reclassified from one day to the next. The wolf may be classified as a “Story Animal” today and as a “Forest Animal” tomorrow!

A 2015 research study showed that young children were more creative, more interactive and more verbal when they were playing with sets of animal figures than with other toys (Trawick–Smith et al. 2015). These findings were consistent regardless of gender or background.

The takeaway? Every classroom needs a basket of animal figures!

What’s so great about a basket full of plastic animals? It doesn’t come with a rule book!

When children play with toys such as small animals, people or vehicles, they create elaborate make-believe scenarios and engage in rich discussions about those scenarios. Perhaps best of all, they learn to play cooperatively with their friends. 

As educators, we know that children love to play with baskets of plastic animals. Now we have research to prove what we’ve known all along: that open-ended, imaginative play will naturally lead to sorting and classifying—and you’ll be checking off those early math learning standards in no time!

Looking for an Early Math Counts lesson plan that involves sorting and classifying?  Check out Cereal Sorting!

Do you have collectors in your midst? Those young children who can turn a five-minute walk into a 15-minute treasure hunt? The children who fill their pockets with treasures and then load up your pockets with the overflow?  I love these kids. They can wreak havoc with our daily schedules, but they help us slow down, take a breath, smile and find beauty in unexpected places. They also make me smile when I remind myself that these impromptu, child-led collecting and sorting expeditions are worth their weight in gold as we work with young children to build a strong foundation for later math learning.

We collect lots of natural loose parts like acorns and buckeyes, feathers and rocks. But we also collect colored gems, bottle caps, keys and other odd items. This, my friends, is the rock-solid, hands-on play that lays the foundation for number sense.

At all ages, children classify intuitively to make sense of a world that seems largely out of their control. By the time infants are two weeks old, they can distinguish between objects that they suck on and those they do not. By the age of two, toddlers form sets of similar objects. In preschool, children begin to sort objects into categories according to a given attribute.

If it attracts their attention and they touch it, that’s the moment the child-led learning begins! So grab a bag, a basket or a bucket, take a walk and see what sparks the imagination of the children in your life. A good pocket comes in handy on these expeditions!

Along the way, observe the collecting habits of your budding mathematicians. What captures their attention? What treasures do they deem worthy of pocketing? Does one of the younger treasure hunters in your group need guidance or mentoring?

During your expeditions—and other daily outings—keep your eyes out for heart rocks. It’s a great opportunity to build some early math skills, whether you’re waiting for a table to open up at a restaurant or killing time before an appointment. Hidden in those landscape rocks, there is sure to be a heart rock!

Children will naturally begin to sort their collected treasures into piles or “sets.” Separating will come very naturally as children sort acorns into one pile and bottle caps into another. They may group by colors, shape, texture or weight. They may also organize their objects in a line by size or other attributes.

As they sort the objects that they collect, children are building their analytical thinking skills, which are the lifeblood of mathematics. This is a great opportunity to introduce vocabulary words such as more and less.  Young children have an inborn sense of more and less. They always know if someone has more than they do!  Children can learn number sense simply by playing with their collections!

If the grouping of sets leads to counting, this is another great opportunity for young children to build foundational math skills. Regardless of how high a preschooler can rote count, a child’s sense of what those numbers actually mean develops gradually. We call this “understanding number sense,” and it requires relating numbers to actual quantities.

There are three core counting principles:

Counting Sequence 
There is an ordered sequence of number names. Counting involves using the same sequence each time, starting with one. By using counting songs and moving each object as you give it a “name,” you can help children learn the counting sequence.

One-to-One Correspondence
One number from the counting sequence is assigned to each object in a collection. Instruct the children to put each object into a container or slide it across the table as it is counted.

Cardinality
The last number assigned to an object when counting a collection indicates the total quantity of objects in the collection. Ask: “How many?” If the children don’t know the answer to this question, count the objects together and note the last number that you counted as you push the objects all together into a group.

By turning counting into an enjoyable, hands-on activity, you are also introducing the children to mathematical concepts such as place value and addition.

Remember to take it slow and make it fun. Children develop at different rates and have different learning styles. They will master early math concepts in their own time and in their own way.

So let the children set the pace. Enjoy the cooler fall temperatures as you embark on your collecting expeditions—and see what collections land in your pockets!

Looking for some great activities to introduce sorting and counting to your early learners? Look no further than the Early Math Counts lessons page.

Here are a few of my favorites to help you get started:

• Cereal Sorting
• Laundry Sorting
• One Fish, Red Fish

“Hey, Evelyn!  Go get your cell phone and meet me at the stumps!” calls Noa.

My head whirls around as I check the classroom to see if a cell phone has actually made its way into school today. Then I see Evelyn running to the basket of dominoes to get her “cell phone.”

Whew! Instant relief and a touch of humor added to my day.

Dominoes have been around for centuries. They’ve been used for all sorts of games around the globe. We have baskets of dominoes scattered around the classroom. We use them for everything from building and matching to chain reactions. I’m fairly sure that we’ve never played an actual game of dominoes with these versatile learning tools!

I love these little blocks. Whatever the game, dominoes are always a Developmentally Appropriate Play (DAP) item, regardless of the ages of the children playing with them.

This morning’s “cell phone” incident got me thinking about Developmentally Appropriate Practice.

We need to trust that the teachers who work with young children on a daily basis know what’s appropriate for these children and understand how they use their materials.

Dominoes may not be designed for toddlers and preschoolers—and may even be considered to be Developmentally Inappropriate if used as intended.

Yet, by adding dominoes to our play areas and using them as manipulatives and loose parts, we can expose our early learners to a wealth of STEM learning opportunities such as building, counting, matching and even dramatic play.

Whether we’re building with our dominoes or standing each domino on end to create a chain reaction, we are laying the foundation for strong math and science skills.

This is when parents and administrators may misconstrue active learning for mere play.

When this happens, it’s our responsibility to help parents and administrators “see” the learning that is taking place. Show them how their children are developing spatial skills and an understanding of concepts such as “location” and “ordinal position.”

“Wow, Michela, your tower is getting really big!” Jameson stops to watch as Michela carefully adds another block to her structure.

Jameson has been struggling to build a tower that rivals Michela’s in height. “My tower is too wobbly,” he moans. “It keeps falling down. It’s impossible!” He stomps his foot in frustration and crosses his arms over his chest.

“You need to go very slow, like this,” responds Michela without taking her eyes off of her tower.

Michela is demonstrating the practice of science and engineering. We have geometry unfolding before our eyes as Michela uses symmetry, visualization, spatial reasoning and geometric modeling to solve problems such as balance and continuity.

By observing and asking questions, sharing ideas and solving problems, the children are working as a team to build a greater understanding of what works and what doesn’t.

This is a form of early data collection. If you are studying force and motion, a domino chain reaction is a great activity to demonstrate potential and kinetic energy.

I watch as four-year-old Thompson counts the pips (dots) on his dominoes and begins exploring concepts such as quantities and attributes.

Across the table, two-year-old Joseph is learning rote counting skills and gaining a rudimentary sense of one-to-one correspondence. By playing with the dominoes, he is also seeing the grouped pips (dots) in number formations that he will continue to see throughout his life.

I watch as an older friend mentors Joseph. In no time, Joseph is matching attributes—sometimes by pattern and sometimes by color. This is math!

We are exploring concepts such as “matching,” “same and different” and “up and down.” We are counting and beginning to understand numbers and number names. We are comparing quantities, subitizing and measuring objects and quantities. We are identifying common attributes, patterns and object relationships.

We are engaged in deep, hands-on, child-led play—without worksheets, themes or circle times. This is developmentally appropriate learning!

By providing more opportunities for children to explore, discover and investigate through active play, we are meeting one of the most important goals of early childhood education.

Invest in a variety of materials to meet the needs of children with different learning styles. It’s worth the cost. Think of it as an investment that will pay off in the future success of your early learners.

So grab those dominoes off of the shelf, place them in a basket and let the STEM learning begin!

Enjoy!

“Hey everybody! Look at all of the tomatoes that are ripe today!” shouts Jacob to the gang.

“Can we eat them for lunch? Can we?” asks Lucus.

“Can we eat them now?” pleads Elizabeth.

It’s early September and preschoolers around the country are learning about apples, but we have tomatoes at our fingertips. The same tomatoes that we planted in the spring, watered, watched and then forgot about and ignored. But today these plants are full of red, ripe, juicy tomatoes. For the foreseeable future, our curriculum will revolve around tomatoes!

There’s been a lot of talk recently about curriculum themes and how they fit into early childhood education. So much of the learning that takes place in early childhood settings is spontaneous, rather than intentional. This doesn’t mean that early childhood educators shouldn’t be intentional about their curriculum development. They should. But great teachers are always willing to set their planned activities aside to seize a great learning opportunity when it arises.

I call these unplanned learning opportunities “teachable moments.” In so many ways, the child is the curriculum. By observing our early learners closely to see what ignites their curiosity, we can identify and build on the teachable moments that we encounter throughout the day.

Once we’ve identified a teachable moment, we can make the most of these spontaneous early learning adventures (and meet our early learning standards) by sharing our insights and asking questions that encourage children to dig deeper and make more connections as they engage in rich, authentic, hands-on learning that only looks like play.

After we engage in these impromptu investigations with our early learners, we can share the fruits of their learning adventures with parents and administrators, so that they can begin to understand how teachable moments can be harnessed to help prepare young children for the transition to kindergarten and success in the larger arena of life.

Soon, the stores will be filled with crisp, delicious fall apples, which will give rise to many of their own teachable moments, beginning with the letter “A.”  But today we have tomatoes, so we’re seizing the moment to harvest, sort, count, compare and investigate nature’s bounty!

It is only through genuine interactions and availability that teachers can identify these moments and act accordingly and spontaneously. Teachable moments require you to “think on your feet” and be flexible enough to stray from your planned path. If children’s interests take them in a direction that you hadn’t anticipated or planned for, you have to be ready to seize the moment and use it as a gift. Follow the joy of your students and your curriculum will develop organically!

“Look how many tomatoes are growing on this one vine!” Owen exclaims to his friends.

We are now collecting data and comparing attributes. Spontaneous discussions unfold as the children explore topics such as where the sun shines in the morning and which tomato plants get the most sunshine.

But how do the tomatoes ripen and turn red under all of those leaves? By observing, investigating and learning that living things grow and change, the children are building a strong foundation for future learning in earth science and life science.

We keep it simple. This type of learning is always developmentally appropriate because the children’s investigations are guided by each individual’s level of brain development.

“Avery, don’t eat them all!” cries one child as Avery pops a couple of freshly plucked tomatoes into her mouth.

We are exploring the concept of “many vs. few.”  But some of the children are too young to care about this concept and just want to experience the sweet deliciousness of a ripe tomato straight from the vine.

Our tomato harvest has all of the hallmarks of a true STEM learning adventure: investigation, discovery, collaboration and discussion. The children are learning through their senses: the visual task of surveying the tomato plants and comparing and categorizing the tomatoes as unripe (green or pale orange) or ripe and ready for harvest (deep orange); the tactile pleasure of separating a plump ripe tomato from its green stem; and the delicious sensation of biting into a tomato, still warm from the sun, and feeling it explode on the tongue. All of the goodness of nature and little brains in motion!

While two-year-old Lauren is more focused on picking the tomatoes and filling her bowl, some of the preschool-age children are busy trying to collect as many as possible. “Look how many I have!” squeals Linnea. “I have more than you!”

As the children explore the physical properties of the tomatoes, we are suddenly counting, estimating, comparing attributes and organizing by color and size. We have vocabulary and math flowing off of the children’s lips, which are stained with the juice of the ripe tomatoes. We are meeting our early learning standards—and the children are developing their own curriculum as they go!

Children construct their own understanding of the world when we provide them with a rich learning environment (in this case, our tomato garden) and ample time to explore, discover and investigate. We want children to think for themselves and not simply follow a preconceived curriculum or theme.

By taking advantage of authentic learning experiences in sensory-rich environments, we are setting the stage for the natural integration of early learning standards and successfully incorporating STEM knowledge into the daily lives of our early learners.

When you foster the development of a creative learning environment where children can find joy in learning, you will discover that your curriculum and lesson themes will spontaneously arise. In other words, let the children lead and the curriculum will follow!

Once the children have “followed their bliss,” introduce the books and thematic materials that support their interests. Build on their energy, enthusiasm and inquisitiveness.

If you head to the tomato garden, I think you’ll agree: early childhood STEM education has never tasted so good!

“I see the daddy cardinal, do you know where the mama bird is?” Four-year-old Noah, binoculars in hand, is busy counting birds in our outdoor classroom.

Are you aware that the annual Great Backyard Bird Count is coming up later this week? This is a great opportunity to create a bird-watching station and knock out some STEM and early learning standards while encouraging family involvement.

Mark your calendars for Feb 12-15 and join us for this fun and educational week!

February and March are good months for bird watching and bird counting in our program. This is a great way to accelerate STEM learning on days when below-zero wind chills make outdoor play impossible.

We have bird feeders set up right outside of our windows so that we can set up indoor bird-watching stations to give the children close-up views of their feathered friends.

We provide clipboards, books, binoculars and our abacus to help with the bird count. We also use this opportunity to teach our students how to tally on a tally chart. We reference the eBird website, which shares local sightings of different bird species.

I take the top ten birds sighted in our area on the eBird website and add pictures of those birds to our abacus. To do the same thing, just add your location to the eBird website and you’ll see which birds are sighted most often in your area. It’s quite fabulous!

We also like The Cornell Lab and the Audubon Society. I have the Cornell Lab Merlin Bird ID app on my phone to help us identify birds by their songs.

Your local U.S. Fish and Wildlife Service may also be able to provide free materials for bird identification. There is a big difference between bird identification books for children and those that were written for mature bird watchers. I would check some out at your local library or bookstore before purchasing.

This is a great opportunity to practice not only counting, but grouping by attributes or close observation of the differences between a downy woodpecker and a red-bellied woodpecker.

We try to keep a ruler nearby for our older children to use to determine whether they have spotted a six-inch downy woodpecker or a nine-inch hairy woodpecker. This offers the children an opportunity to use estimation and practice using real tools for observation.

This is also a great time to introduce Venn diagrams for clarification and documentation.

By creating a comfortable and inviting place for the children to birdwatch—complete with pillows, chairs and tables with baskets of binoculars—you can encourage them to slow down and observe more often.

By planting native plants in your outdoor classroom, you will also attract more birds to your bird-watching stations.

We remind our kids that outdoor birds are hard to spot but easy to hear. We ask them to close their eyes and point to where the song is coming from. I like to teach common mnemonics like the American Robin’s cheery up, cheerio, which can be picked up on almost any bird walk in the United States. Learn some mnemonics for common birdsongs here.

We have tried the inexpensive plastic binoculars from school-supply stores and toy aisles. They really didn’t work well and broke the same day that we brought them out. Smaller, child-sized binoculars are much easier for little hands to manage. Children enjoy using “real” tools and will treat them with much more respect than a pair of cheap plastic ones. I often teach them how to focus the binoculars to get a clear image. I place these binoculars in a basket, along with the identification books. We also stock our bookshelves with a wonderful collection of books about birds, nests and hatchlings.

We talk so much about STEM these days. This is one of the easiest and most magical ways to create a learning hub that can inspire young learners to engage in STEM exploration and discovery.

By participating in these learning adventures, you can learn right along with the children as you observe, ask questions, draw conclusions and discuss your findings with your early learners.

When we observe birds from our indoor birdwatching stations and then take those same observational skills outdoors, we have a deeper understanding of the birds we see and the birdsong we hear.

By adding the technology from the websites mentioned above and building bird feeders from oranges or peanut butter and seeds, we can include engineering in our learning adventures. We can include math as we count the number of birds arriving at the feeder and then subtract the birds that fly away. By grouping, measuring and comparing the birds, we can meet our early learning standards and benchmarks.

I hope you will join us in our Great Backyard Bird Count this year. Birds of a feather flock together. Come join the fun!

One bright fall morning, I notice that the noise level at Under the Gingko Tree is exceptionally low. A quick glance around reassures me that all of my early learners are safe and accounted for. Then I notice a quiet but intense play buzz happening in our rain garden, so I wander over to see what has captured the children’s unwavering attention for so long.

“See? We are using the log to make our hill!” Jameson explains to me. 

“We are rolling the rocks down the hill, but our hill has a tunnel!” giggles Noa. 

“They go in and then they roll down!” two-year-old Tariq tells me, trying to keep pace with his older friends.

“This rock is flat on this side. It won’t roll, just like Ricky!” Jameson reminds me. 

The rocks in the rain garden and a hollow log have triggered an idea from another one of our favorite books: Ricky, the Rock That Couldn’t Roll.

Ricky is a flat rock that can’t roll with his friends on their favorite hill. Ricky’s friends help him overcome his challenge and find a way for Ricky to play like everyone else.  

Suddenly we have piles of rocks that have the same names and characteristics as the rocks in the book. I love it when an idea takes hold and inspires creativity and collaboration as the children begin to plan an activity on their own.

We have a STEM morning unfolding in our outdoor classroom! When the children start using words like “in,” “down,” “over,” “under” and “next to,” they are laying the foundation for geometry. Oh, this is going to be a fun morning! 

As I watch the children design and develop models that represent their ideas, I think to myself, “This is what early math and science learning looks like.” Planning and carrying out simple investigations like this one will make your assessment nightmare seem like a dream. Math and science overlap so much in this morning’s quest for understanding. This is the kind of play that hones children’s problem-solving skills and enables them to meet important early learning milestones.

I see the young friends sorting and classifying piles of rocks—grouping the flat rocks together and then creating another classification for the rocks that will fit into the tunnel. I observe and listen as they demonstrate their comprehension of the sorting and classifying process by comparing and sharing descriptions. When children use words such as “short,” “wide,” “heavy” and “light,” they are using descriptors for measurement. When they are guessing, predicting, classifying and putting rocks in a specific order, they are engaging in early algebra. 

By making predictions, changing designs and collecting data for their next rock, the children are building the foundation for more advanced learning in data analysis and probability in the years to come.

“I think there is something blocking it in there….”  Jameson’s voice trails off as he inspects a rock more closely to see why it didn’t tumble in the way that he had expected. He has observed that the rock is encountering some resistance. This is friction!

This is how we lay the foundation of early science through childhood investigation and teamwork. Today, the children are learning about persistence and problem-solving, propelled by the simple but profound joy of creative play.

Now the children are discussing another STEM concept. “Should we flip the log on its other side or move it to a higher rock?” Jameson asks.

I introduce the vocabulary word for their latest STEM adventure: “elevation.”

“Like an elevator! It goes up to the top of the building!” Jameson declares.

I smile. It’s like throwing seeds into the wind. I never know which ones will land on a rock or take root in a little brain. Either way, this is learning through play. Changing the height (elevation) to get a faster roll is working with speed!

The children are also exhibiting a developing sense of spatial awareness as they work out where and in what direction the log should be placed.

“Maybe if we push it, it will go faster!” Sarah suggests.   

When you are working on those early learning standards, listen to the words that your students are using. When Sarah uses the word “push,” this is a change that leads to an action. The outcome of that action is an effect!

This is scientific investigation in progress. Words like “push,” “pull,” “launch” and “force” are all science action words. 

Ricky—the rock that started this play—is long forgotten. We have naturally moved on to racing our rocks down the tunnel. I am not sure that any child actually remembers which rock is “theirs,” but they know which rock came in first, second, third and last. These are the vocabulary words that tell us that the children are mastering rudimentary skills in numbers and operations. This is a morning of assessment magic! 

If you have ramps in your classroom, or this is the type of play that sparks your energy, try reading the book, Ricky, the Rock That Couldn’t Roll, aloud to the children. Then place some rocks that roll, along with rocks that don’t roll, in your block area. Observe the investigations that take place and check off some early learning standards of your own!

Happy November, my friends. Stay safe and keep playing!

]]> https://earlymathcounts.org/rock-and-roll/feed/ 14 13204 https://earlymathcounts.org/rocking-through-early-learning-standards/ https://earlymathcounts.org/rocking-through-early-learning-standards/#comments Tue, 15 Sep 2020 11:00:19 +0000 https://mathathome.org/?p=12229   Rock balancing or CAIRNS has found its way into our play again this week! Stacking and balancing rocks encourages math and science investigations that are always developmentally appropriate. My adrenaline starts flowing and a smile grows on my face when a two-year-old child exhibits an innate sense of how to balance many more rocks […]]]>

Rock balancing or CAIRNS has found its way into our play again this week!

Stacking and balancing rocks encourages math and science investigations that are always developmentally appropriate. My adrenaline starts flowing and a smile grows on my face when a two-year-old child exhibits an innate sense of how to balance many more rocks than her much-older peers. Children have their own unique gifts; we just need to give them opportunities to discover their strengths and talents.

For the record, environmentalists strongly discourage this practice because it disrupts the natural order of nature. I get that. When we are hiking or playing in the woods, we follow that rule. Our outdoor classroom has a dry creek and wonderful rocks collected from parking lots and estate sales. These are our math and science rocks that are used for play.

Children who are math-and-science ready are great problem solvers. When our friends explore the concept of stacking, they make observations, collect data and investigate shapes and sizes and weight. We count, we estimate, we balance, we hypothesize. It’s science, math, language and play all wrapped up in the beauty of nature. Nothing makes me happier than finding hidden stacks of rocks somewhere in our play yard—stacks that have been left behind by inquisitive children who didn’t need to please anyone but themselves.

Two-year-old Lauren created the “ant house” above. I love that she decorated her house with flowers. I watched as she wandered over to the sandbox on the other side of the play yard to return with a handful of sand to sprinkle on the roof. I love that intentionality and vision. I love that she is barefoot with a toenail that is black and blue and may fall off, evidence of some already-forgotten adventure that didn’t go as planned. I love that she is laying the foundation for later learning in math, science and engineering through play.

You can call it STEM, STEAM or STREAM, but it’s basic childhood play. It’s long hours of uninterrupted exploration as a child works to bring an idea to fruition. It’s the brain on fire, building the synapses of learning. It’s the cement in the foundation of a lifelong learner—the evolution of a visionary, problem-solving, risk-taking master.

I often hear early educators worry out loud about meeting the benchmarks or standards required by their programs. My tip for this is to bring in natural materials, give your children TIME to play, take photos and sit down with your standards. You will be shocked at how easy this can be. Engaging young children in daily problem-solving activities will help them develop the processing skills that pave the way for future lessons in math and science. This rock-stacking experience is all about shapes and spatial reasoning. This is geometry! This is engineering! This is spatial orientation as our rock stackers exhibit an understanding of location and ordinal position. Our young stackers are often meeting standards and benchmarks before they have the vocabulary to tell us what they are doing. They gather data about their surroundings as they figure out how to balance a specific rock in the stack. And if that rock won’t balance, they’ll try another. This is organizing data and information. They are busy making predictions about outcomes by playing with rocks.

Always bear in mind, however, that brain development varies in children.

Some children may not yet be ready to meet certain standards. Some may be advanced in one area, while others may be advanced in another.

This is when you are smarter than the standards! You can’t teach a rock to balance if the rock can’t balance. You can’t teach a brain a concept if it isn’t developmentally ready to process that concept.

This is why it’s important to reassure parents that their children will be just fine in life, regardless of their child’s test scores on any given day. You can look parents in the eye on Parent Night and share all of the standards that their children have mastered through play. Then you can assure them that play is laying the foundation for the brain development and problem-solving skills that will serve their children well throughout their lives.

So bring in the math rocks. Your students will soon be sorting, comparing and working with attributes. This is an early educator’s dream.

Best of all, it’s fun! Fun for the child, a true delight for the teacher to behold and such wonderful food for the brain.

Stay safe and keep on rocking on!

Out of the corner of my eye, I am drawn to the persistence of three-year-old Saaliha. She is calmly and patiently working her way through a rainbow puzzle.  Her friends are busy in other parts of the classroom, but Saaliha is problem-solving her way to mastery. I sit down next to her to observe her skills. She is so deep in her learning that she doesn’t notice.

Open-ended materials such as these often create learning scenarios that allow long periods of deep concentration, and today is no different. Although this puzzle often lands in the block area as a snake, a tunnel or a flowing river, today Saaliha is trying to fit it back together the way it is stored in the tray.

Puzzle play is a great time to build cognitive and fine-motor skills. Besides finding the correct sequence of sizes, Saaliha needs to evaluate which directions the blocks sit so that she can complete the puzzle. I watch as Saaliha flips, turns and rotates the pieces to figure out where they go and in what order. This is spatial transformation. I love watching her learning style and seeing how it corresponds to her developmental level. I see her set aside pieces that are not needed at the moment. Saaliha’s spatial awareness is growing with each try.  

Watching Saaliha play with the puzzle, I can see her choices and strategy change. She begins to recognize and understand how the pieces fit together to complete the puzzle. I watch her sorting and testing pieces of different sizes and moving them in different directions until one piece fits properly. Through this task, Saaliha is developing small-muscle movements and dexterity in her hands and fingers, along with critical-thinking and problem-solving skills. This creates a learning adventure in which the eyes, hands and brain are working together to make the puzzle pieces fit. 

Saaliha is soon joined by her two-year-old buddy, Eleanor. These two best friends are 11 months apart in age—with different learning styles and levels of brain development. They work together to fit the yellow arch into the puzzle. There is discussion as they describe their strategies to one another. The collaboration is delightful as Saaliha patiently watches her younger friend try to master the same issue that she is having. Saaliha never reaches over to remove the piece from Eleanor’s hand. She is observing and reasoning as deeply as she had been moments earlier when the puzzle piece was in her own hand. Eleanor quickly loses interest, but Saaliha perseveres!

Saaliha tries new pieces and new directions. I can see the wheels turning in her head. She is collecting ideas and working out theories. She is not rushed or agitated.  She is riveted to this learning opportunity. She doesn’t ask for assistance. She just keeps trying new patterns and new pieces. 

Suddenly it all clicks into place. The lightbulb of understanding goes on in Saaliha’s mind and I can see her confidence surge as she fits the pieces together more quickly. She’s got it! She’s figured it out! There is no celebration, just a smile of satisfaction. She studies the finished project. Before I can capture her expression of satisfaction, she disassembles the puzzle to do it over again.

Saaliha continues to struggle and I continue to observe her strategies and methods of choice. Her perseverance continues to reward her with success and a better understanding of the puzzle in front of her. She is a finely tuned machine, working on all cylinders as she masters the task at hand with patience and confidence. 

Puzzles offer a wide variety of developmental benefits and enable children to learn important skills as they play. From critical thinking and problem solving to concentration and attention span to spatial awareness, playing with puzzles adds layer upon layer to our strong math foundation! 

It started simply enough with the bowl of beautiful autumn colors and loose parts pictured below:

The children began sorting the items in the bowl almost immediately—without any prompting. There was no discussion about what we were doing. This was very intentional and calculated. When children sort materials, they begin to understand that certain things have similarities and differences.

Let’s think of these groupings as sets. Sets are a collection of items that have been classified together because they have something in common. Defining these sets of matches is a prerequisite for counting and comparing. Before we can figure out how many pine cones there are, we need to separate the pine cones from the buckeyes.

Classifying is the skill of grouping or sorting items by similar characteristics. Being able to match items and explain why they go together is an important part of cognitive development. Children between the ages of three and four enjoy sorting and classifying objects by one characteristic. By allowing more time for exploration and play, you will will give the children opportunities to increase their classification by more than one characteristic.  

Matching is a simple form of sorting. Matching helps children identify attributes that are the same and take notice of details that are a bit different. Children can match by size, shape, color or one to one. 

Seriation is arranging objects in order by size, location or position. There was great discussion and collaboration as we discussed the sizes of pine cones and what order they should be arranged in. 

Patterns are sequences that repeat. The ability to recognize patterns supports math skills. Pattern recognition helps children make predictions about what will come next. Patterns are an important part of spatial thinking. Once children begin to spot patterns, they will see them everywhere in their surroundings and their daily routines.  Pattern awareness is a form of early algebraic thinking.

The children were engaged and spent a great deal of time arranging their materials in many sorted piles and patterns. By engaging in these simple mathematical experiences, the children became more proficient at problem-solving, reasoning, making predictions and making connections in their world. To help the children in your care develop these foundational math skills, keep it simple! Take your students outdoors! The curriculum is waiting for you in those autumn treasures just waiting to be found! 

I am so honored and excited to be the Math at Home blogger for the next year! I love math, and I love watching math happen with children every day. My goal for the next year is to avoid how high and fast our children can rote count. I want to build the deepest, strongest foundation for learning and let the children build their own house of math on that foundation. I hope to give you a collection of pictures from my own program, quick-reading ideas, some great books to find at the library to build on the literacy skills and math understanding and a question to get some dialogue going about math and kids and life. We want to immerse them in math environments without worksheets or set times for math. It will come naturally, through play. I promise to keep it fun and easy.

Let’s start with a quick look at the brain. We know that the right brain develops first. It is really busy building our children’s imagination, creativity and intuition for the first three to four years of life. The left brain starts to kick in developmentally at about the age of seven. It gives us logic, language, literacy, numeracy. The right brain is full of sensory, play, relaxing. I like to think of it as RIGHT BRAIN=RECESS. That left brain over there…whoa, that looks like school/office to me. My own students are in the right-brain zone, age-wise. They are playing with rocks and friends, being creative and using their imaginations while learning how the world works. I really like recess, just like I did when I was five. So let’s stay out here in recess land for as long as we can! It will build the foundation for that school/office side of learning. I promise that play really will get us ready for the left-brain part of life. So, let’s get started!

Collections

Do you have a collector in your midst? That small child who can turn a five-minute walk into a 15-minute treasure-discovering adventure? You know, that child who slows us all down to look at the world below our feet or above our heads?  I love these kids. They make me crazy, wrack my nerves and raise my blood pressure, but they also make me slow down, take a breath, smile and find beauty in the oddest of places. And they make me smile really, really big, when I remind myself that this is the gold treasure chest of math’s foundation.

At the Ginkgo Tree, we are full of collectors!  We collect lots of nature’s loose parts like acorns and buckeyes, feathers and rocks. But we also collect colored gems, bottle caps, keys and other oddities. THIS, my friends, is the rock solid, hands-on, building the foundation of great solid math brain that we look for in early childhood play.

If it attracts their attention, and they touch it, they own it. They own their learning at this moment! Grab a bag, basket or bucket and take a walk and see what speaks to your children. A good pocket is priceless. Keep your phone in your own pocket and give your child the gift of time. What treasures do they find? What captures their attention? Do you need to mentor collecting? Keep your eyes out for heart rocks. We love a good heart rock, and it’s a great pastime when waiting at restaurants or appointments. Hidden in those landscape rocks, there is sure to be a heart rock!

When you return home, dump those treasures out. Before we can begin to count our collections, we need to figure out which are acorns and which are bottle caps. This will come very naturally as a child sorts the acorns into one pile, the bottle caps into another. We can sort into groups, we can arrange by size, color, shape, texture or weight! Remember, back in kindergarten and first grade, these were referred to as sets. Before you could count sets, you needed to separate into sets. If your child hit the jackpot on a particular item, you may wish to give it a special home. Perhaps a small box, a canvas bag, a Ziploc bag or an egg carton. These treasure are chock full of math potential.

Regardless of how high a preschooler can rote count, a child’s sense of what those numbers actually mean develops gradually. We call this “understanding number sense,” and it requires relating numbers to real quantities.

Young children have an inborn sense of more and less. What is fair or equal? Who has more ice cream, acorns or toy cars? They know! Children learn math sense by working with small sets of collections. Math sense refers to relating numbers to real quantities. Slow it down and let’s work on small groups. One to three objects for the wee ones, five objects for our preschoolers. If the grouping of sets leads to counting, try moving each object and giving it a number. Number sense is the ability to understand that the quantity of the set is the last number name given in that set. By making counting hands-on fun, children are learning place value and addition. Take it slow and keep it fun. Children will be exposed to the idea that the same collection can be sorted in different ways. Sets can be flexible. (Ugh oh, I saw your math brain go to sixth-grade math, where sets started getting a bit confusing. Pop out of that left brain! Get back here in recess!) Math is being taught a whole new way. They are removing that obstacle, your left brain might not have learned this new way, so relax and just sort the rocks!  Remember, not all skills come in a certain order. They will come at different times for different children and in different learning styles. It will come. Baby steps. Strong foundation. Let’s stay out for recess and enjoy the ride.

So, that’s it. Collect some treasures and we will meet later in the month and start putting those collections into play. In the meantime, head to your local library, neighborhood bookstore or Amazon and cozy up with your child for some great books on collections!  Amazon is easy, fast and convenient, but we want to keep our book resources alive in our neighborhoods!

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Left-Brain Adult Lounge

I would be absolutely terrified if I knew how many hours my brain has tried to come to terms with my students playing with…bottle caps. Beer caps, specifically. Craft brewers are knocking out some crazy creative bottle caps! They are fabulous for sorting! I DESPISE branding and have removed most of it from our program, so am I branding alcohol preferences to my three-year-olds? Is this early math politically correct?  Am I totally overthinking this? I asked the parents of the students for guidance. They looked completely baffled and said, “I know you have thought this out, and you must have good reason for it!” If they only knew. So, I observed the kids as they separated the caps by features (dogs, colors, whatever popped out at them.) They can’t read. The letters are foreign to them because, remember, that’s left brain and their brain development isn’t there yet! I grew up next to a state park, and I collected bottle caps as a kid. They clinked like coins, they were easy to find, carry in a pocket and sort into categories.

I flip, I flop, I struggle. Somehow, bottle caps always win. And here’s why:

Numbers and Letters!

Sequencing!

I kid you not!  How funny is this?

Same but different!

HELP! What are your thoughts on this topic?  Am I overthinking all of this? Do I justify all the goodness of a bottle cap?  Apologies in advance, if this sends havoc to your brain space on the ethics of early childhood education! Have a great week!