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Mathematics: Numeracy

wood sound number puzzle

From Reciting to Understanding

When reciting numbers in ascending order or saying the alphabet, young children are usually simply demonstrating memorization skills. Numeracy and literacy require understanding the meaning those symbols and being able to put that knowledge to work. A number represents a specific quantity and is used in counting and calculating. Letters combine to form words.

Patterns Emerge

The particular arrangement of numerals signifies a particular arithmetical value. A specific arrangement of letters creates a specific word. The same numerals and letters can be arranged in multiple ways with very different meanings. Take the numerals 1, 2, and 3. These three numbers can be arranged to become 123, 132, 213, 231, 312, and 321. The letters o, p, and t can be arranged to read opt, pot, or top. Making calculations  and reading demand our attention. Numbers and letters are symbols we learn to decipher while developing reading, writing, and arithmetic skills.

Activities of Daily Living

We’re planting seeds of understanding when we impart information during daily activities. Dressing provides numerous opportunities. Naming the garments and enlisting cooperation as we’re putting each one on is one way. Guiding an arm into a sleeve while saying “let’s put this arm in this sleeve, one arm, one sleeve, there we go” gives meaning to the number one and shows one-to-one correspondence. One is one, whether an arm or a sleeve. The body offers many opportunities for learning words and numbers. From head to toes-two eyes, one nose, two ears, one mouth, two hands, 10 fingers, two feet, 10 toes.

Mother Goose and Finger Play

Nursery rhymes provide early lessons in literacy and numeracy. Thank Mother Goose for “This Little Piggy.”  Jennifer Griffin writing in Humpty Who? provides accompanying finger play that delights infants and toddlers.

This little piggy went to market,

Wiggle baby’s big toe between your thumb and index finger

This little piggy stayed home,

Wiggle second toe.

This little piggy had roast beef,

Wiggle middle toe.

This little piggy had none.

Wiggle fourth toe.

This little piggy went

  Wee, wee, wee,

  all the way home.

Wiggle the little toe and then run your fingers up      

the baby’s foot and leg as far as you can get.

At the Supermarket

Young children learn numeracy from everyday activities too. While at the supermarket buying fresh fruit, we can point out the number of bananas in a bunch or count apples as we’re putting them in the produce bag. This shows a child that a number represents a specific, unchanging quantity, regardless of what is being counted, and reenforces the sequence of numbers.

Zero is A Cardinal Number

When we’re learning to count, typically we begin at one. We can see one-to-one correspondence and understand quantity. Yet our cardinal number system starts with zero, and understanding that concept is critical. While shopping for produce, show an empty bag and ask “how many apples are in the bag?” Answer, “zero.” Point out that the bag is empty. Then add an apple, and again ask “how many apples are in the bag now?” When buying number puzzles, choosing one that begins with zero re-enforces the concept of 0: naught, no quantity, no number. When children learn 0 through 9, they’re better able to understand how our number system progresses. Consider Sound Puzzle Numbers. Under every numeral is an illustration of the quantity the number represents.  The space below 0 is blank. This puzzle also shows how easily the numbers zero to nine become 10 to 19. Playing around with the individual numbers creates new ones. Different arrangements, different values.

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Mathematics: Geometry

Shapes and the arrangement of relative parts within a whole are the subject of geometry. Consider the construction of spider webs. The arrangement of petals forming a rose. Study the facade of a cathedral. The angles and the fitting together of its architectural elements. Or all the parts in myriad shapes that combine to make an automobile. Both the natural and the human-made environments are studies in shapes, angles, and intersections.

Best Shape Sorter Toys

Through observation and experience children learn about shapes and parts. First come basic shapes: round, square, triangular. Among early childhood play experiences are sorting and matching of shapes using a shape sorter. Simple ones are best for beginners, and Ambi Toys Lock A Block is best of class. High contrast between the bright white top and the color matched raised rims outlining each opening facilitates “hitting the target.” Equally importantly, its three dimensional shapes drop easily into place.

As shape discrimination, eye-hand coordination, and fine motor skills improve, children are ready for the next shape learning toys. Fitting two-dimensional shapes into corresponding holes. Sound Puzzle Box is a popular choice that rewards proper placement with distinct auditory responses.

Basic Shapes Puzzles 

Puzzles are all about shape. Again starting simple is key. Chunky shapes facilitate placement. Shapes that fit only in their proper places make a truly self-correcting learning experience. Left to right orientation models the direction of reading and writing. Children are ready to identify and match more unusual shapes only after they easily recognize basic shapes.

Interlocking Pieces Puzzles

After learning individual shapes through puzzles, children move on to explore the arrangement of shapes as parts of a whole. Start simple. The more pieces and the smaller the pieces, the more challenging a puzzle is. Wooden puzzles with thick pieces are easier for small hands to manipulate than thin cardboard ones.

A single layer, wooden 8-piece fish shaped puzzle for toddlers, Rainbow Fish, invites exploration of color and shapes and the way parts fit together to make a whole. With only one way to complete the puzzle, the child has to sort out and make sense of the pieces. Then work out how the parts go together to create the whole, a sometimes frustrating experience that benefits from adult encouragement.

Layered Puzzles 

Layered puzzles introduce perspective and offer graduated challenges. As always, start simple and progress gradually. More layers offer more challenge; however, the number of pieces is a more accurate indicator of difficulty.

Mathematical Concepts Puzzles 

Although most puzzles go together in one and only one way, others offer options, and these literally open doors to understanding of mathematics.

The Binomial square wood puzzle introduces mathematical concepts through observation and experience. Children develop proportional reasoning, area concepts, and place value understanding when they discover four small squares cover the same area as the rectangle and four rectangles the same as one large square. And that’s only the beginning of the possibilities.

Power of Two Puzzle encourages experiential learning of important mathematical ideas from fraction equivalents, fraction multiplication with a common factor of 1:2, proportional reasoning, and area. The 10 puzzle is cut into one-half, one-fourth, one-eighth, one-sixteenth up to 1/128th. Clearly challenging, the beauty of Power of Two lies in the multiple ways the pieces can fit together and the arrangement of relative fractions.

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Mathematics: Measurement

red, white, blue, yellow nesting cups

Measurement is a basic math concept for time, quantity, size, weight, and volume. Children learn these properties naturally through play. Think about the concepts learned while filling and spilling, nesting and stacking. Fill the pail. The pail is full. Spill the contents of the pail. The pail is empty. Full or empty, the pail has weight and dimensions. The pail is its lightest when empty, heaviest when full. Between empty and full, t volume and  weight vary.

Variety of Materials

Children learn sizes, order, and spatial relations as they explore, stack, and nest boxes and cups in a variety of materials, each with its own properties. Consider graduated boxes. These may be constructed of cardboard, wood, or molded plastic. Both plastic and cardboard will be lighter than wooden. Experience with a variety of nesting and stacking toys broadens children’s understanding of the properties of different materials and the ways those materials predict how the toys can be used.

Size, Order, and Spatial Relations

 Nesting Cylinders and Nesting Boxes give children an opportunity to experience nesting and stacking different shapes. Exploring both invites an experiential understanding of similarities and differences. Similarities include three sizes of each shape. Measuring confirms the dimensions of each and shows their corresponding heights. Weighing each shows their corresponding weights. During play children discover differences as well. The small cylinder will fit inside the medium box while the small box stays on top of the medium cylinder.

Learning Words

Such play enhances emerging cognitive, language, and mathematics skills. Learning words to describe the relative positions of the boxes and cylinders develops spatial awareness. And sets the stage for geometry. Think of the concepts being explored: small, medium, and large. Smaller and larger, shorter and taller. Lighter and heavier. Inside and outside. On top of, in the middle, on the bottom.

Wooden toys are classic and durable, apt to withstand rigorous play and be handed down to the next generation. That said, sturdy plastic nesting and stacking toys invite sand and water play that would be ill advised with their wooden counterparts.

Volume

Children explore volume as they fill and spill the 10 round, graduated, plastic baby stacking beakers. Pouring sand or water from a smaller into a larger beaker demonstrates differences in volume. The child readily discovers that what fills one beaker is too little or too much for another. Experimentation may lead to discovering how many of the smallest beakers are needed to fill the largest.

Developmental Age Matters

How far a child goes with such experimentation varies with developmental age and personal interest. The play and learning development of a one-year-old obviously differs from that of a three-year-old. Dropping the smallest beaker into a larger one, then dumping the smaller one out, over and over again, is appropriate beginning play. Learning simple concepts-empty and full, in and out, small and large-lays the foundation for more complex learning. Nesting and stacking require differentiating sizes and ordering the beakers to fit one inside the other or one atop the other. Repetition further solidifies concept acquisition and readies the child for taking the next step in learning mathematics.

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Rain, Rain Come Our Way

girl with rain boots jumping in puddle

After years of drought, we experienced the wettest January in more than a decade, and I celebrated every drop. Granted inclement weather poses challenges, from rain slick streets and highways to mud flows and flooding. Yet week after week of sunny skies during the winter creates severe water storages. Rainfall is absolutely essential.

Shelter In Place

People tend to stay indoors when anything wet begins falling from the sky. I readily admit to  savoring every opportunity to curl up with an engaging book and read and nap the day away. Some people watch favorite movies or channel surf until something interesting catches their eye. Others take pleasure in assembling pots of delicious homemade soup or baking favorite treats. Those passionate about a craft likely lose themselves in their latest project. Sooner than later, however, almost everyone comes down with cabin fever, feeling cooped up and restless.

Head for the Door

Who says we have to stay indoors? In fact, getting outside does wonders for what ails us. All we need is proper clothing for the conditions and a spirit of adventure. Dress yourself and the kids in waterproof boots, pants, and jackets, pull on gloves and a hat, and head out the door.

Splash in  Puddles

Walking in rain or snow is invigorating. Decades ago when our son Edward was four years old, we had 10 consecutive days of rain. And everyday we’d don our wet weather gear and take a walk. Always in search of puddles, he happily splashed his way around the neighborhood. Watching him delighted me.

Engage Your Senses

Engage your senses and experience the world around you. Breathe in the fresh, cold air. Open your mouth, stick out your tongue, and taste what’s falling. Feel it fall against your face. Watch as puddles form or powder covers the ground. The world looks altogether different with rain dripping off leaves and running in gutters or blanketed by fresh snow. Listen to the sound of rain falling and the silence of falling snow. Splash around in puddles. Make angels in the snow.

Savor Your Experiences

When you’ve had enough, go inside, shed your outer wear, and head to the kitchen for a steaming bowl of soup or cup of cocoa. Expand the rainy/snowy day experience. Talk about your exploits. What did each person enjoy most? What was the least fun? Write stories, draw pictures of what you saw and all you did. Savor the memories.

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Children Learn While Playing

Girl with green hoodie and bubbles

Play is essential. Children learn while playing, and we adults do irreparable damage to children when we ignore this truth. By play, I mean self-directed, open-ended exploration and discovery. When playing, children use of what’s available, decide what they want to do, and put their energy into doing it. When a challenge arises, they assess the situation, re-think possibilities, and go from there. During play they develop creativity, problem solving, and executive planning skills. Playing with others, they learn vital social skills: how to articulate their ideas, to listen to others, cooperate, compromise, respect.

PlayopolisToys has pinned article after article to our Pinterest board Children Learn While Playing offering research demonstrating the value of play and lamenting its decline. Among these pins is a reprint of a speech by child development specialist Nancy Carlson-Paige, the author of Taking Back Childhood. An educator with 30 + years experience teaching teachers, she sums up her dismay over current practices that leave children little time to experience the benefits of unstructured, “free play”  by saying, “…never in my wildest dreams could I have imagined that we would have to defend children’s right to play.” Yet we do.

In “How “twisted” early childhood education has become – from a child development expert,” Valerie Strauss, writing in The Washington Post, reprints the speech Carlson-Paige gave when accepting the prestigious Deborah Meier Hero in Education Award. Read what she had to say. If you’re a proponent, your passion for play will be validated.  If you’ve never given much thought to the issue, you’ll find plenty to think about.

Then settle in and find out what children learn from traditional open-ended play with blocks and bubbles, puzzles and play dough, and so much more.

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Fidget to Pay Attention

Distracted? Not Paying Attention?

Is there anyone alive who hasn’t been admonished to pay attention? We’re all prone to distraction. When we’re absentminded, daydreaming, or preoccupied, our minds are miles away. We’re not alert and observant, not on the ball. That can be deadly. Think of the consequences of texting while driving. Fortunately most inattentive moments are not that disastrous.

Even so, getting the most from any activity requires being engaged. Many children and adults aren’t wired to sit still and pay attention. They’re restless, as if they actually have ants in their pants. Their constant squirming prevents them from focusing. Impedes their learning. And ultimately causes disruption. Finding ways to cope is critical.

Counter Intuitive Solution

The solution is counter intuitive for those of us who recall teachers scolding doodlers for not paying attention. By doodling the student was actually self-regulating. Having discovered a way to calm her ants, the doodler could listen and learn.

That’s the key. Figuring out ways to convert restlessness into controlled movement enhances focus. The sensory input of the activity enables self-regulation. We can pay attention. But that’s only half of its benefit. The motion itself involves crossing the midline, the imaginary line bisecting the body from top to bottom. The two hemispheres of the brain are connected by the corpus callosum, the site of the largest concentration of white matter in the brain. This white matter facilitates communication between the hemispheres. What we learn crosses the midline and gets disseminated throughout the brain. Consequently learning improves.

Fidget Toys

Fidget toys are an easy way for kids and adults alike to redirect their restlessness into controlled movement. Think stress balls. Transferring the ball from hand to hand. Squeezing. Pressing down with the palm and rolling the ball back and forth on a flat surface. Flattening the ball. All these activities involve controlled movement and relieve stress, making paying attention easier.

Stress Balls for All Situations

Some stress balls are smooth, others spiky. Some light up. Still others make a sound. What works best depends on individual preference and the situation. Sensory seekers prefer the tactile input of a spiky ball. The most tactilely defensive may dislike the feel of all of the balls. In a classroom or a meeting, a light-up or sound ball could be a distraction to others. One is never enough. Best to have multiples and keep one handy in all the places you’ll likely to need one. What’s your favorite?

Smooth and squeezable, Bead Ball and DNA Ball are quiet stress balls. 

Glitter Bead Ball makes a soft crunching sound, reminiscent of walking on hard packed snow.

Light Up DNA Ball and Flashing Spiky Ball are all about flashing light. Light Up DNA is smooth, soft, and squeezable. Flashing Spiky features soft spikes and flashes when bounced or whacked against a flat surface.

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How Play Increases Concentration and Focus

What’s the attention span of a goldfish? What’s yours? According to a Microsoft study, a goldfish averages nine seconds, one second longer than the average human. Not so long ago – at the turn of this century – the average human attention span was 12 seconds. Not long, but longer than a goldfish. Our waning ability to concentrate causes problems for children and adults alike. When we’re inattentive, our productivity suffers: tasks take longer, we make more mistakes, become frustrated and stressed out. What are we to do?

Play more. While engaged in play we naturally pay attention. We’re concentrating on an activity that gives us pleasure. We’re in the present, oblivious to time, not easily distracted. Relaxed and confident, we’re apt to take glitches in stride, assess the situation, and apply our creativity to finding solutions.

Play is recreation, an activity we choose to do for the pleasure we derive from doing it. Play relieves stress, giving us a fresh perspective and  renewed focus. Play is essential for everyone, at every age. Playing games is a traditional pastime adults and children can enjoy together.

Find It, a series of thematic games designed for players six years old and up, requires players to search for objects hidden among plastic pellets in a cylinder. These intergenerational “contained adventures” both require and reward concentration and focus.

The top cap of each game lists the objects hidden in the cylinder. An enclosed guide assigns a point value to each object: one point for the easiest to find and 20 for the often elusive penny hidden inside every Find It.

A pack of double-sided playing cards expands play possibilities for two or more players. Finding objects is the aim of the game, whether played alone or with others, cooperatively or competitively.

Find It game about mythical creaturesConsider Mythical Creatures with 40 hidden objects. What better way for a child to learn about folk tales and supernatural beings from around the world than with a favorite adult who might know what’s what? Some objects will be familiar, but expect to be baffled and have to search for answers.

Otherwise, when you see the word hippocampus, you might think of the region of our brain thought responsible for emotions and memory. That’s true, but you’re looking for a fish-tailed horse from Greek Mythology. The fun is in finding out who’s who and what’s what. While concentrating on finding out about the Jersey Devil, a kraken, or a troll or taking note of the similarities and differences between a hippocampus and a manticore, you’ll feel more relaxed.

Play is essential. We learn while playing. Play more. Stress less. Pay attention. Concentrate. Focus. Thrive.

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Balls, Blocks, and Babies

There are a multitude of distinctions for babies to discover between and among balls and blocks. What’s likely their first impression? Balls are round, blocks square? I suspect experiential learning of the difference between roundness and squareness marks the beginning of awareness. When a six month old grasps a ball between the palms of her hands and senses its roundness, she internalizes this basic attribute. Taking hold of a block, she’ll explore, with her senses, and internalize its squareness. Although lacking words to describe these concepts, she’s taking in and processing information.

stacks of wooden nursery rhyme blocksThat she uses multiple senses is important. Multi-sensory exploration leads not only to discovering more about blocks and but also to developing emerging skills. Take mouthing. Grasping and purposefully bringing a block to her mouth takes coordination. In doing so, she’s developing skills that will eventually allow her to successfully feed herself.

If the blocks are wooden, she’ll likely bang a couple together delighting in the sound. Repeatedly. Baby has discovered her actions cause reactions, and like any scientist, she needs to replicate her results. As she gains muscle control, she may vary the force of her banging and discover she can create a range of sounds, thereby developing sound discrimination.

Baby transfers both balls and blocks from one hand to the other and in stretching to reach for a ball or put down and pick up blocks, she is likely to cross her midline, an imaginary line down the center of her body. Such spontaneous crossing of the midline develops fine motor skills that strengthen hand dominance. Writing and reading both depend upon our ability to reach an arm and a leg across the center of our body to the opposite side. Crossing the midline develops our ability to track from left to right, a critical skill for reading and writing.

Just as baby delights in filling and spilling activities with balls, when she drops blocks, she’ll likely look for them on the floor. Learning object permanence, the concept that an object exists even though we cannot see it, can evolve from playing hide-and-seek while looking for a dropped block. Someone hides a block under a cover and prompts baby in a search for the missing block. Following the hints shows emerging cognitive and language skills.

We learn while playing. Play is essential. For all ages. Become an official citizen of play.

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Observing Play Preferences

Play, at its best, is self-directed. As a result, children develop personal preferences while engaging in a variety of different types of play. Observing children engaged in spontaneous play allows us to learn what they like to do. Knowing this, we can provide opportunities and props that support and enrich their preferred play experiences and show that we’re paying attention and respecting their choices.

Because children develop at different paces and are drawn to different activities, kiddos of the same age display markedly different competencies even when all are developing within typical ranges. One 12 month old may be so fascinated by the different ways to open and close the fasteners on a lock box that he has no interest in walking. Another is on his feet happily exploring his environment from a new perspective.

The first child’s passion requires figuring out how the locks work and using his fingers and hands. Mastery incorporates cognitive, problem solving, and small motor skills, perhaps beyond developmental expectations. The second delights in having gotten the hang of walking and focuses on learning more ways to move his body. Mastery requires developing gross motor skills – balance, coordination, and strength. When learning anything new, our focus and concentration are on the task at hand. Mastery requires trial and error, repetition, and time to process what we’re learning.  Once we’ve achieved one goal, we’re ready for another. Personal needs and preferences often dictate what we choose.

Through observation, we also learn what a child shies away from, and this gives us valuable insights too. Observing your child when she’s playing spontaneously is the best way to learn her play preferences. Take note of what she does most often and what toys or other objects she incorporates into her play.

Does she enjoy artistic pursuits, music, or dance? Fantasy? Imaginative Play? Is she drawn to activities that involve analytical thinking – sorting, classifying, categorizing? Does “puzzling” over spatial relationships intrigue her? What about building with blocks? Does she prefer fine motor activities or gross motor ones? Does she like sensory play?

Observing a child at play not only gives us insights into her preferences, but it also reminds us that play is essential. Children learn while playing. The more children engage in self-directed play, the more experiential learning they do. Kids naturally learn how to learn through play. So encourage children to play.

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Make Play a Priority

Play is universal. Spontaneous. Joyful. Stress relieving. Any activity we do for pleasure. Whether we’re engaged in a solitary pursuit or interacting with others, as long as we’re enjoying ourselves, we’re playing.

Play is essential to our well being. When doing something pleasurable, we relax. As we de-stress, we loosen up, slow down, unwind. We can actually feel our muscles relax, our minds calm. Going with the flow invites new ways of thinking and gives us fresh perspectives. We become centered, more confident, more creative, more positive.

When we’re playing, we’re enjoying ourselves. What’s enjoyable to one person, of course, can be anything but to another. Some people are happiest and at their most relaxed baking. Others can’t believe that’s even possible. Children have play preferences too. Some adore finger painting, and getting up to their elbows in paint is pure joy. Others want nothing to do with anything that feels so “yucky.” That reminds me of the adage “one person’s passion is another’s poison.” That translates as what’s fun is play, what isn’t, isn’t. Fun makes an activity play.

For adults, our main challenge is likely carving out time to play. Everyone is busy, and often we feel we don’t have the time. When we allow ourselves to play, we realize what we’ve been missing. We haven’t been giving ourselves permission to pursue joy often enough. Once we make play a priority, we quickly learn how enriching the experience is.

Sometimes children need encouragement to engage in active play – the child directed, open-ended engagement with objects, people, or pets that is essential to learning. The lure of electronic devices has reduced the time children spend in such traditional play. Balance is essential and moderation the key.

In active play children develop skills, from fine and gross motor to cognitive, communication, and social. They strategize, experiment, and adjust their thinking in response to their observations and experiences. While playing with others, they’re communicating and collaborating, learning to negotiate and compromise. And they’re enjoying the process. That’s the power of play. Children learn while playing.

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