Posted on Leave a comment

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.

PlayopolisToys – for the diverse needs of the citizens of play

Posted on Leave a comment

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.

 PlayopolisToys – for the diverse needs of the citizens of play

 

 

 

 

 

 

 

 

 

 

Posted on Leave a comment

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.

PlayopolisToys – for the diverse needs of the citizens of play

Posted on Leave a comment

Developing Math Awareness and So Much More

Children writing equation solution on chalkboard

April is Mathematics and Statistics Awareness Month. That got me to thinking about ways children learn mathematical concepts during play and through daily activities, observations, and conversations. Consider the infant gazing intently at the face of the person cuddling her. The human face is intriguing, each unique yet sharing similar features in a particular order. Thus begins an awareness of patterns, of similarities and differences, both precursors to language and mathematics.

Children are naturally curious. As adults we encourage their learning when we supply words that describe their daily experiences and set the stage for cognitive and language development. Washing up is a perfect time to point out and name features—ears, nose, fingers, toes. Think of nursery rhymes that reenforce this information. Remember Mother Goose? Now’s the time for playing with toes and saying,

This little piggy went to market, 

This little piggy stayed home, 

This little piggy ate roast beef, 

This little piggy had none. 

This little piggy went…Wee, wee, wee, all the way home!

 Of course, that naturally leads to a comment on how many feet and how many toes the child has. This rhyme becomes an introduction to the concept of one to one correspondence, key to understanding the meaning of numbers. One foot, five toes, two feet, 10 toes. For numbers to have meaning, initially the numbers need to correspond to concrete objects. Abstract thinking comes later.
Dressing invites talking about clothes and the process of putting on and taking off. The process involves sorting out what goes on first, then next. That’s sequential order, an important executive skill involved in everything from independent dressing to reading and math. Chatting about the sequence helps toddlers understand its rationale. Of course, there’s some leeway in how we get dressed, but why do we put socks on our feet before sticking our feet in our shoes? You know, but someone just learning might not.
This is also a good time to talk about color, a distinguishing feature of any garment. Knowing the names of colors makes communicating easier. So, if the weather requires a jacket and the child has two, one red, another blue, offer a choice. Identifying the jackets by color, ask her whether she wants to wear the red or the blue one. She may not identify the one she wants by color, but she’ll begin to associate the colors with the words that describe them. Through such experiences children learn the value of language.

Children learn from interacting with people and objects in their environment. Quality toys invite exploration and open-ended play that build skills. Moving forward, we’ll explore how, beginning with math awareness.

 PlayopolisToys – for the diverse needs of the citizens of play

 

 

 

 

 

 
 
 

Posted on Leave a comment

What Children Learn from Water Play

Where would children be without water play? Water provides opportunities galore for playing and learning, and in the height of summer, what child doesn’t enjoy cooling off by running through sprinklers and playing in a splash pool?

Flooding sand with water creates another realm of play as children scoop, mold and sculpt the wet sand. Digging and filling channels with water expand the experience as children float objects in the canal, discover what floats – a leaf – and what sinks – an acorn – and figure out why. As the sand absorbs the water and the channels run dry, children discover more about the properties of sand and water. That’s experiential learning at its best.

Filling and pouring, measuring and mixing, using containers of different shapes, sizes, heights and diameters lead to a developmental milestone known as conservation of liquids. This means that a child understands that a specific volume of a liquid is the same whenever the shape, size, height or diameter of the container into which it is poured.

Consider this classic conversion experiment. An adult fills two short, fat beakers with an equal volume of colored liquid and asks a child to verify that the two beakers contain exactly the same amount of the liquid. Once the child and adult agree, the adult pours the contents from one beaker into a tall, narrow one and asks the child if the two beakers contain the same or different amounts. A child understanding the conservation of  liquids  knows the volume remains the same.  One who does not will insist that the taller beaker holds more. Why? Because it’s taller, an opinion based on external appearance. Typically children master this concept between five and seven years old.

More ways to play and learn with water:

add food coloring or bio-colors and explore color mixing

experiment with freezing and thawing to observe how water expands when frozen and contracts as it melts

add leaves, acorns, twigs to water, freeze and observe how being frozen changes the appearance of the findings inside the ice

 PlayopolisToys – for the diverse needs of the citizens of play