cardinality – Early Math Counts https://earlymathcounts.org Laying the foundation for a lifetime of achievement Wed, 31 May 2023 12:00:02 +0000 en-US hourly 1 183791774 Fingers, Fingers, 1-2-3! https://earlymathcounts.org/fingers-fingers-123/ https://earlymathcounts.org/fingers-fingers-123/#comments Thu, 01 Jun 2023 12:00:41 +0000 https://earlymathcounts.org/?p=155374  

“Fingers, fingers, 1-2-3…how many fingers do you see?”  

We are playing one of our favorite finger games. I hide one hand behind my back. When I bring it forward, I hold up some fingers and the children shout out the number of fingers that they see.

“Three!” shout the friends playing the game.

Finger games can be played anywhere at any time because our fingers are always, well…handy! Besides, there’s a lot of math to be learned in those little fingers. Fostering a love of math in children begins with building a basic understanding of numbers.

I watch as two-year-old Jade repeatedly looks at his fingers and then back at mine as he attempts to duplicate my patterns. Children learn through their senses, and Jade is visually and physically working his way through an early math skill. He is also engaging in a sensory-motor experience that helps build abstract thinking skills.

When children engage in finger play, sing counting songs and play counting games, they are building a strong number sense. Number sense is a person’s ability to understand key math concepts such as quantities and the numbers that represent those quantities, as well as concepts such as more or less. Children with good number sense can think flexibly and fluently about numbers.

While using his fingers, Jade can feel and see the difference between the numbers 2 and 4. This developmentally appropriate math game is helping Jade connect a quantity to its numeric name—and his vocabulary is growing as he chants along with the rhyme.

Compelling new studies are also revealing how hands literally “help the brain think.” According to the website Science Translated—which educates students and the public about ongoing scientific research in a simple, jargon-free way—”Children clearly ‘think’ with their hands while learning to count.”

Neuroscientists and educators agree: Children who learn to use their fingers as a mathematical tool in the early years experience more success in math than those who don’t.

When children use their fingers to count, they are strengthening their number knowledge and their ability to visualize numbers in their minds. Counting is more complex than simply memorizing and reciting number words. Children need to understand the counting sequence, as well as one-to-one correspondence, cardinality and subitizing.

  • Counting sequence: Counting involves using the same sequence each time, starting with one.
  • One-to-One Correspondence: Exactly one number from the counting sequence is assigned to each object in the collection.
  • Cardinality: The last number assigned to an object when counting the collection indicates the total quantity of objects in the collection.
  • Subitizing: The ability to recognize a small group of objects without counting.

Watching and listening to children’s counting will help you see what they know and what they still need to learn. Once the children have a strong understanding of the numbers up to five, try adding your other hand to the game. For example, I show two fingers on my right hand and three fingers on my left hand. The children have to add the two sets of numbers to give me a total number.

“1- 2-3, let me see…the number two!”

We also use our fingers to play with shadows. Using the sun as a light source, I call out a number. The children then hold up the appropriate number of fingers to represent that number, casting “finger shadows” on a wall or on the sidewalk. 

This is a great way to help children build their number sense. It allows the children to work on:

  • Finger-isolation activities such as pointing with the index finger, counting out the fingers on their hands or wiggling all of their fingers individually
  • Thumb-opposition activities such as touching the thumb to each finger to build strength and dexterity for pencil-holding and cutting with scissors

These are all good reasons to add some finger play to your days! Keep it fun, keep it spontaneous and keep it simple. What looks like child’s play will help build a strong foundation for later math learning. You can count on that!

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Baby, It’s Cold Outside https://earlymathcounts.org/baby-its-cold-outside/ https://earlymathcounts.org/baby-its-cold-outside/#comments Wed, 15 Dec 2021 12:15:14 +0000 http://earlymathcounts.org/?p=153966

“LOOK! We have icicles!”

“Can I have one?  I need one!”

On this brisk winter morning—much to the children’s delight—nature has given us the gift of icicles. The children’s fascination with these frozen treasures leads to an abundance of “teachable moments” as we engage in some STEM learning while getting some fresh air and exercise.

Soon we are counting, sorting and measuring the icicles. I can practically see those little brain synapses firing as the children use their senses to investigate the properties of the icicles and revel in the joy of being able to choose, hold and taste their STEM lesson for the day.

“My icicle is longer than yours!”

“I like the little icicles! They fit in my mouth better!”

“I like the thick ones, they last a long time! Look how fat mine is!” 

When I hear my students discussing size, comparing attributes and sharing their math vocabulary with their friends, my heart just soars. Mathematical language is one of the strongest predictors of children’s early mathematical success. Whenever children discuss relative concepts, they are doing math!

Aww! I dropped mine and now it is in little pieces!” Janelle wails, holding back tears.

“They still taste good!  Now you just have lots of icicles!” says the ever-optimistic Claire. “Before you had one, but now you have more! You have 1, 2, 3, 4, 5!  You have five icicles!”  

Claire touches each icicle as she counts. The ability to count in sequence and use one-to-one correspondence to determine the number in a set is known as rational counting.

Janelle has the ability to rote count, reciting the sequence in the correct order without an understanding of one-to-one correspondence or the concept of cardinality (the number of elements in a set). “I do have five!” she shouts.

“Look, I can drop mine and it doesn’t break!” yells Owen as he drops the thickest icicle to the sidewalk, only to have a few pieces chip away.

It is difficult to ask children to compare quantities if they don’t know what “more” or “less” means. If they can understand “before” and “after,” they are more likely to know, or be able to understand, what number comes after four. When children learn this language in a math context, they are ready to move on to more advanced mathematical concepts. We are building our math foundation!

“How did you make these icicles? We don’t have them at my house,” asks Rowan as she chomps on her icicle. 

“I know!” chirps Robyn.When the sun warms up the snow on the roof it melts and turns the snow into water and the water starts dripping and then it gets cold again and makes an icicle! “

We take a long look at the ice melting off of the neighborhood roofs and other inclines and see that the dripping has indeed created icicles. We discuss how warm temperatures melt the snow and that is why our clothes often get wet, even when the snow is frozen solid on the ground. Now we have science! I love it when our play leads us right down the path to new STEM experiences and investigations.

“Oh, when our hands are warm in our mittens, it melts the snow? I never knew that!” Logan has processed the information in a way that many of his younger friends don’t have the brain development to do. He seems quite astounded by this realization. Together, we hypothesize which icicles will melt faster or whose icicle will get eaten faster.

Then we swap out our wet mittens for dry ones and hunt for more ice to expand our STEM  vocabulary.

Discussions about the weather are often rote and meaningless in early childhood classrooms. Classroom activities that involve calendars and weather patterns can be boring for young children because they are removed from the actual seasons and weather events.

But bringing the children outside to experience the weather firsthand or bringing the snow inside to be investigated on a water table is interesting. Involving the children in hands-on investigations is a much better way to teach concepts such as “winter” or “cold” than directing a child to walk over to a window and report that “It is snowing outside.”

During this busy holiday season, give yourself and your students a chance to escape the heated classroom and venture into the great outdoors to breathe in some fresh air and find your curriculum in the natural world.

I promise you that this approach will lead to far more STEM learning than talking about the weather during circle time!

 

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