The Five Senses of Math

posted by Diann Gano

We spend a lot of time outdoors. Playing. That play involves math in such natural ways that it is easy to overlook how often math comes into our lives. Research has found that early math proficiency is a better predictor of future academic success, high school graduation and college attendance than any other childhood skill. (National Governors’ Association, Unlocking Young Children’s Potential: Governors’ Role in Strengthening Early Mathematics Learning

So, here at Under the Ginkgo Tree, we encourage that investigation and provide materials that support children’s development of math concepts. Outdoors, the process for mastering the fundamentals of math is truly enhanced in a holistic and inviting environment. Come see how we create these opportunities using all five senses for all types of learners.

SIGHTexamining a tree trunk

Regardless of the season, we often spend time seeing how tall or small our friends are using resources that are available to us. Sometimes we use tape measures, but often we have other ideas.

Adding magnifying glasses, kaleidoscopes, and binoculars will slow your children down. They will look closer, longer, and think harder. Remember, we are giving them lots of time to investigate and explore and enjoy their childhood. Add these to your play space!

measuring with apples

 

 

 

 

mesauring with carrots

 

 

 

 

 

 

 

magnifying glass

 

 

 

 

 

dandelionsHOW MANY DANDELIONS?

Right! Three! Did you count? No, you subitized! We love to subitize. Subitzing is seeing a small amount of objects and knowing the number without counting. Playing with dice, you roll a six and without counting the 6 pips, you know it is six. We often play this game with fingers. We place both hands behind our back and then bring forward one hand with a few fingers showing. As they get better at this, we make it faster, or change the finger arrangement, or add both hands. We also work with subitizing outdoors with any given object. Kids love this game and I encourage you to play it often. Restaurants, long car rides, or waiting rooms are all great places to subitize! If you have fingers, and a bored child, subitize!

TASTE

cutting vegetables cutting vegetables 1 snacks

Well, this one is almost too easy. If you put six cookies in front of three children and tell them to figure it out…they will. F A I R is a favorite math word that we hear around here. Everyone has to have EQUAL amounts of everything! Every meal we serve has some sort of math discussion available.

I invited the four-year-olds to help set up lunch. When they asked if they could cut the cucumbers, we discovered lots of investigation on size, direction, more, less, and equal.

When it came time to put out the fruits and vegetables, they created sets and counted out tomatoes, cut sandwiches in half. We had a math buzz going on!

Cooking is a great opportunity to bring in math vocabulary and concepts. When cooking with children, we always try to have enough bowls, utensils and, of course eggs, for each child to make their own portion. Think about it, if you watch your friend whip up her award-winning recipe, it’s just not the same as doing it side by side with your own version. This also offers great opportunities for mentoring and scaffolding with their peers on tricks for measuring and cracking eggs. It may not seem like math, but it is. If your body and brain don’t have the energy to deal with the egg mess on any given day, we have been known to cheat with the infants and cracked the egg into the measuring cup. That counts as an egg turn for anyone not old enough to roll her eyes at the thought of it. (Usually your four- year old.)snacks

SMELLsmell dandelion holding an iris

Those little noses often lead us to food. We routinely have

discussions about how many raisins or chocolate chips are in our cookies. We also like to smell in gardens and parks. Did you know that there is a math pattern in nature called Fibonacci? Some refer to Fibonacci as nature’s number system. From the pattern of florets on a flower to the bracts of a pine cone or the leaf arrangements in plants, the same number pattern appears over and over. The basic pattern is 1,1, 2, 3, 5, 8, 13, 21, 34… The next number is found by adding up the two numbers before it. It forms a spiral. This is a bit complex for most of the young learners in our program, but we talk about it and the spirals that we see in pineapples, and pinecones and flowers.

bunch of flowers

We often count the number of petals on our flowers. Last summer we planted perennials to our play space and included a number of flowers that include this Fibonacci pattern. Cala lilies have one pedal; euphorbia have two; triilium and some iris have 3 petals; buttercups and columbine have 5; bloodroot have 8, black-eyed Susan’s have 13; shasta daisies have 21 whereas other daisies can be found with 34, 55 or even 89 petals. Isn’t that crazy fun?

spring flowers

 

baby at fence baby ringing the bellSOUND

We live a block from a college campus and the bell tower. So every hour on the hour we have some counting sound opportunity in our own backyard. Music is an easy way to add math to your outdoor play space.

We have bells placed throughout our play area. We often have obstacle courses that include ringing a bell or drumming on a drum. Music is a big part of our lives. Singing songs, counting rhymes and fingerplays combine music and math. Really is there any better place for those loud drums, bells, tambourines and maracas? What were we thinking? These are outdoor toys!

 

 

 

bells on deck
baby with tamborine children with musical instruments

 

 

 

TOUCHacorns child holding an acorn

When you give children real materials to touch and smell and feel, the learning is deeper and more authentic. There is a major difference between touching real apples and moving them from basket to basket, than counting apples on a worksheet. Looking at stripes and circles on a page is not the same as touching and understanding that each rock has stripes or circle textures or has six shades of green. It makes sense to them. They control it. They aren’t rushed to move on to the next box on the worksheet. Give them real materials.

We talk about blocks and rocks often in our program. Those two things create an unbelievable amount of building. Building is math. We spend hours and hours building things that we may not ever even play in or with. We have spent days making forts. Sometimes, we don’t ever actually play IN them. We just build them. We build zoos, and fairy homes and squirrel traps. It is the building that is the fun, the creativity, and the play. Give your children time to touch, and think and process, and arrange and rearrange. It’s all good.stack of rocks

We also play games where one child plays a rhythm and the other needs to repeat it. There’s very often pattern play going on with this. For many children that rhythm and counting go hand in hand. When we follow singing commands to go in or out, or up and down, around and through, those build spatial awareness and reasoning skills that are important skills for geometry. Everyone is happy when we have music in our lives. Make your own or fire up Pandora!

Have fun this week noticing how often math is in your child’s life. It will make you smile and give you peace to know that you are doing just fine as a parent and an educator. Keep creating math environments and playing with your kids. It’s all quite simple. Put the worksheets away. It will come when their brain development is ready and it is relevant to them. Until then, just watch, listen and smell the learning coming their way!

 

 

 

 

Setting the Stage for Outdoor Math Experiences

posted by Diann Gano

rocks and shellsAs I look around me I see busy, happy children. Avery, Linnea and Anderson are busy seeing how high they can stack their rocks. Maya and Noa are near the sandbox creating a tea party for fairies, while Rowan and Parker are creating homes and meals for the squirrels over in the rain garden. It is calm. Everyone is happy and learning. We call this a play buzz.

When I stop and take a closer look, I recognize that not only is everyone happily playing, they are all working on math. M A T H! Did you know that nearly half of all children’s play involves math? (Seo and Ginsburg, 2004). The latest research also shows that early math skills are a better predictor of academic success than early reading skills! So here at the Gingko Tree, we are creating even more opportunities to introduce math concepts and problem-solving through play. As a family childcare with a Nature Explore Certified Outdoor Classroom, we spend a great majority of our time outdoors.

The environment IS our curriculum. When we add natural elements to their areas of play, it leads to playing in math-rich environments while creating and problem-solving in very deep and complex ways. As more and more classrooms and families are returning to the outdoors, simply giving our children the gift of time will lead them to mathematical play. It comes very easily to them without worksheets or number cards or dreaded memorization that may not be developmentally correct for where their brain development is at this time. As spring arrives, take this opportunity to create math-rich environments in your own backyard or play space. The only thing you can do wrong is not to do it! Bringing math into your outdoor or indoor environment is easy and even better it’s often free! In outdoor classrooms or family backyards, educators and parents are learning the beauty of loose parts in children’s learning and play experiences.

Architect Simon Nicholson, first proposed loose parts back in the 1970’s. Nicholson believed that we are all creative and that loose parts in our environment increase and empower that freedom to create. Loose parts are materials that can be moved, carried, combined, redesigned, lined up and taken apart and put back together in multiple ways. They are materials with no specific set of directions that can be used alone or combined with other materials. (Kabel, 2010)

We like to think of loose parts as shells, rocks, sticks, acorns, feathers, pinecones, flowers, flower petals, material, water, sand, dirt, moss, leaves, bark, rocks, pebbles, pine needles, seeds and else whatever may be native to your region. We also use blocks, people, animals and other manipulatives. Loose parts can range from dramatic play props to play cars, pots, pans, and pouring devices. If your environment doesn’t already contain those things, bring it in. If you have those, take them out! We rarely take walks without bringing home all kinds of the loose parts or “treasures” listed above. Use what you have. If it’s little, and your child hoards them in containers just to carry around and create “things” with; your child is playing with loose parts! Take advantage of what you have around you. Those are your tools for setting up a math rich environment. Let’s get started!

Storage is an important part of loose parts because it gives a sense of order and allows children access and knowing where those materials are. Indoors, I try to keep our natural loose parts materials in wood bowls, sturdy baskets, or other natural containers that look nice and add calmness to my environment. Outdoors we have used galvanized buckets, plant containers, crates, or any container source that we have nearby. Use your imagination. I can tell you from practice, the happier the container makes you, the more relaxed you will be with loose parts. Also, be aware that buckets and baskets may get dumped from what you are “storing” to become a piece of their loose parts puzzle. That’s a struggle for me. Usually, it means I need more containers for them to carry around or create with. The beauty of loose parts is that they can be moved, and so the child has power to create new adventures every day. Storage and carrying pieces are an important piece of the puzzle.

buckets of shells

I recycled our spring planting containers. These worked out well, and were free! Win, win! We have these next to our sandbox. They are full of rocks, shells, bark, and birch branches today. We change our materials often. By “locking” these in under the fence, it kept them permanently placed without getting dumped.

buckets of rocks and shells

We have galvanized buckets in a wire window box. You can find galvanized buckets at IKEA, Farm Stores, and Amazon.

As more and more of your outdoors space becomes filled with natural materials and less plastic and branded play toys, you will see your child’s play change. It will become deeper, more focused and more creative. Trust me. It’s amazing.

Now we can bring in the materials! Do you have rocks nearby? Take a walk. You will find some. We have found some very pretty river rocks at the Dollar Tree. If you take a vacation, the rocks in different regions are often different colors, shapes, and textures. Add those to your collection. We love rocks and they often come home in pockets and backpacks.

rocks and feet

stack of rocks

We play with rocks a lot. They line them up; they stack them up. They sort them by color, size, and texture. All of that is early math. They use them for food and phones and building. They rarely throw them. Honest. Call them your math rocks. There are throwing rocks and math rocks, and we only have math rocks.

Find some shells. Goodwill, Salvation Army, and garage sales have been our gold mines for shells. Any found on your own are even better because there is a story and memory behind it.

picking shells

Bring in small tree branch slices, driftwood, bark or small twigs. We’ve used all of them. Pinecones, acorns, buckeyes will all add new discoveries and wonder to your math center. Children are full of math vocabulary, more or less, bigger or smaller, fair or equal. Loose parts will add this vocabulary into your child’s world on a daily basis.bucket of wood slices pile of wood slices

 

 

squirrel trap

It’s a squirrel trap. You already knew that, didn’t you? It’s also logical thinking, creative problem solving, measuring length and size, comparing and estimation. Whew! That’s a lot of math in a squirrel trap built by a group of kids under the age of 5. This is where that gift of long, uninterrupted time is so important. Fifteen-minute recesses are not enough. Give them time.

If you want to learn more or see great examples of loose parts, I highly recommend looking at Dr. Carla Gull’s Facebook page, Loose Parts Play. She has great ideas on there, and contributors from around the world!

We love, love our mancala boards. mancalaWe use them with shells, stones, seeds, and pretty glitter marbled stones. You could use egg cartons or ice-cube trays, also. These are perfect for one to one correlation for teaching numeration. You won’t need to mention that of course. They will play with them where they are developmentally at that moment. It will all come. You are setting the stage to make it come so very easily, through play.

geoboardsWe also use our geoboards a lot. Besides all the geometric shape experiences they create, this also works the small muscle development and fine motor skills they will need when it is time to start writing. It may not look like math to them, but we know better!

This is a “family” of leaves. It started innocently enough with a Daddy leaf and the play took off from there. Children are exposed to math vocabulary anytime size or comparison is involved. All these experiences are building blocks for early math development.

When four-year-old Gabe, discovered that the oak leaf was torn like the number three, it set off a flurry of creating numbers. We captured it on clear contact paper to admire and share with parents.

feathers

Math is all around us. Creating a math environment into your children’s play assures your child of future academic success. Including loose parts into your play area will create a learning environment that your child will be drawn to effortlessly. They will be learning. If you thought you needed worksheets or flashcards or screen time to prepare your child for school, I hope you will give this a try. You will be excited about the learning your child is experiencing. You will see it. They won’t. They will think they are playing. Which is just what we want our children to be doing. If you build it, they will learn. It will be fun for both of you! Go play!leaves in size order numbers

Symmetry in Nature

posted by Lindsay Maldonado

Despite being an urban metropolis, Chicago is surprisingly a great city for nature lovers. We are lucky enough to have access to some incredible natural spaces, both inside and outdoors. Two of my go-to nature spots in the winter are the Peggy Notebaert Nature Museum and the Garfield Park Conservatory. It’s been a mild winter, but when the temperatures start to dip, we all seek the refuge of somewhere warm and humid – and, these two ‘museums’ are the place to go for nature. And, nature just happens to be full of opportunities to talk about math!

One of the smaller museums in Chicago, the Nature Museum brings together a living collection of animals with a collection of animals that were once alive. Its most notable exhibit, the Judy Istock Butterfly Haven, immerses you in a tropical paradise surrounded by nearly 1,000 butterflies (and some moths too). A true haven for Chicagoans in the winter, this exhibit offers the perfect opportunity to observe math in nature. Specifically, butterflies give us the chance to explore symmetry. Exploring symmetry helps young children recognize patterns and hone their observation skills. There are many ways an object can be symmetrical. The simplest form of symmetry is bilateral or mirror symmetry – and, butterflies are a perfect example of mirror symmetry. Take a look at the butterfly pictures below. Can you see the symmetry? What makes them symmetrical?

Buckeye butterfly

longwing butterfly

atlas mothMirror symmetry is seen when one half of an object (or insect in this case) is the mirror image of the other half. If we held a mirror at the line of symmetry we would see the same image reflected on the mirror (it is not recommended to hold a mirror to a butterfly, unless of course, you have a butterfly that was once alive).

mirror symmtery

In the case of butterflies, the line of symmetry runs along the body of the butterfly. It runs directly between the butterfly’s antenna, lengthwise along its head, thorax, and abdomen (in case, you want to add some science content too).

longwing butterfly line of symmterySymmetry in nature is fairly easy to find. Leaves are another great example of mirror symmetry.

FernsThis picture of the fern room at the Garfield Park Conservatory provides unlimited opportunities to observe mirror symmetry. Let’s not forget about the other kinds of symmetry that exist though! It’s hard to pick my favorite place at the conservatory but my family really loves the desert house. And, what do you know? The desert house is a great place to explore a different kind of symmetry: radial symmetry! Objects that have radial symmetry can be equally divided like a pie. Do you see the radial symmetry in the pictures below?

succulent

succulent radial

 

 

 

 

 

 

 

 

You can continue to explore symmetry in the classroom with these activities.

Thanks for exploring museums with me this month! There are so many more museums in Chicago that we couldn’t have possibly visited them all for these posts, but with all of these museums there are even more opportunities to apply the big ideas of mathematics. With a deeper, more focused look you can find math anywhere. Next time you visit a museum, look around and ask yourself, what big ideas of mathematics can I find here? Now that you’re thinking in this way, I bet you’ll find math ideas with ease and you won’t be able to un-see them.

 

 

Pattern walk at the Field Museum

posted by Lindsay Maldonado

Today I visited the Field Museum of Natural History. Another one of my favorite Chicago museums. The Field Museum houses thousands of artifacts from dinosaur bones to pottery and clothing from ancient civilizations. Again you may be thinking, math? Isn’t this a natural history museum? With thousands of artifacts on display, math is easy to find. Just a quick walk through the halls brings you upon any number of dioramas with countless animals of all shapes and sizes.

It’s easy to count animals (Big Idea: Counting) or classify animals (Big Idea: Sets) by their varying attributes like size or color – but when you start to delve deeper into the exhibit halls you’ll come across other kinds of artifacts. There are cases upon cases of decorative clothing and art from cultures near and far. In my recent visit I happened upon the Hall of Native North Americans exhibit.

Native North American exhibit

At first you’ll be enamored by the craftsmanship. You’ll wonder how long it must have taken to create something so beautiful and intricate. You’ll wonder why Native North Americans wore such adornments but then you’ll notice something else; you’ll notice the shapes and patterns woven together or threaded with beads that make up each artifact. There are circles, squares, rectangles, diamonds, and triangles intricately designed to create simple and complex patterns. We see color patterns too.

Patterns exist in the world, as we see here, and also in mathematics. Through patterns, we find sequences bound by a rule (e.g., a chess board is made up of black and white squares, with a predictable black-white, black-white or AB, AB pattern) that brings predictability and allows us to generalize. Hence, we can predict, with a good amount of certainty, what comes next. Let’s look at a couple of these objects. What patterns can you find?

 

beaded ornaments

beaded bagThe beaded bag has blue and orange flowers arranged in a simple ABAB pattern. Each row alternates orange flower, blue flower, orange flower, blue flower, etc. It’s easy to predict what comes next. We see a similar ABAB pattern in the beaded ornaments (i.e., yellow blue, yellow blue). One big idea of patterns is just this; the same pattern can come in different forms.

We also see more complex patterns when you look more closely at shapes. Can you see the pattern?

 

decorative artPatterns are found in many places and children are particularly attuned to patterns. As we observed, patterns offer a sense of predictability, which children desire (e.g., we create routines for children to add order and predictability to their lives). When children understand the rule of a pattern they are able to extend that thinking to other situations.

Keep talking about patterns in the classroom! You can search for more activities about patterns here.

Museums and Math: The Perfect Pair

posted by Lindsay Maldonado

The shedd aquariumMuseums are likely the most common setting for informal learning. Unlike formal learning (i.e., traditional classroom learning), informal learning is voluntary, unstructured, and learner-led. These settings provide a variety of learning experiences for a diverse group of learners. Museums offer opportunities to be hands-on with objects and even live animals. Museum visitors can observe objects and animals, engage with exhibits, participate in programs, and listen to chats and presentations. Museums afford visitors with flexibility and choice, offering a more customizable learning experience. This is particularly important when you consider the variability of learning styles within one classroom or one family. The ability to create an experience that suits the needs of many makes museums an ideal learning setting.

But you might be asking, museums and math? You might be thinking; how do I teach children math at a museum? There are science museums, art museums, natural history museums – but, there are no math museums. Well, there is one museum in New York that is dedicated to math but in general, math museums are hard to come by so it’s a good thing that math is all around us — all the time, no matter the setting.

Growing up in Chicago I remember visiting Shedd Aquarium often as a child. I would stand in front of the habitats, gazing up to observe small fish, big fish, colorful fish, dull fish, and everything in between. I was in awe of the diversity; it was kind of like reading Dr. Seuss, “One fish Two fish Red fish Blue fish.” There were so many fish, but there were also fish of every color, size, and shape. At the time I wasn’t thinking about math, but as I reflect back on that experience I know that math really was all around me. This experience is not unique; I see thousands of children visiting Shedd every year. As they gaze into the same habitats I did many years earlier, I can see the sense of wonder and awe in their faces. Knowing what I know now, though, I think about taking that moment of wonder and creating a math moment too. I think about using that awe and excitement as a springboard to a conversation about how many fish, how are the fish different, or how are the fish the same. These teachable moments are all around you when you visit a museum.

As we explore museums and math together in the posts to follow, let’s first consider the big ideas of early mathematics: sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. These nine ideas laid out by Erikson Institute’s Early Math Collaborative provide the foundation for exploring mathematical concepts in and out museums. We’ll touch on many of these ideas as we explore some of my favorite museum exhibits. So for a moment, let’s focus our exploration on math in museums. Let’s reflect on the ways in which these big ideas exist in museums. Come join me on a mathematical adventure!

Using Children’s Literature to Reinforce Classification

posted by Dr. Jeanne White

When older children and adults perform chores such as doing laundry or putting away dishes, they may not even realize they are making decisions about how to classify objects into categories—washing the white clothes together and putting the plates together on a shelf.  Young children can begin to see how objects can be sorted into categories with the help of several children’s literature books.

Young children naturally sort objects by color.  Have a variety of books available that introduce colors and show objects of a particular color so children can make associations with the object and the color.  A fun book that can be used to explore colors is The Color Box (Dodds, 1992), in which a monkey named Alexander crawls into a box to discover a world where everything is black, then another where everything is white, then yellow, and so on until he ends up back in his world where there are objects of every different color.  Then provide groups of objects that can only be sorted by color such as Unifix cubes or square tiles.  Once children have sorted these objects by color, they can count the number of cubes or tiles in each group and compare them—which group has the most?  Are there more red cubes or more orange cubes? Then make several types of objects available for children to sort by color such as beads, tiles, cubes and blocks.unifix cubes scatteredunifix cubes and other shapes

After children have had several experiences sorting objects by color, they can begin to explore other attributes.  In the book, The Button Box (Reid, 1990), a boy visits his grandma and finds a box with hundreds of buttons inside.  He sorts them into categories such as buttons covered with cloth, sparkly buttons, metal buttons and buttons from uniforms.  He also lines them up based on size and color.  At the end of the story, the boy and his grandma close their eyes and each choose a button from the box.  Then they look at them and talk about all of the ways the two buttons are alike and the ways they are different.  Follow up the story with a game similar to the one in the story, by comparing two buttons or other toys that have similar attributes such as two dolls or two cars.

Another book that can be used for classification of objects is How Many Snails? A Counting Book (Giganti, 1988).  On each page there are illustrations of one type of object but they vary by size, color or design.  On the first page there are eight clouds for children to count.  Then there are more questions to answer, “How many clouds were big and fluffy?  How many clouds were big and fluffy and gray?”  Children can use their toys to count, sort and answer questions such as, “How many frogs?  How many frogs are yellow?  How many frogs are yellow with a green stripe?”  Incorporate science by introducing various types of insects and asking children to tell you how they can sort them—by putting all of the insects that are the same color together or by putting the insects with wings in a group. four frogs

When children sort and classify objects into groups, they are building a foundation for graphing and data collection.  grasshoppersThey can create unique ways of sorting objects into groups and once they know how to put objects into categories, they can help with all of those chores!

Using Children’s Literature to Reinforce Patterns

posted by Dr. Jeanne White

Young children naturally begin to create patterns with objects such as Unifix cubes or colored tiles, even if they do not realize what they’ve created is called a pattern. A child’s early knowledge of color or shape patterns can lead to later recognition of more complex patterns in large numbers and within the four operations.

A book that can be used to introduce young children to patterns in the environment is the book Math Counts: Pattern (Pluckrose, 1995).  The book contains photographs of patterns found in nature such as on leaves, flowers and insects.  The book also shows patterns found in familiar objects such as on a car tire, the sole of a shoe and wallpaper.  Encourage children to draw or photograph their own pattern discoveries such as on clothing, jewelry or furniture

.bracelets

jewelry boxAnother book that can be used to introduce patterns is Rooster’s Off to See the World (Carle, 1972).  In the story, one rooster decides to travel and meets two cats, three frogs, four turtles and lastly, five fish.  As he meets each set of animals, pictures of the animals are displayed in the upper corner of the right page.  Children can see the growing pattern of animals from one rooster up through five fish.  Eventually, all of the animals disappear, starting with the five fish.  The pictures of the animals appear in the upper corner of the left page and gradually disappear until only a picture of one rooster is there.  Children can see another pattern as the number of animals decreases from five down to one again.

Set up activities following this book such as displaying familiar object to create an AB pattern (using only two different elements in the pattern) for a child to continue.  Start with color patterns and say the colors aloud as you display each one, “Red, blue, red, blue.…”  After several examples of color patterns, use toys and say the name of the objects as you display each one, “plate, spoon, plate, spoon….”

patternspoonsOnce children have practiced recognizing and repeating patterns with cubes, blocks, toys and familiar objects, they can begin to listen for patterns in songs, stories and nursery rhymes.  A book that can be used as an example of a pattern set within a story structure is The Napping House (Wood, 1984).  It’s a rainy day and everyone is napping in the house, including a snoring granny.  But then the granny is joined by a dreaming child, followed by a dozing dog, then a snoozing cat, a slumbering mouse, and a wakeful flea.  Each of these nappers pile on the bed with granny one by one, and are introduced on each page, one by one, adding to the words from the previous page:  “And on that granny there is a child…and on that child there is a dog…and on that dog there is a cat….”

Encourage young children to listen for patterns when you read stories or to look for patterns in photographs and illustrations in books, on posters and other media.  Recognizing patterns sets the foundation for algebraic thinking—analyzing patterns, relationships and change throughout the study of mathematics.

Using Children’s Literature to Reinforce Geometry

posted by Dr. Jeanne White

As young children are formally introduced to the names of shapes, they begin to notice these shapes in their surroundings.  They see their plate as a circle and their napkin as a square when they eat dinner.  They look at the windows and doors in a room and recognize them as rectangles.  Tana Hoban’s book Shapes, Shapes, Shapes (1986) uses photographs of familiar objects such as pots and pans, and scenes such as construction sites, to present various shapes. Children will find more shapes on each page as they look at the photos again and again, and as they learn to name more shapes such as trapezoids and ovals.

An activity that can follow the introduction of this book can be allowing children along with family members to take photos of shapes in their home, their neighborhood or school.  They can display and compare the photos and name the shapes in each other’s photo.a door

a bureau

a lamp

In addition to two-dimensional, flat shapes, young children should be introduced to three-dimensional, fat shapes.  Reading the book, Changes, Changes (Hutchins, 1987), can open a child’s mind to the endless possibilities of how to arrange 3D blocks to build structures.  In this wordless picture book, a wooden couple builds a house but it catches on fire, so they must build a fire engine, then a boat to deal with all of the water, and so on.  Encourage children to find 3D objects in their environment such as food containers that represent cubes, cylinders, and rectangular prisms.  They can build their own structure with these containers and name them as they build.a pic of food boxes

Once children are familiar with the names of shapes, they can expand their vocabulary to include attributes of shapes.  The book, If You Were a Triangle (Aboff, 2010), includes illustrations of triangles that are slices of watermelon, Yield signs, faces of pyramids, designs on wallpaper, and more.  The text repeats the phrase, “If you were a triangle…” and lists attributes such as “three sides,” or “three corners” and introduces the terms polygon and angle.  At the end of the book, specific triangles are shown—equilateral, right and isosceles—along with examples of these triangles put together to form a new, composite, shape such as a rectangle or rhombus.  Children can look for triangles in their environment as well as practice putting the triangle Pattern Blocks together to form new shapes.a pic of 2 shapes red and greana pic of 2 shapes blue and green

Another concept children learn in early geometry is relative position.  Young children are gradually exposed to words used to describe the position of an object or person relative to other objects or people such as above, below, beside, in front of, behind, and next to.  Young children are also starting to distinguish between their right and left and are learning to move, and count, forward and backward.  A book that is fun for children to use to learn these concepts is Bug Dance (Murphy, 2002).  The bugs in this book go to school together and in gym class they learn a dance that teaches them to take steps to the right and to the left, then hop forward and backward.  Young children can perform the dance as the book is being read over and over.

After children have practiced their dance moves they can practice the terms in the book, as well as other position words, to describe the position of Pattern Blocks.  For example, children might say: the square is below the hexagon; the triangle is on the right of the square; the trapezoid is on the left of the square; the triangle is next to the square. a pic of 4 shapes

There are many children’s books that are written to introduce shapes, however many use the word “diamond” instead of rhombus.  I try to avoid these books or let children know a diamond shape is called a rhombus when we are learning math.

Using Children’s Literature to Reinforce Counting and Cardinality

posted by Dr. Jeanne White

Young children love it when an adult sits down and reads a book to them, carefully studying the illustrations before the adult can turn the page.  Why not seize these opportunities as a way to introduce or reinforce mathematical concepts?  There are four reasons why I like to use children’s literature as a mathematical resource:

  1. Literature can offer examples of real-life problem solving.

When I read The 3 Little Pigs to a child, we discuss how many pigs there are and how each one has a way to solve the problem of how to prevent the wolf from blowing down their house.  Even though pigs can’t really talk or build a house, the young child begins to understand the idea of a problem and solution as well as the lesson that sometimes we have to go back and try a new solution.

  1. Children can discuss and demonstrate how characters use math.

In the book, Pete the Cat and His Four Groovy Buttons (Litwin, 2012), Pete the Cat sings a song about his four buttons.  But as he loses one button at a time, he alters his song to include three buttons, then two, then one.  Young children can see, and hear, how Pete the Cat uses math in his everyday life by counting the remaining buttons each time he loses one.

  1. The text can provide common language and context for problem solving situations.

When I would read the book, The Doorbell Rang (Hutchins, 1986), to my primary students, we used little chocolate chip “cookies” cut out of brown tagboard and small paper plates to act out the story.  On the first page, Mom makes 12 cookies for Victoria and Sam to share.  This provides an opportunity for children to talk about how to distribute the 12 cookies on the two plates and then how to make sure the same number of cookies is on each plate.  Throughout the story, more children come to the house to share the 12 cookies, which are continuously distributed evenly among the growing number of children.

  1. Children can apply mathematical concepts with literature.

In the 12 years I have been teaching math methods for the pre-service teachers at Elmhurst College, the teacher candidates are always amazed at the number of children’s literature books used to teach mathematical concepts, from PreK through eighth grade.  I have also conducted workshops for preschool and kindergarten teachers, as well as for families of young children, who are also surprised at how easy it is to use literature to teach and reinforce mathematical concepts including counting, patterns, geometry and sorting.

Using Children’s Literature for Counting and Cardinality

red dots in a row

Young children learn to count to ten with meaning—they should not only be able to rote count from 1 to 10 but be able to count up to ten objects.  Adults and older children can become role models for counting and demonstrate the concept of cardinality, the awareness that the last number said is the total amount. When first introducing the concept of counting, use a book with the same objects on each page such as Ten Black Dots (Crews, 1986).  As you read each page and model how to count the number of black dots on each page, the child only has to pay attention to quantity since each object is the same size, color and shape.  Then practice counting up to ten circle counters so the child is only paying attention to the quantity.red dots in groups of 5

 

Once children are able to count objects that are the same size, color and shape, read a book such as Math Fables (Tang, 2004), in which animals are shown in different configurations along with a rhyming fable, from one spider up to ten beavers.  This book can be read to children again when they are ready to break down numbers and group them into more manageable and familiar amounts.

colored frogs

 

An activity that can follow this book can be counting familiar objects such as toys or food.  Allow the child to touch each object while counting, whether counting illustrations in the book or toys on a table.  The child should also be able to repeat the total number of objects.  For example, “One, two, three.  Three frogs.”

yellow dots

 

Once children can count up to ten objects, they can begin to learn the complements of ten (one and nine, two and eight, etc.) with the book Ten Flashing Fireflies (Sturges, 1995).  In this book, two children are outside collecting fireflies in a jar.  First there is one firefly in their jar and nine fireflies in the night sky.  Then they catch another firefly and two can be seen in the jar and eight in the night sky.  After repeated readings of this book, try playing a game in which some “fireflies” are in the jar and some are in the sky.  Show the number of fireflies in the sky and have children figure out how many are in the jar.  They can have ten counters of their own to help them figure out the math problem.

 

I hope you have as much fun as I do, reading children’s literature and creating related math activities to introduce and reinforce these counting and cardinality concepts.

Math is fun? Really it is.

posted by Lisa Ginet

“Let’s do math!” I often say at the start of a workshop. This may lead to some panicked looks or trips to the bathroom. If I say, “no pencils or calculators involved,” then a few people will laugh, and most will look more willing to try what I suggest …

math-workshop

What are these people doing? The Counting Calisthenics! If you need a break from the computer, you can do it, too! Stand up and count while you move:

Touch toes – “1”

Touch knees – “2”

Touch hips – “3”

Touch shoulders – “4”

Throw hands up – “5!”

Continue counting while repeating movements

(toes, 6; knees, 7; hips, 8; shoulders, 9; hands up, 10 …)

Keep going until you want to stop.

After you sit back down, consider this question: If you kept doing the toes, knees, hips, shoulders, hands up counting calisthenics, what movement would you be doing at “456”?

It would be quite exhausting to actually keep doing the counting calisthenics all the way to 456, but I expect that, if you think about it a little, you will be able to figure out that you would be touching our toes at “456.” You probably noticed that your hands were up in the air every 5th number, and then the cycle started again. So, your hands would be up in the air for “455” and back at your toes at “456.”  You are using what you know about the structure of our base-10 number system and the pattern of the calisthenics movements to arrive at an answer. You are doing math!

We at the Early Math Collaborative want to encourage you, and all adults who spend time with young children, to build new math ideas and new math associations by engaging in fun and meaningful math activities. Why? If adults are going to engage children in doing real math and constructing authentic mathematical understanding, then the adults need to exercise their own “math muscles.” Because many adults have bad memories of math in school, they often avoid doing math with children. It can be hard to engage adults in exploring foundational math if they don’t feel good about math and don’t think they can do math. Just as learning math facts from flashcards is not an effective way for children to become fluent and flexible problem solvers, blindly following activity directions will not help adults understand the math in the activities or respond effectively to children’s comments and questions.

“Counting Calisthenics” is just one of our Adult Learning Activities. While they involve basic math concepts, Adult Learning Activities are not children’s math that we are asking adults to do; nor are they activities to repeat with young children. We have designed these activities so that they:

  • pose a puzzle or problem;
  • are interesting enough to capture and retain adult attention;
  • are easy to implement;
  • may have more than one solution or route to solution;
  • clearly focus thinking on foundational mathematical idea(s).

We hope that having fun doing math will help convince you that the world is not divided into those who are good at math and those who aren’t. We can all be doers of math, and we can build the same confidence and excitement in the children in our lives.