Water, Worms and Measuring

shadows Have you ever seen a child with a tape measure? They are in all their glory! We have small tape measures that sometimes make it on our walks around the neighborhood. We like to measure seedpods, sticks, each other, our shadows, you name it. Did you find a worm? We are measuring machines. We like tape measures that are small enough to fit in a pocket, because you just never know when you will need to measure something. We may not know the numbers or what the spaces means, but it is fun! It exposes them to the concept and the visual number, when their brain is ready the important parts will fall into place.

mesauring tape

Living on the Mississippi River, each spring we get sucked into watching our beloved bald eagles. When we decided we should make our own nest, out came the tape measures! Did you know the average eagle nest is six feet wide? This is the perfect time to grab a tape measure and create a nest!

boys in the shrubs

We use worms to teach length and we sometimes measure them with tape measures but we honestly do a lot more observation and estimating with them because they are perfect just the way they are. We love worms. Did you know that worms don’t have teeth? Worms don’t have pinchers or stingers. They have no eyes, no legs, no arms. They will never hurt us. We try equally hard not to hurt our worms, but when you are two and investigating…well, sometimes it doesn’t end so well.wormsWe love worms because they help create healthy, beautiful lawns, which is hard to do when you have lots of two legged friends playing on it all day. People often ask how we “get” our kids to hold a worm. We read a lot of books about worms, we watch them for long periods of time, and if you have one brave friend, you are pretty much assured the bravery will come. Patience and calm, whispering voices can help also. Worms like moist ground, which leads us to water.

water pump

I love water play almost as much as I love blocks. When you have water in your play area, it is the equalizer among all children. Regardless of their age or language or social ability, water will bring them together. We love water play so much that we created our pump with the help of a buried rain barrel. Water gives us plenty of opportunities to understand volume and measurement and estimation. It turns dirt into mud, which makes it easier to find worms! It is a loose part. It may be my absolute favorite loose part. Be sure to add it in some form to your play area because it is so incredible.

This is one of our favorite stories, about water and time and discovery. We had our pump and I had some fabric in the yard as a loose part for making forts or whatever. These boys decided they wanted to capture water in the fabric.

I knew it wasn’t going to work, but why would I say no to such a learning opportunity. So,

boys measuringthe boys started pumping the water into the bright blue fabric.

 

 

 

 

 

HUH????? No way! Oh my goodness! Who knew that fabric was actually waterproof? collecting water  Ha! So now we had ourselves a project!collecting water The boys quickly decided this could create an amazing mote in the sandbox.

 

 

 

 

 

WOW!

boys with collected water

Another lesson learned in giving children long periods of time, never stopping the obvious and the importance of loose parts. Look at the delight on their faces! Okay, well maybe one is carrying most of the load, but the other two are thrilled.

 

Let them play!muddy mess

So, let’s talk some more about water and containers. Many cities are giving away rain barrels or offering them for sale. These make fabulous sources of water, specifically if you have a spigot for your child to control. Think of the math opportunities of measuring, estimating, mixing.   If you don’t have a water resource nearby, take some out with you. Think about milk jugs or buckets or big thermoses with spigots. Children love spigots. It gives them power to control something. You will also love having a source of water to wash your child before they return indoors.

Oh, how we love to cook. We do a lot of cooking around here, often outdoors, with loose parts and water. We spend hours mixing and stirring and adding and serving. Cooking is a math-athon of opportunities. (Yep, I think I made that word up. I like it!) It is important when you are cooking for play or cooking for actual consumption that children have their own bowls and utensils. It adds to the learning value. Watching your friend is not the same as having your own bowl, measuring spoons and spatula. We have been through many types of pots and pans and spoons and measuring devices. I recently jumped on a deal for a plastic children’s toy tea set to add to our play. I normally stay away from such things, but I’ll admit it, the price and the reviews sold me. Sadly, I didn’t love it. Within six months it was stained, and ugly and just not nice to look at. It didn’t seem to bother the children, but it bothered me. For the same amount of money, I could have purchased A LOT of real pots, pans, spoons, measuring cups and utensils from a garage sale or Goodwill. Keep it real. Include pots and pans, pouring pots for sure, and utensils and most importantly sand and water. We have tried to get away from plastic shovels but they really are nice for what we use them for. Metal shovels are sharper and heavier and just don’t seem to work as well for us. Metal works well for dirt. In sand, we use plastic.

coolking with mud

Sand. I know, I know. A lot of parents hate it. I promise you it will bring you hours and hours of deep, calm, investigative, creative play. The bigger the area, the bigger the creations and the more friends can play. Mud kitchens are all the rage right now and for many of the same reasons. I, personally prefer sand. It’s easier for me to clean up with a household of little friends. Sand, dirt, and mud are essential parts of loose parts play. Think of it as a short-term investment for long-term brain development. Sand and dirt support children on the mathematical learning journey. Children will explore space and measurement and shapes. They will start making comparisons of dry and wet and how that affects what they are building or mixing.

girl wiht leaf

This is where loose parts will come in handy. They are the ingredients and the spices. You will want lots of rocks, flower petals, grass clippings, native prairie grasses, sand, small sticks, and feathers. The more choices the better, because every experience changes the recipe! There’s a whole lot of math going on.

toddler baking wiht mud

 

 

cooking mud

 

 

 

 

 

 

 

 

 

 

 

If I still haven’t sold you on sand or water play, let’s try rice. We color our rice with liquid watercolor, but plain rice is just fine. I have really gotten away from using our sand and water table very often. They aren’t nearly as easy to use as tubs on the ground. We like to use these big tubs. You could use those long, plastic storage containers for under the bed or oil drip pans from the auto supply store for a fraction of the price I paid for these, and the colors will be much less annoying. The long, plastic storage containers also come with the bonus lid, which is great for storage. We like to lay out a large sheet or blanket to help with clean up. Be sure to add funnels and all the utensils listed above. The measuring and pouring and learning will bring you hours of quiet time. The rice is very calming and it is so very inviting.outdoor sand tables

I watched these four-year-olds as they investigated the rice one day. I knew it was coming.

 

 

 

outdoor sand tables 1

 

 

 

 

 

 

outdoor sand tables 2

 

 

 

 

 

 

………yep, yep, there it is.

sitting inside sand tables

 

Good stuff that rice is. Just like a day at the beach. Cheap, because that’s math, and we like cheap. Buy the big 25-pound bag because like sand, more is better. Your child may need to crawl into it someday!

 

 

 

 

 

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.

Researcher for a day: What kinds of animals live in the Amazon?

posted by Lindsay Maldonado

By day, I’m a researcher at Shedd Aquarium. I study people though, not animals – but, at Shedd, there are also a lot of people who do study animals. Some of these people are conservation research scientists or aquarists, who use math, and science, to help them learn more about the animals in their care, or animals in the wild. No matter who, or what, your subjects are, collecting data helps researchers collect information (i.e., data) that can provide answers to important research questions. For example, I might want to know how many visitors learned something about how they can help animals after their visit; or a conservation researcher might want to know how many seahorses live in a certain area of the world. So, to get us started, let’s pretend we are research scientists. We have our clipboard loaded up with our data collection sheet, some pencils, and our observation eyes. Now we’re ready to start collecting data!

penguin survey

Data analysis is one of the big ideas of early mathematics and can serve as a foundation for introducing other big ideas like sets, number sense, and counting — and, what better place to apply these ideas than at the aquarium with real living animals.

We have some important research questions to answer, so let’s get back into scientist mode. Today we want to know how many different animals live in the River Channel – and, we’re going to answer this question by observing animals (i.e., gathering data) and documenting what we see (i.e., organizing and describing data). These are all important steps to data analysis! If we want to know what animals live in the River Channel, we first need to make some observations. What do you see? A variety of animals live in the River Channel. How many animals do you see? Can you count them? I see 8 animals.

how many animals

Like the Amazon River, this habitat shows the diversity of animals that live in the river. What kind of animals do you see? I see turtles, stingrays, and fish.

kinds of animalsWe can sort the animals in the River Channel in a number of ways. First, we can sort by the attribute: type of animal. There are fish, turtles, and stingrays. Let’s put these animals on our graph. Representing data, in this way, is an important part of data analysis and allows us to interpret the data we collected.

blank graph

Let’s revisit our research question. We want to know how many types of animals live in the Amazon River. Through observation, we saw that fish, turtles, and stingrays live in the Amazon River so there are three types of animals in the River Channel. But how many of each live there? Let’s use our graph to help us organize our data. How many fish do you see? How many turtles? How many stingrays?

animals on graph

In what other ways can you sort these animals? You can use any number of attributes to sort the animals in this picture. We used the attribute of type (turtles, stingrays, and fish) but you could also sort these animals by size or shape. Observing animals at an aquarium is full of math possibilities. You can use data collection and data representation as the foundation for exploring the big ideas of early math. Keep exploring data analysis in the classroom. Try more data activities 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!

Let’s sort this out!

posted by Dr. Bilge Cerezci

sorting rocksAt all ages, children classify intuitively to make sense of their world that seems largely out of their control. By 2 weeks of age, infants distinguish between objects they suck and those they do not. By 2 years, toddlers form sets with objects that are similar. In preschool, children begin to sort objects according to a given attribute and form categories. Many parents have likely walked into a room to see their four-year old putting their blocks or other toys in piles based on color or type. So why sorting is important you may ask. By sorting the objects around them, children start using their analytical thinking skills that is the lifeblood of mathematics. Studies have even been shown that by comparing objects to one another and understanding the relationship between set of objects, children engage in transitive thinking: A blue block is bigger than a red block and smaller than a yellow block. So, blue blocks need to go into a medium-sized block pile. Practicing sorting skills also provide children with models for organizing things in the real world, such as putting toys into the right toys boxes or putting the socks in a sock drawer and underwear in the underwear drawer.

Sorting Ideas

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s sorting skills. Here are some of the sorting ideas you can implement in our home:

* Collect real-life objects such as rocks, marker caps, marbles, and buttons. Ask your children to guess which objects will together and which items will not. Ask the children to sort them according to different attributes such as; color, texture, type and etc.

* When it’s clean up time, ask your child to sort toys by attributes. For example, ask your child “Can you pick up all the toys that are the same color as this?”

* Encourage your children to name groups of things or activities. For example, at the dinner table, talk about attributes. You might say “2 people at this table wear glasses, 4 don’t.” or “3 have curly hair, 3 have straight.”

While you are doing these activities, use words such as “same,” “different,” “math,” “group,” “collection” and “set” as they apply and encourage your child them to use when they are describing their groups and comparing the groups they have created to one another. You may also ask your children questions such as, “Can you figure out what goes together?” “Can you sort these a different way?” “Why do these go together?” “Why do these not go together?” These kinds of open-ended questions will allow you to better understand your child thinking and push your child to be more precise in explaining their mathematical thinking processes.

Different children, different decisions

Children at different development stages are equipped with different mathematical abilities. A younger child will likely require less categories (sorting by two attributes) while an older child often can handle three, four or more. What you use for sorting also depends upon the age and ability of the child, as well as their interests. Some materials may be more challenging to sort for younger children (e.g., visually ambiguous materials) while others too simple and even boring for an older child (e.g., colored unifix cubes). Using real-life objects and situations to provide sorting experiences is always beneficial for all-around learning for all age groups. The bottom line is to know your child’s abilities, interests and to meet them where they are at, so you can just give them the right amount of challenge without underwhelming or overwhelming them.

Focus on Attributes!

posted by Dr. Bilge Cerezci

As she sits on the floor, a three-year old starts stacking blocks with various shapes and sizes. After some experimentation, she realizes that it is hard to build a tower if a block lays on its curvy side.

 

What does this 3-year-old discover about shapes?

From an early age, young children notice different shapes have different characteristics, even if they don’t know their names yet. They realize that some shapes have points while others have none. They also discover some shapes have flat sides while others don’t. Traditionally, we teach children the names of basic two-dimensional shapes: circle, square, triangle and rectangle and assume that being able to name these shapes indicates a higher level of geometrical understanding. Unfortunately, this can be any further from the truth. In reality, young children need your help to focus on attributes of shapes rather than overall appearance. For example, as you build a block tower together, encourage your child to pay attention to defining attributes of the each shape you are using. You might say, “I see you are stacking up the blocks that have flat sides. Look, all of its sides are flat. How is this one (i.e., cube) different that this one (i.e, half circle block)?” As you continue with the activity, encourage your child to use her fingers to trace and feel the shape. Give them a plenty of time to feel the shapes, count the sides and even ask them to find an item in your home to that resembles that shape.

As children manipulate various three-dimensional shapes, they will eventually build deeper understanding geometrical shapes such as flat faces of solid (three-dimensional) shapes are two-dimensional shapes.

There are many ways to encourage and help your child to learn about shapes. Here are some of the games you might play with your children at home:

* Drawing shapes in sand or foamshapes in shaving cream

* Walking around shapes drawn or taped on ground

shapes on the floor

* Making shapes with bodiesbodies making shapes

Shapes are all around us and it is easy to play games like these at home, outside and elsewhere. Most importantly, make sure to have fun while doing it.

Number Sense: Make it Real!

numbers opaqueposted by Dr. Bilge Cerezci

Young children are motivated to explore mathematical concepts they encounter in their everyday interactions with the world. Through these interactions, they develop a range of informal understanding of numbers including ideas of more or less and one-to-one correspondence. For example, a child as young as two knows if she gets more or less crackers than her friend next to her. She also exhibits her basic understanding of one-to-one correspondence when she insists on getting a cookie because her brother had one and she had none. Such intuitive understandings of number sense may help lay the groundwork for later understandings of numerical equivalence and operations, such as addition and subtraction. While serving as important building blocks, such understanding does not necessarily help young children explicitly examine and interpret their experiences in mathematical forms. So, how do we help young children make connections from these informal knowledge around numbers to a deeper, more concrete understanding of numbers?

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s developing number sense. For example, when you are setting your table for breakfast, ask your child to join you. You can ask them how many plates do you need to set the table or whether you have enough eggs for everyone or not. While they are taking the plates from the cabinet, encourage them to count. When young children practice counting, they’re also learning one-to-one correspondence. A child that understands one-to-one correspondence knows that 4 plates equals 4 or that 5 eggs equals 5. To help them practice this concept, give your children large groups of objects to count. For example, you are making a strawberry cake for dessert and you only need 10 strawberries. You may ask your child to help you figure out whether you have enough strawberries or not. As they are practicing this skill, children may count some of the strawberries twice and/or skip counting some of them. Therefore, it is important to closely observe your child as she is counting. When she is double-counting some of the strawberries, does she realize what she has done? Does she self-correct? In such instances, resist the temptation of correcting them. Instead, ask her to double-check her answer and give them enough time to check their work and self-correct their mistakes. If she is struggling, provide them with some strategies she can use(e.g., moving strawberries to a different pile as she counts).

Taking this kind of approach not only allows children to see math as fun, but also helps them see numbers as useful tools that they can use to make sense of the world around them. While doing these kinds of activities, the most important thing you can do is to help your child see math is something that makes sense and it is practical and enjoyable. This will help your youngsters to build a strong understanding of math and develop a love of learning math that will last a lifetime.

square blocks