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.

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!

What is Math?

posted by Lisa Ginet

When you hear or see the word “math,” what do you think of? Your high school algebra class? Balancing your checkbook? A geeky engineer with pocket protectors? When you add “early childhood” to “math,” what do you think of then? A little one learning to say, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10”? A bright poster with a circle, triangle and rectangle neatly labeled? All of these are common ideas about what math is and how math starts, but none of them are what I mean when I say “foundational math.” Before I tell you what I do mean, I want you to try something.

Look at this image:
shapes-pictureConsider this question:

Which of the figures are the same?

Often when I ask this, a person says, “They are all different from each other.” Another says, “They are all the same; they are all shapes.” Both of these answers make sense, but I often ask people to keep looking to see if anyone can come up with another answer. Usually, people then generate these six answers:

  • top two shapes are both orange
  • bottom two shapes are both green
  • left two shapes are both striped
  • right two shapes are both solid
  • top left and bottom right are both circles
  • top right and bottom left are both triangles

In fact, although none of the two shapes are identical to each other, any two of them are “the same” in some way. Figuring this out involves logical thinking about the attributes of the shapes.

This shape activity demonstrates one definition of mathematics – a logical way of thinking that allows for increasing precision. We can use math to make sense of the world. We can use math to solve problems. To use math in these ways, though, we cannot just memorize facts. We must build our own understanding, so that we can think flexibly in different situations. Without a strong foundation, a tall building would not stand for long. Likewise, without a strong foundation in mathematical concepts, children can struggle to understand the more complex mathematical thinking they need later in life.

At the Early Math Collaborative, we have developed a set of 26 “Big Ideas” – key mathematical concepts that lay the foundation for life-long mathematical learning and thinking. While these concepts can be explored at any early age, they are powerful enough that children can and should engage with them for years to come. As you engaged in the shape activity earlier, you were using two of the Big Ideas:

  • Attributes can be used to sort collections into sets.
  • The same collection can be sorted in different ways.

Most likely, you were not thinking about these ideas consciously; rather, you were looking at the shapes and thinking about them. You were using math to make sense of the puzzle I posed and to come up with a solution. This type of math may not match your prior notion of math as quickly-recalled facts and properly executed procedures. You may need to set aside some of those notions in order to develop a deep understanding of foundational math that will help you have fun doing math with children.

 

Tools that Support Mathematical Understandings in a Preschool Room

Over the years, I have blogged about 100+ kinds of manipulatives, from the homemade variety to the expensive stuff, from the kinds designed for toddlers to tools for early school-aged children.  I really like interesting, diverse, multidimensional tools that can be used in a variety of ways and for many developmental levels.

Today, let’s take a look at how tools are used to support mathematical understandings and how tools can be misused so they are not really effective in terms of meeting early math outcomes.   IMG_0103 FullSizeRender-10

Here you can see a few sorting trays designed so that children can create, extend, and copy patterns (green tray), sort and organize items by attribute (yellow tray), and graph (blue tray).  IMG_0105

This red one is divided into quadrants so that more or larger items can be grouped or sorted in other ways (I.e., animals that fly, animals that swim, animals that walk on 4 legs, animals that walk on 2 legs).

These all come in a set and are beautifully made, large enough that children can use smallish items with them but not so smallish that they present choking hazards.

So, if you had these in your room, how would you use them?

The day I saw these in a Head Start classroom, they were sitting out on a table with several bins of small manipulatives nearby.  A few children were playing with them and from my observations, it was clear that they did not know or understand the purpose of the trays.  They were using each tray much the same way they might use a plastic plate, as a receptacle for putting the toys, storing the toys, and moving the toys around.  The teacher never came over and neither modeled how to use the trays nor explained how to use them.

Here you can see how one child was putting dinosaurs into the spaces of the tray in a disorganized fashion.  At no time did a teacher support his play by suggesting alternatives, or sitting next to him and encouraging more purposeful use of the materials.IMG_0104

It reminds us that our role as “set designer” and “provocateur”  demands that we do not put materials out in a haphazard fashion but systematically think about our curricula, materials and environment in thoughtful ways.  We  must observe the children to know where they are developmentally and what they need from us so we can support their growth.

These tools are not meant to be put out on a table at the same time without direction.  They are meant to be used to support developing mathematical competencies.  That is NOT to say that young children should not use them to play.  Of course they should.  In fact, before I used them for their designed purpose, I would allow  the children to explore the trays, one at a time, over a period of time, to see how they explore them organically, without direction.  Eventually, I would take one over to group time and show the children how they can make patterns in the green tray or sort items in the yellow tray.  I would show examples and sit at the math table and work on patterns with the children, creating them and asking the children to extend them.  I might ask children to create their own patterns and see if I can extend them. I would set out very specific manipulative that have 2 or 4 attributes so they can be easily distributed in the sorting trays.

I would set the scene and facilitate the play.  I would use math language throughout these interactions and make it fun.  I would show excitement about the challenges these trays present and pose thoughtful and stimulating questions that the children could answer.  I would encourage the children to “try” and get excited at their efforts.

In short, I would do my job by being the best, most thoughtful teacher I could be.

Think before you set up your materials and arrange your space.  How are you going to be the best teacher you can be?

Recycling

I had a meeting this past week with a center director and the assistant director to discuss some ideas for upcoming professional development.  We went across the street to have lunch while we talked and when we finished we were supposed to go over to the recycling center to sort and dispose of our garbage. This was no easy task as I never know if my soiled napkin is considered “Paper” or “Landfill” and the group couldn’t agree.

IMG_1900

It got me thinking about organic ways to get children involved with environmental issues as well as a simple way to have children sort their garbage every day.  It didn’t seem quite possible at this center because the children would have to cross over to the other building with their garbage, but when we went back to the center side, lo and behold, they had their very own recycling station there.

IMG_1902

I tried to put myself in the place of the classroom teacher and imagine how difficult it would be to have all of the children walk down the hall with their garbage so they could sort and recycle it.  I suppose it could be a hassle, but maybe there was a way to sort it out in the classroom and then have a few children tote it down each day with a teacher.  They could put “Glass, Metals, and Plastics” on one shelf of the cart, “Landfill” on another and “Paper” on the top.  The cart then could travel down to the Recycling Station and a the recycling team could sort it into the appropriate bins.

Or, you could set up a recycling station in each classroom with 3 bins labelled with pictures so that children participate in the process all of the time.  Not only does it require sorting when disposing of the garbage, but it requires that children recognize attributes (plastic, dirty paper vs. clean paper, etc.) and categorize the items appropriately.

This is one of the classroom systems that is easy to set up and makes sense if you are playing the long game with children.  It may be hard today and even this week, but in the long run, it will be worth it.

Crawling, Flying, Hopping or Slithering

Categorizing insect and bug attributes by size and color is one way to separate and sort them.  It might be more fun to use your insect and bug collections to create gross motor movement activities using the attributes of how they move rather than how they look.

Some bugs fly (butterflies, ladybugs, bumblebees), some bugs crawl (spiders, beetles), some bugs hop (grasshoppers, cicadas), and some bugs slither (worms, caterpillars).  Using these attributes, children can sort themselves into groups who move the same way. Using your giant bucket of bugs, have the children close their eyes and pick one out.  They can then decide if their bug hops, crawls, slithers or flies.

At group time you can introduce the song about Sammie. It goes like this.

This is a story about Sammie.

His father sent him out to buy bread.

But Sammie didn’t feel like walking,

he wished he could fly instead.

“If I was a  butterfly (pick a bug that flies), I would fly to the store, fly to the store, fly to the store.

If I were a butterfly, I would fly to the store to buy bread.”

 

This is a story about Sammie.

His father sent him out to buy bread.

But Sammie didn’t feel like walking,

he wished he could crawl instead.

“If I was an ant (pick a bug that crawls) I would crawl to the store, crawl to the store, crawl to the store.

If I was an ant I would crawl to the store to buy bread.”

You continue this until all of the bugs have had their turn.  Sammie is an absolute favorite and a great way to get the kids moving.  Remember to discuss how the bugs are the same and how they are different.

Sorting Bugs

While looking through math materials the other day, I came upon three interesting classroom tools that focus on sorting bugs.

Scoop a bug sorting kitThis first one is called “Scoop-a-Bug Sorting Kit” and is pretty interesting.  The bugs are clearly fake, with exaggerated attributes, such as bright and vivid colors, which are easily identified by children. The scoopers look a bit like scissors with wide holes for fingers but rather than blades there is a clear scooper that can pick up the bugs in order to place them in the clear specimen jars.  Break this set out onto your math manipulatives table and I bet the kids are drawn to it like moths to a flame (get it?).

bug sorting trayThis second set is simply called “Real Bugs Discovery Kit”.  The sorting mechanism is far less interesting but the bugs themselves are really cool.  They are real specimens encased in clear acrylic so the children can see them from all angles.  It comes with a book of information about each specimen (there are a dozen in all).

Bug sorting bogNext is a set that focuses on size and sorting.  The bugs come in small, medium and large and can be sorted into each section of the box. You can change the categories to yellow, blue, and red, or legs, wings, or shells.  These options make it a bit more interesting but if you already have a set of classroom insects, you could create your own sorting map, or sectioned box with any attributes you choose.

Supporting Early Math Skills at Home

laundry

This week I thought we could think about ways to encourage families to support  early math concepts at home with some simple ideas that anyone can do.

Everyday chores may be horribly boring to the adults who do them (ME!) but children can find joy in the same tasks if they are approached as fun, participatory games.  Take laundry.  For me, this is the worst of the worst.  The never-ending piles of dirty clothes, followed by the never-ending piles of clean clothes that need to be put away followed by the never-ending pile of dirty clothes.  It is a cycle that never ends.  Even when all of the baskets are empty and everything is put away, it only lasts a moment – not even long enough to appreciate it.

The following ideas can be incorporated into a parent newsletter.  Be sure to let them know that encouraging early math skills at home is easier than they think.

There is so much math in laundry, you just have to find it.  

From the dirty clothes pile, have your children find all of the white clothes and pile them together.  Then ask them to find all of the jeans, and make another pile.  This act of sorting can be made more fun if you hide three baskets around the room, with one example of each kind of clothing at the bottom (jeans, whites, and everything else) so they have to find the place each kind of clothing belongs.  This might be very hard, since you are asking them to think of more than one attribute at a time. For younger children, just divide the clothes into two categories.

Once the clothes are clean, have the children find the matching socks and show them how to roll them together.  Then have them practice their aim, by tossing them back into the basket.  This simple activity encourages matching skills, aiming skills, spatial knowledge,  attribute definition, and sorting.  This also means that you don’t have to find the matching socks.  See, it makes your life easier.

Putting away laundry can also be fun.  Set the basket with all of the clean clothes near the bedrooms.  Make sure that the children know and can identify everyone’s beds.  Then, give each child an item of clothing and have them determine who it belongs to.  Once they have it figured out, time them as they run to the owner’s bed to deposit the item of clothing there.  Do this activity before you fold anything, since everything will come unfolded during the game.  Once the clothes are distributed on each bed, have the children determine who has the most clothes, who has the least, who has the biggest, and who has the smallest.  If they aren’t sure about sizes, have them bring items from two beds back and compare them so they can see definitively which items are bigger or smaller.

Over the next few weeks, I am going to describe other simple daily tasks that can encourage early math skills.  What I like about many of these is that the home provider can also try many of these ideas out.  Let us know if you do.

Continuing to Unpack the Standards- Goal 8, Learning Standard A

Goal 8 of the Early Learning and Development Standards is to Identify and describe common attributes, patterns and relationships in objects.

Learning Standard A – Explore objects and patterns.

Benchmarks

8.A.ECa – Sort, order, compare and describe objects according to characteristics or attributes.

8.A.ECb – Recognize, duplicate, extend and create simple patterns in various formats.

Example Performance Indicators

Compare and describe various objects (e.g., describe different rocks by referring to their size, shape, weight, etc.).

Create a simple repeating pattern using classroom objects (e.g., build a tower of alternating blue and red cubes).

Replicate patterns in music (e.g., repeat a sound pattern by clapping or tapping foot lightly; sing a repetitive song such as B-I-N-G-O; play finger game such as Open, Shut Them).

Sort objects according to different characteristics (e.g., sort crayons by color and size; sort small blocks by shape and color).

Order objects in a series by a single attribute (e.g., order fire trucks from shortest to longest; order rocks from smooth to rough).

_______________________________________________________________________

Patterns, groups, attributes- these concepts can be seen all over the ece classroom.  With the right materials children will naturally sort, classify, and organize their stuff into groups or patterns without much prompting from the adults around them.

imagesAlternating Unifix Cubes – by two’s no less.

matphotoviatka

 

Nesting Dolls- From big to small

Peg board 1

 

Peg Board – Only the orange ones.

Click here, here, or here to read more about sorting and attributes.

 

Using Large Block Play to Enhance Attribute Knowledge

wood-blocks-advancedBlock play is one of those areas of the early childhood environment that is teeming with learning in every developmental domain.  Children are drawn to the large blocks as a place to play independently, in a parallel way, or cooperatively.  The children’s natural curiosity in the block area involves mathematical thinking, which is easily observable if you sit back and watch.

Children will consider the size of the blocks they choose in a systematic and organized way.  They will consider the attributes of each block they choose so that the block can perform its specific function in the building.

Imagine a child is building a tower.  She knows that in order to make it tall, she will either need the long blocks, or several short blocks to build it high.  She will consider the width of the blocks to determine if the ones on the bottom will support those on top.  She won’t choose the rounded blocks for the base, as they won’t provide enough of a foundation to build the rest of the building.  This spatial knowledge is underlined by her ability to determine each block’s attributes and apply them accordingly.  We see this in even very, very young children.

If a teacher comes over and enhances the play by providing rich vocabulary words to help define the attributes, even better.  Using language like “edges,” “faces,” and “corners” to describe the flat blocks, and “arches,” “rounded,” and “circular” to describe the rounded blocks will build mathematical vocabulary while providing another means of exploring attributes.