Thursday, March 10, 2011

Mathematics and Preschoolers

I noticed that there are a lot of posts with regards to literacy and though I've touched on mathematics here and there I really haven't given many details.  An activity we did this week made me think about it a little more.

Okay, I see scissors- gray cloud.  I see literacy- upper and lowercase R rain drops.  What's the math?  We were reviewing 1:1 correspondence and counting to 10.  Preschoolers need quite a bit of experience with 1:1 using concrete objects and activities so that they can internalize 1:1 for counting with meaning.  Underneath the cloud were black line raindrops.  The children were given a bowl of raindrops.  Some had R, r on them and others did not.  They sorted the raindrops and glued (liquid glue bottles helps children strengthen their hand muscles and teaches them control!) a raindrop to each black line raindrop. That is a 1:1 correspondence activity.   When counting sets of objects, I encourage my students to "touch them".  You know a child has internalized 1:1 when they can put 1 finger on one object in a line and continue through the set with 1 finger on each object and counting one number higher and make it through the whole set.  Typically, I see very young preschoolers just run their finger over a line of objects as they count, sometimes randomly.  As they gain experience they make it to the 3rd or 4th object before their oral counting or their finger gets ahead of the game.  So it's important to do activities to help children internalize this 1:1 concept.  Here are some more hands-on approaches that you can incorporate in your activities.
   *  Icecube trays:  Use tweezers or small tongs and encourage them to put on pom pom (or other object) into each section.  You can also use muffin tins.  Here's an idea for Spring since we all are looking forward to it.  Back to Pre-K pages.  Check her website out if you haven't yet already!

   * Math Mats:  You can make these relatively easily on your own.  I do mine in Print Shop, if I have a specific theme in mind.  My most basic one is called "Cover-Up".  That way I can use it over and over and adjust the manipulatives according to the theme.  The children are given dice.  Use only one if they can only count successful to six.  Use two if they can count higher than six.  If they can't make it to 12 yet, that's fine.  The larger the number...the larger the grid needs to be.  You can help them along.  I like foam dice because 1) they are typically bigger so the dots are easier to count and 2) they are quieter!  Children roll their dice, count the numbers and place that many objects in each square.  They finish when the grid is filled.  I've used theme related stamps, stickers and erasers. has many options for small erasers.  Ours never get used for "erasing".  All used for math manipulatives.

   *  What child doesn't like to play with water?  Those little rubber ducks you can get through Oriental Trading and other places can be used for 1:1 reinforcement.  Fill a shallow bowl with water-I like to use a blue tub to represent a "pond", have a good number of ducks handy. Have them roll the dice, count the number of dots and place that many ducks in the pond.  Continue as interest keeps.  You don't have rubber ducks?  Cut a few from yellow or white craft foam.  They float.  Add a spray or squirt bottle and see if they can make the ducks swim by squirting them with water.  And of course, you can also do a paper pond and paper ducks...but the water does add interest.
  *  You can create 1:1 activities using objects around the house like...putting 1 hat on each doll.  Or you can use pictures...have clipart of children in rain gear and encourage your child to give them each an umbrella (I've used craft foam and pipe cleaners for umbrellas.)
  * Also remember that setting a table incorporates quite a bit of 1:1.  Most preschoolers can have success at this family chore!


Another math concept that I've touched on in the past is conservation of number.  Children tend to think that quantity is influenced by size.  That's because they depend quite a bit on visual cues.  This concept is really only internalized with experience so slip them in when you can.   No reason for frustration.  Children will eventually get it.  You just provide the experience. Here's a youtube video:  
   *  When you have a set of objects that you are counting, one time squish them all together and count them.  Then spread them out into a longer line and ask how many there are now.  Most preschool children will begin to count again because they think there are more now.  Do it a couple of times to show that, really, it's the same number.  You can do this with two identical sets of objects...squish one set together but spread out the other and compare and then count together.
   *  With playdough, create two equal sized balls.  Talk about how they are the same size.  Then have your children make a snake and then you make yours into a snake, either larger or smaller.  Then talk about which one had more/less playdough.  The answer is, they were the same amounts of playdough.  Show them that by rolling the snakes back into their balls and comparing the sizes.
   *  If you are focusing on a specific number, then provide some material that the children can make various sets out of.  So maybe you are working on the number 9.  You have provided a bowl of elbow noodles.  (Hey, get that literacy component in there...nine noodles :-)).  Then have your child make nine sets of nine.  Encourage the children to glue them on together in a set, arranging them differently.  I have used a different colored marker and circled around each set when they were done so they didn't confuse one set from another.  Then of course, we reinforced counting to nine, how many times?  18-20.   :-P First when we were introducing the activity, then as we counted out nine sets of nine, then we counted each individual set as we glued it to the paper, then to "check our work" we counted the sets on our paper to make sure we had nine sets. 


Our K standards state that a child should orally count to 10 before Kindergarten.  10?  I guess, if a child has minimal experience.  But most of my students can count between 20-30 before going to Kindergarten.  It's all about experience.  And once they learn the pattern of counting they are good to go.  Counting orally has it's place.  It's like singing the ABC's.  It's memorization and it's a good intro to numbers and numeral names.  Here is a skill that seems so simple to us.  I do not formally teach this skill.  It's another skill that comes in time with experience and when the teacher/parent is aware of it, then they are more apt to reinforce it whenever possible. To eventually be able to add and subtract, children must first recognize a number and be able to give a concrete example of the number. In preschool, we "count with meaning".  Counting with meaning is that of counting a concrete set of objects, using 1:1 correspondence and knowing that the last number you say is the total for that set.  So try it...does your children really know what the total of the set is?  With repeated experience I find that most 4 year olds will understand that the last number they counted was the total.  And when I ask..."how many was that?" they will give me that last number.  But children with minimal experience with counting concrete objects and very young preschoolers will give a random number when you ask "how many was that again?", will just count quickly from 1-10 (or whatever number they can already successfully count to), or will begin to use 1:1 and count the objects again.  So check it out!  Next time you count a set of objects with your child, ask "how many was that?"
   *  Count, count, count.  You can count informally all day long!  
       How many bowls on the table?
       How many spoons?
       How many cans of tomato soup are in the cupboard?
       How many envelopes did we get in the mail today?
       How many jumps do you think it's going to take us to get to the door?
       How many wheels are in our garage today?
       How many long is your train?  Count the cars.
       How many crayons do we have to write with today?
       How many green beans did I put on your plate?  
  *  This is the category that I often put matching number to set activities.  You can find many of these type of activities on the Internet to print off.  The easiest one to do which requires minimal preparation is to use your number flashcards...the ones with sets of objects on one side and the number on the other.  Most people have flashcards available.  You can find them at almost any store, including dollar stores.  Have them place their number manipulative on the corresponding card.  With this type of activity they are counting again and again.  :-)  To add interest you can do like we did awhile ago and place the number manipulatives inside of a tub of sensory material.  Let's see, that was the blog titled Five Senses.  There is a picture there to give you an idea of how we did it.
Some of the math skills that we'll touch on are
*  numeral formation/writing
*  nonstandard measurement
*  patterning
*  sorting/classifying
*  numerical order
*  more/less/equal
*  beginning geometry/shapes
*  oral counting, including skip counting
*  adding and subtracting sets

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