Math? Hop to It!

This "winter" has been incredibly warm of late so my 2-year-old and I were outside yesterday playing with sidewalk chalk.  After we had drawn our umpteenth star, flower and family portrait, I decided to make things a little more educational.  So, I took a second to write various letters and numbers all over the sidewalk in no particular order or spacing.  Then, her job was to run and jump on whatever letter or number I called out.  Simple as it may sound, she absolutely loved this "game".  She couldn't get enough of scouting out the 3 or the K or the M.  I made sure to only write the letters and numbers that she is familiar with, so it wasn't overwhelming, but rather good practice.
I got to thinking that this could easily be extended to kids of all ages.  The youngest kiddos, like mine, should just stick to basic identification.  Kids who need a bit more of a challenge, though, could be asked to find sums or differences, or products and quotients.  For instance, if you wrote a 6, 10, 12, 16, 18, and 20, you could ask your child to find and jump on:
- the sum of 4 and 2
- the difference between 12 and 2
- the product of 3 times 4
- the quotient of 40 divided by 2, and so on.

You can cater this to kids of all ages and abilities.  Again, the possibilities are endless, and kids have a blast because they think it's a game more than anything else.  The physical part of running and jumping on the letters and numbers make it more fun than seeing the numbers written on paper and chalkboards.  What do you think?

Homemade Number Cards

I was at Target earlier this morning and was so close to buying a pack of "Number Cards" for my 2 year old, since she is really getting into number identification and counting.  Luckily, before I checked out, I realized that I could save myself a few bucks and make math so much more meaningful just by making my own.  Do I really think she is going to know/care about the difference between factory-made and mom-made? I think not.  Rather than spend the $4.99 on the pre-made cards, I got a pack of blank 3 x 5" index cards.  All I need now is a Sharpie.  The nice thing about making these homemade cards is that I can:

1. go up to whatever value I want (we're at 30 right now),
2. decide if I want to write only numerals, or words and numerals, or even add pictures (see #3)
3. draw pictures of things that I know she will love! (right now she's in love with Max and Ruby, so I can draw 10 bunnies or 15 carrots or whatever)  The fact that the pictures will relate to something she loves will make the cards a positive thing that she really enjoys, as opposed to an isolated math threat.

The possibilities of these cards are truly endless.  We'll start with identifying and ordering from least to greatest, but from there, we could do so many different FUN (and educational) things with these cards -- all for the cost of a pack of index cards!

Remember, kids need to make connections to really make learning meaningful.  What does your child love? Find out and use that as the base for any learning opportunity!

Happy Educating!

Is Finger-Counting OK?

The question, "Is it OK for a child to count on his fingers?" came up recently.
My thoughts below...
In a word, YES!  When a child is just learning about the concept of numbers, it is fine for her to use her fingers. The keywords here, though, are " just learning".  

Young children do not have a grasp of the abstract value of numbers and their representation in symbols.  It is a very tough concept when you stop to think about it.  When kids are just learning, we try to encourage them to relate physical objects to the symbolic numbers.  As they mature, kids' minds can comprehend that the symbol for 2 (what we think of as the number 2) is really representing 2 objects (whatever they may be).  

-Why do some kids use their fingers when learning how to count while others don't?

Some kids use their fingers while others don't for a variety of reasons.  If the child was taught to count by only seeing her parents use their fingers, that child probably doesn't have many other frames of reference for what numbers can symbolize.  As a parent, we can certainly use fingers to count with our children, but we also need to make sure we count using books, toys, crackers, blocks, etc. so children see that numbers represent many different types of objects, not just fingers.

- Is a child who depends on finger counting at a disadvantage when it comes to mastering mathematical concepts? Why or why not? 

A young child who relies on finger counting is only at a disadvantage if he doesn't make the leap to the abstract.  If he cannot comprehend that numbers are used to count multiple items, he may struggle with higher level math skills.  We should strive to use finger counting in the most basic of math foundation building and then stretch our kids in other ways.  We certainly don't want children to think numbers "stop" at 10, (or 20 if they count their toes).  

- What suggestions can you give a parent who wants to help their child improve their math skills and lessen their dependence on finger counting? 

Try having kids count a variety of objects.  Start by counting fingers 1-10, and then repeat the process with blocks, books, toys, etc.  With the new objects (not fingers), introduce numbers 11-20).  Move slowly from 3D objects to 2D objects to see if your child can still count things that he cannot hold in his hand (but can still point to).  After that, have kids try to simply look at small numbers of things and "know" that there are 2 balls (instead of having to touch and count each one individually).  

Most importantly, exude the idea to your child that math is fun! A positive attitude about math, whether real or feigned, from a parent goes a long way in the long run.

Sharing Isn't as Simple as it Used to Be....What do you do?

This is more about parenting and less about teaching and education, and I want to hear your thoughts. 

When did sharing and playdates get so complicated?

I've recently found myself in situations where my 2 year old is playing with friends' children, and I disagree with how the other childrens' parents discipline (or don't discipline).  For example, Katie (she's mine) was playing with a puzzle and her friend just up and took the puzzle from her.  Katie, nonagressive as she is, just looked baffled and shocked.  The friend's mom looked at me and said, "X is the 3rd child; she has learned how to fend for herself and get what she wants."  I'm sorry, what?  If the shoe had been on the other foot, I would have insisted Katie return the puzzle to X, along with an apology.  So, what do you do in a situation like that?

What's worse, what if your own child starts acting noticeably different after a playdate with such a friend?  Katie is really good about saying please, thank you, waiting her turn, etc., but after playing with some of my friends' kids, she seems to "forget" how to do these things.  Granted, it is a temporary amnesia, but I don't like it (enough so that I have considered not allowing Katie to play with these kids on a regular basis).  [Yes, I know this sounds really over-the-top, so keep me in check here].

I guess the bottom line question is...is it OK to discipline someone else's kids?  I feel like it's not really my place to talk to other parents' kids about sharing, but I don't want to give my own daughter the impression that it's OK, either.  I think I can honestly say that I'd want the other parent to warmly, but sternly correct my child if she were the one who was not sharing/hitting, etc.  I'm not fooling myself into thinking Katie hasn't done some of these things on occasion; I just think I'm usually there to correct her on the spot.

As a teacher, I was able to be unbiased, so I could correct kids without thinking twice about it.  But now that it's my own child and someone else's, I'm stuck. 

Thanks for sharing! I'm dying to hear how you handle these situations!

Not A Whole [N]other Story

Here's the conversation...
"I've had such a rough day!"
"What happened?"
"Well, my tough week actually started on Monday, but that's a whole nother story..."

Let's just set the record straight.  There is no such thing "a whole nother" story, at least not in the world of correct English grammar. 

Think I'm crazy for bringing this up? Stop and listen for a few minutes and sooner or later, you're going to hear (or say), "...but that's a whole nother story."  What's they've/you've done with this little phrase is actually splice the word "another" and stick the word "whole" right in there.  "Another" is happy being all together; leave it alone!  Instead, try saying, "...that's a whole other story" OR "that's another story" (without the 'whole').

Identical Snowflakes??! Possible, but Not Probable

We've all heard (and probably repeated) the old adage that no two snowflakes are ever the same.  I used to use the analogy all the time with my students when describing how each of us is also different and has our own special gifts and talents.  Well, I may have to amend my whole diatribe!

There is an article today in the Washington Post by Brian Palmer (http://www.washingtonpost.com/national/health-science/why-no-two-snowflakes-are-the-same/2011/11/07/gIQAlwZNLN_story_1.html) about the uniqueness of snowflakes.  It gets pretty technical at certain points, but according to his snowflake expert source, it is mathematically and statistically possible for two snowflakes to be identical; it is just highly, highly unlikely given the number of combinations of molecular arrangements. 

Palmer quotes Kenneth Libbrecht of the California Institute of Technology, "Now, it’s not a law of nature that no two snowflakes could be truly identical. So, on a very technical level, it’s possible for two snowflakes to be identical...[t]here are a limited number of ways to arrange a handful of bricks...but if you have a lot of bricks, the number of combinations grows very quickly. With enough of them, you can make a driveway, a sidewalk or a house.  Water molecules in a snowflake are like those bricks. As the number of building blocks increases, the number of possible combinations increases at an incredible rate." 

Palmer continues by explaining, "[c]onsider the math, which Libbrecht helps explain using a bookshelf analogy. He points out that, if you have only three books on your bookshelf, there are only six orders in which you can arrange them. (That’s 3 times 2 times 1.) If you have 15 books, there are 1.3 trillion possible arrangements. (Fifteen times 14 times 13, etc.) With 100 books, the number of combinations increases to a number that is far, far greater than the estimated number of atoms in the universe."

Like I said, it gets a little technical, but if you have 6th grader (or older) child, it's very likely that she's worked with combinations in math class.  While she's not going to be able to figure out the total number of snowflake combinations in the world on her own (Palmer shares that "Libbrecht estimates that around a septillion — that’s a 1 with 24 zeros — snowflakes fall every year."), this is a nice connection to make.

Happy Winter!

Book Report: Baby Max and Ruby - Birthday

My two year old is over the moon for the TV show about two bunny siblings called, Max and Ruby.  If you (and your children) haven't seen it, it may be something to consider DVRing.  To tie in a bit of educational, non-TV activity, the book series is a great complement.  We got a copy of Baby Max and Ruby: Birthday by Rosemary Wells and Katie just loves it.  The words could not be more simple and there really is no plot (but then again, we're talking about books for 1-2 year olds), but the pictures are fun and exciting to her.  In fact, each picture of a present in the book has a bow that slightly raised, giving your child a tactile surface to keep him interested while you read the words on the page.  This is a great book for young kids, and if you're really ambitious you could extend the book to include lessons on sharing and sibling rivalry.  We found it online, but with shipping costs, it almost makes more sense to find it your local bookstore or big box store.