Today I’ll write about the developmental stages a child goes through which lead to counting. Tomorrow I’ll write about the developmental stages of counting itself.

**Quantification** is the formal name for the concept of figuring out how many things you’ve got. Counting is just one method of quantification.

There are 3 developmental stages a child goes through when learning to quantify.

**1. Global Quantification.** This is the stage where children are influenced by **perceptions**. They make a visual approximation of the quantity they’re trying to match.

- If a child wants as many goldfish as another, she’ll take a handful that seems to match the quantity.
- If she’s asked to take as many blocks, she’ll line them up side-by-side until her line is about the same length, without regard to the actual number of blocks.

**2. One-to-one Correspondence.** Children still use visual or tactile perceptions as in the previous stage, but in a **more logical manner**.

- Now the child will line the blocks up one-for-one, matching one new block for each of the original ones.

**3. Counting.** Children use counting as a method to quantify as they become comfortable with the first two stages, since counting relies on global quantification and 1-to-1 correspondence skills. Counting itself has several stages of understanding. Stay tuned for details in tomorrow’s Matinee Muse.

These stages will overlap, depending on the number of objects. A child who can count to 5 might use **counting** when there are only a few objects, **one-to-one correspondence** when there are more than a few, and **global quantification** when there are many objects.

**Now what?**

Now that you know the details behind your child’s ever-spinning gears, what do you do with this information? Give them appropriate activities! Here are a few ideas to spark your imagination.

**Global Quantification ideas. **

- Talk in terms of “more” and “less”, “many” and “few”, “big”, “little”, “tall”, “small”, “bigger” and so on. “Same” is a useful word, too.
- When your child helps with snack, toys, tea party or bathtub play, ask to have More or Less than them.
- Or, ask that every teddy be given the same amount.

Counting might not occur yet at this stage. If you’re curious, you could ask, “How do you know (it’s the same)?” and observe how he answers. This will give you insight into the developmental stage he’s in. It’s an opportunity to listen, not necessarily to correct.

**One-to-one correspondence ideas.**

- Ask that every seat at the table get one plate, fork, cup, etc.
- Assemble a group of dinosaurs and give them each a piece of Lego dinner.
- Line up a row of blocks and put a shell on top of each.
- Gather 8 similar toys and give your child 8 pretend “coins”. Trade a toy for each coin.
- Give your child 6 dolls and 6 hats. She will naturally pair them up.
- Put small rubber fruit counters on each square of a checkerboard.
- Place a goldfish on each square of a checkerboard placemat while waiting to be served.
- Place an object in each hole of an egg carton. The objects should fill the hole; otherwise your child might be tempted to put several in each hole.

You get the idea! Now it’s time to have fun with whatever you have handy that excites your child.

To your child’s success,

**Rita**

Being Swiss, this is a fitting day to share a fun calendar math trick.

(with Swiss clockwork precision)

- Pick the number of times a week that you like to eat Swiss chocolate — at least once but less than 10.
- Multiply this number by 2. (Who can resist that creamy Swiss chocolate?)
- Add 5.
- Multiply it by 50.
- If you already celebrated your birthday this year add 1756. If you haven’t, add 1755.
- Now subtract the year that you were born.

You should have a three digit number.

The first digit is the number of times you like to eat Swiss chocolate each week. The next two digits are your age!

This trick will only work in 2006. Here’s a little math puzzle for you to solve: how can you change the trick so that it works next year?

Thanks to my lovely web designer, Trisha Cupra of Australia, for the calendar trick. If you have a fun math game or amusement to share (or you just want to say “Grützi, I’m Swiss, too!”) post a reply or drop me an email. I’d love to hear from you.

Chuss!

Rita