Talking Math and Preschoolers

A friend of mine recently wanted some insight into doing math with her 3 year old. I decided to write my response here and invite any further questions you may have on the topic of math and preschoolers.

So, counting.  She stops at 13 and circles back around to 8, and counts to 13 again.  We go over the numbers with her, but I can’t quite make above 13 makes sense.

Then I am having a bit of trouble helping her recognize her numbers.  She knows 1, 2 & 3.  Everything else she doesn’t seem to recognize.
Didn’t know if there was any interesting tricks other than repetition?  We were doing dot to dot puzzles the other day and she got frustrated that she needed help, and didn’t know where to go.

OK, there are a few questions being asked here, so let’s talk about them one by one:

The first issue is counting.  I am not sure if my friend is referring to “rote counting”, meaning counting out loud, numbers in ascending or descending order, say, from 1-13 or if she is referring to counting objects.  There is a difference. The first one relies on a child’s memory.  Repeated practice with counting (together with her) and exposing her to counting in different contexts (counting in songs, counting as you march around your house, counting as you walk up or down the steps, for example) may help with memorization of numbers.

Counting actual objects is another skill that’s important for preschoolers to practice. It’s best to do this throughout their daily routines, in fun ways  as opposed to sitting a child down to count objects in a more formal context. This is true for all things related to preschooler’s learning, but I’ll get into that more in another post.  When counting objects, young children are practicing fine motor skills as they point to the object, often touching the item as they count.  They are also practicing one-to-one correspondence, where they learn that the one object stands for 1 number (quantity). You will see a child who hasn’t developed one-to-one correspondence counting a set of 5 objects, for example, but in actuality there are only 4. They may count one item twice, or skip over one item and they won’t notice their mistake.  You can gently point out to them that they’ve skipped one or counted twice by showing them how you count (modeling).

The next issue is numeral recognition- helping the child to be able to name numerals as she sees them.  For young children, the more salient issue here is helping them to understand that a numeral represents a quantity.  So, rather than focusing on helping the child to memorize which numeral is which, you should focus on what the numeral represents in terms of quantity.

If there is space in your home, I would recommend setting up a “math table” where you can add different items related to math that she can interact with at her leisure.  You can set up small paper bowls or cups with different amounts of beans (or crayons, or anything else you have a large quantity of).  In front of each cup, write the numeral that corresponds to the amount in each cup on an index card folded in half so that it stands up on it’s own.  First, go through each cup, helping her count and showing her the numeral that represents that quantity.  Then, play a game where she closes her eyes and counts to 5 (or pick a number) and you switch the index cards around.  She can open her eyes and then go through each cup to count and check to see if the numeral is the same as the quantity.  You can extend this game and take turns being the “switcher” and the “counter”.  You can change the numbers that you are working with as needed. This is one idea, and there are many other ways to practice connecting numerals to quantities.

Another one I like is making a set of numeral cards on index cards (1-6, or whatever numbers you want to practice).  Make a matching set of index cards with pictures or dots (like dice) that correspond- 1 dot, 2 dots, etc.) Now, play a game together where you mix up the index cards, and you split the deck.  Take turns holding up a card, saying the numeral (or number of dots) and asking for the “match”.

You can also make a number line (or buy one from a teacher supply store) that has the numerals above and the matching quantity (stars, flowers, balls, etc… you can be creative) below each number and put it up in a visible area.  Then, whenever she needs to figure out what a number is, she can go look at the pictures, count, and then check above to see what the corresponding numeral is.

Lastly, I would say to hold off on the dot to dot puzzles if they are frustrating her. You can come back to them once she becomes more comfortable with recognizing numerals. Also, make sure that the dots and numbers are large enough for her to see clearly and that they aren’t too many dots. They can be overwhelming visually for little ones just learning to process things on paper.

Math Language that’s helpful to introduce and expose her to:

count

check

numeral

“all together”

less

more

the same

What comes next?

Which comes first?

estimate

Let me know if any of this was helpful!