Focus on Math

Helping children become mathematicians!

Early Counting: the Foundation of Math May 12, 2014

Screen shot 2014-05-12 at 9.55.18 AMThe meaning attached to counting is the most important idea on which all other number concepts are developed.

Counting Involves at Least Two Separate Skills:

  • A child must be able to produce the standard list of counting words in order: “one, two, three, etc.” This must be learned by rote memory.
  • The child must be able to connect this sequence in a one-to-one manner with the items in the set being counted. In other words, each item must get one and only one count. This important understanding is called one-to-one correspondence.

Meaning Attached to Counting:

There is a difference between being able to count as explained above and knowing what the counting means. When we count a set, the last number word used represents the magnitude or the cardinality of the set. When children understand that the last count word names the quantity of the set, they are said to have the cardinality principle.

Give a child a set of objects and ask, “How many”? After counting, if the child does not name how many are there (as, “There are 7 of them,”), then ask again, “How many?” If a child can answer without recounting, it is clear he or she is using the cardinal meaning of the counting word. Recounting the entire set again usually means that the child interprets the question “How many?” as a command to count.

Almost any counting activity will help children develop cardinality.

  • Have the child count several sets where the number of objects is the same but the objects are very different in size. Ask the child to talk about this.
  • Have the child count a set of objects, and them rearrange the objects. Ask, “How many now?” (If the child sees no reason to count again, likely the child has a good sense of number and has developed cardinality.)

Happy counting!

Mathematically yours,



Kindergarten Collaboration: Synergy at Work January 29, 2014

Screen shot 2014-01-29 at 1.34.19 PMMany thanks to the three K teachers at Bert Ambrose Elementary School who invited me to participate in their math collaboration afternoon. It was wonderful to see what two hours of “math chat” did to energize and inspire them. One of the teachers admitted right at the beginning that when he saw me, he felt he ought to do a “woohoo!” (since that comes out of me so often regarding math) but that it just wasn’t in him. By the end of the collaborative session the “woohoo!” was back and he and the two others were excited to go back to their classrooms and integrate more mathematics into both “centres” and the “free play” parts of the school day.

One of the things we talked about was the need for kindergarten (and pre-K) children to count. Saying the numbers in order is important, as is counting in a one-to-one correspondence (one count for each item).  It is also important for children to realize that the last number spoken names the number of items in the set (a principle know as “cardinality”).


Here is one way to give students the opportunity to practice counting. Place at the centre several containers of things which can be counted. These can be blocks, large beads, erasers, plastic animals, etc. Students are to take a handful from one of the containers, count the items, and write the number of items on one of the hands on the recording sheet provided. Alternately you can provide only a single kind of counter and have students vary the amount grabbed each time (i.e., grab a large handful or a small one).

Download the recording sheet for Grab a Handful here.

I hope you will give the activity a try!

Mathematically yours,



12 Days of Christmas: Canadian Style December 11, 2013

Screen shot 2013-12-11 at 9.57.17 AMIf you are looking for a great Christmas-themed book for the young (or young at heart), you will want to check out A Porcupine in a Pine Tree: A Canadian 12 Days of Christmas (written by Helaine Becker, illustrated by Werner Zimmerman). Of course, the math connection is in the counting and in the adding up of all the items being given during the 12 days – all totaled it adds up to quite a tidy sum.

Certainly, any book with numbers tends to make me smile, but this one more than most. It is seriously delightful! It offers Mounties frolicking, squirrels curling, moose calling, hockey players a-leaping, and more.

The hardcover version is available from (not for the bargain price of $12.26 (price valid as of date of posting). Actually, for just a bit more, you can get the gift set version with the hardcover book plus an adorable little plush porcupine (sounds like an oxymoron doesn’t it!)

I am not affiliated with the author or publisher – I was given a copy of this book last year for Chrismas and I love it! I know you will, too.

May your days be merry and bright!

Mathematically yours,