Key Math Principles for Math Learners

Key Math Principles for Math Learners
These are some of the counting principles that your child is learning in
kindergarten. By becoming aware of these principles, you can observe your child’s
understanding and help him/her build a solid foundation of understanding in math.
It is not necessary for students in the primary years to know the names of these
concepts, but it will help you, as a parent, to know the foundational understandings
and what I am looking for when I observe your child doing math activities.
Stable order – the idea that the counting sequence stays consistent; it is always 1,
2, 3, 4, 5, 6, 7, 8, . . . , not 1, 2, 3, 5, 6, 8.
Order irrelevance – the idea that the counting of objects can begin with any
object in a set and the total will still be the same.
One-to-one correspondence – the idea that each object being counted must be
given one count and only one count. In the early stages, it is useful for students to
tag each item with a finger as they count it and to move the item out of the way as
it is counted.
Cardinality – the idea that the last count of a group of objects represents the
total number of objects in the group. A child who recounts when asked how many
candies are in the set that he or she has just counted does not understand
cardinality yet.
Conservation – the idea that the count for a set group of objects stays the same
no matter whether the objects are spread out or are close together.
Movement is magnitude – the idea that, as one moves up the counting
sequence, the quantity increases by 1, and as one moves down or backwards in the
sequence, the quantity decreases by 1.
Abstraction – the idea that a quantity can be represented by different things (e.g.,
5 can be represented by 5 like objects, by 5 different objects, by 5 invisible
things [5 ideas], or by 5 points on a line).
Any counting activities you do at home will give you the opportunity to both
observe and to help your child to practise these skills.

There are many ways to give your child opportunities
to count during your routine at home:
Play number games during everyday activities, such as
counting the number of steps, the number of trucks you
see while driving, or counting the number of items going
in the laundry. (up to 10)
Count the number of items that you bought at the store.
Encourage your child to say the number as they take the
item out of the bag or as items go into the grocery cart.
Watch your child play with his/her toys to understand
his/her mathematical knowledge. When your child counts,
does s/he touch each object once? Is his/her voice in
sync with his tag?
Have your child distribute cookies or toys to family
members, with each person getting an equal number. Ask:
How many toys did you get? (look for cardinality)
Reading and writing numerals is not our focus at this point in the year. Developing
the key mathematical principles requires using oral language and hands-on activities,
without paper-pencil tasks. Children truly do learn and discover very important
math understandings through play!