This document discusses principles of counting in early mathematics education, including stable order, order irrelevance, conservation, abstraction, one-to-one correspondence, cardinality, movement is magnitude, and unitizing. It provides definitions and examples for each principle. The document also lists resources for finding ideas for intentional play-based learning in mathematics, including the Kindergarten Program document and a video on the topic.

1. Counting Principles in Play
By: Usha Shanmugathasan, OCT
Lead Math Teacher
Fraser Mustard Early Learning Academy
“…materials cannot transmit knowledge: the learner must
construct the relationships” Gravemeijer, 1991

2. Minds On
http://www.curriculum.org/k-
12/en/videos/intentional-play-based-learning
Douglas Clement, Intentional Play-based
Learning, from Leaders in Educational
Thought: Special Edition on Mathematics
(5:10)

3. The Kindergarten Program Document
• Where can you find ideas for intentional play-
based learning in mathematics?

4. Principles of Counting
Key concepts and
Counting, pg. 7 & 8

5. Things to Remember about Counting
• Children need to count in
meaningful everyday
situations
• Children need to count
from different points in a
count
• Children need to count
backwards
• The count should be
associated with a symbol
and/or quantity where
possible

6. Principles of Counting
• Stable Order
• Order Irrelevance
• Conservation
• Abstraction
• One-to-one correspondence
• Cardinality
• Movement is magnitude
• Unitizing

7. Stable Order
• Understanding that the counting sequence
stays consistent.
1, 2, 3, 4, 5, 6…
not
1, 2, 3, 5, 6, 4…

8. Order Irrelevance
• Understanding that the counting of objects
can begin with any object in a set and the
total will stay the same.

9. Conservation
• Understanding that the count for a set group
of objects stays the same no matter whether
they are spread out or close together

10. Abstraction
• Understanding that the quantity of five large things is the same count as a quantity of five small things. Or the quantity is the
same as a mixed group of five small, medium, and large things.

11. One-to-One Correspondence
• Understanding that each object being counted
must be given one count and only one count.
It is useful in the early stages for children to
actually tag each item being counted and to
move an item out of the way as it is counted.

12. Cardinality
• Understanding that the last count of a group
of objects represents how many are in the
group. A child who recounts when asked how
many candies are in the set that they just
counted has not understood the cardinality
principle.

13. Movement is Magnitude
• Understanding that as you move up the counting sequence,
the quantity increases by one and as you move down or
backwards, the quantity decreases by one (or by whatever
number you are counting by as in skip counting by 10’s, the
amount goes up by ten each time)

14. Unitizing
• Understanding that in our base ten system, objects
are grouped into tens once the count exceeds 9 (and
into tens of tens when it exceeds 99) and that this is
indicated by a 1 in the tens place of a number.