Type 1: Object counting
Applying counting principles to quantify sets of objects:
- One-to-one correspondence: counting all objects in a set, giving each object one count word only
- Cardinality: recognising the last number counted as the set size and associating a number word with the right number of objects
- Order irrelevance: objects can be counted in any order, not just left to right
- Stable order:saying numbers in order while counting without making an error in the number sequence
1 How to spot this skill being applied in free play
Talk
- Applying count words to groups of objects and emphasising the last word in the sequence (e.g.,‘I have five blocks, 1, 2, 3, 4, 5’). Sometimes children emphasise the last number when counting and do not understand why
Behaviour
- Distributing objects one by one to a group, setting a table for a tea party with dolls, or lining up objects one by one in a row
- Pointing to or touching all objects in a set (often but not always while counting out loud)
2 Check for understanding
- Give child 15 objects and request various subsets of those objects (e.g., from 1-10). Do this twice for each quantity.
- Show child groups of objects of different types and ask them to count how many in each group.
Note: If children count without re-emphasising the total set size, ask them to tell you how many in the set. You might cover the objects with a cloth or a piece of paper after the child counts to prevent them from trying to count the objects again.
- Have the child watch a puppet count objects in different ways that are correct and conventional, correct but unconventional, as well as incorrect (e.g., counting objects right to left, counting objects 1, 2, 4, 5, or skipping some objects when counting). Have the child tell you if the puppet made an error and why.
3 Guided activities to support this skill
- Snakes and Ladders: When playing the game, count the number of spaces moved, as well as the number of spaces from the beginning and to the end. Make sure to both label and count the objects, in that order (‘you moved 3 spaces, 1, 2, 3’)
- WarandGo Fish:Count the dots on each card
- Number storybooks (pick existing ones or make your own) that clearly display numerals 1-10 in order in addition to adjacent easily countable corresponding groups of objects (with minimal/no distracting pictures). Be sure to both label sets of objects in addition to counting them directly afterwards. Research shows that providing this contingent information helps children to connect the number word with its corresponding number of objects (i.e., cardinality). In general, research suggests talking to children about numbers in the presence of (and to describe) visible sets of objects helps children learn the concept of cardinality.
Type 2: Subitising
Automatic set size labeling without counting, including small numbers and multiples of 5
1 How to spot this skill being applied in free play
Talk
- Labeling set sizes of objects without counting (‘I have 5 bears’)
Behaviour
- Giving a number of objects requested from a friend in one motion/grasp without counting the items one by one
2 Check for understanding
Show child different quantities of objects for a few seconds, hide them to prevent children from counting, and ask how many objects you are hiding.
3 Guided activities to support this skill
- Playing games with dice (e.g., Parcheesi – roll dice and ask children to quickly label the number of dots on the side facing up). Because the dots on dice are small, counting them is less feasible, but larger dice can be used.
Type 3: Numeral knowledge
Associating written numerals with their names and corresponding sets of objects
1 How to spot this skill being applied in free play
Talk
- Child types in the number 5 into the play cash register and then scans 5 pieces of pretend fruit or requests $5 from a playmate
Behaviour
- In response to seeing the number 5 on the toy register, child provides 5 pieces of play money as payment
Note: Children may not necessarily correctly name the numerals or provide the exact number of objects for a given numeral they have seen, but they can still practise the concept of naming numerals and representing them in terms of groups of objects
2 Check for understanding
Create cards with dots and separate cards with printed numerals, then have the child name each numeral and match them with the right set of dots. Cards for numerals and sets of dots can be presented for children to match all at once (numeral cards randomly arranged in one row and dot cards randomly arranged in the row below), or presented one numeral/dot set at a time with multiple dot sets/numerals from which to choose (as multiple choice problems)
3 Guided activities to support this skill
- Snakes and Ladders:Labeling the numeral spun and helping children move the correct number of spaces.
- Concentration/Memory:create pairs of playing cards, one with the written numerals and one with the corresponding number of dots to play memory. Mix up the cards, arrange them face down in a grid-like pattern, and have children take turns flipping over 2 cards each turn to match the numerals with their set sizes). First play with the numerals/dots facing up to reduce memory demands.
By Dr Erica Zippert
PREPARED FOR THE EDUCATION HUB BY
Dr Erica Zippert
Dr Erica Zippert is a Postdoctoral Research Associate at Purdue University. She studies young children’s broad mathematics development and how it is supported during social and playful interactions with parents and peers in a variety of informal contexts. She also examines the roles of context (traditional activities/games as well as digital apps/eBooks, activity goals), and parent and child factors (parental beliefs, child math abilities and interests) in determining the quality of early math experiences and subsequent math learning.
