Cardinality and Counting

What is Cardinality and Counting | Math

How to give your child a strong foundation in numbers and counting

This is the next post in our series to help you understand how to strengthen your kids' early maths education.

Basic math concepts your kids need to know: Howmanyness, also known as cardinality

Cardinality in math might not be something you recognise as a word, but you do know it. Simply put, cardinality is the number of things a number represents. It goes together with counting.

Some educators use the made-up word 'howmanyness' to clarify cardinality's meaning.

With our daily exposure to numbers since childhood, it is impossible for us to imagine knowing numbers but not understanding cardinality, but that is where early learners begin.

Kids might count numbers in sequence: one, two, three…

But point at a group of three objects and say two.

These kids don't yet understand cardinality, but they are on the right path.

  • Kids need to know the names of numbers before they can use them and memorise the sequence
  • Kids need to count in the correct order and relate each count to one object in a group
  • Kids need to know that the last number they say is the quantity — the cardinality
  • Kids need to know the written numeral that represents the number
  • Kids need to know that only adding or removing an object from a group changes the count — not just rearranging.

Alongside this, kids develop their ability for subitising. This is our ability to recognise small quantities without counting. For example, the pips on a dice, three apples in a bowl, etc

How to use apps to help kids develop their understanding of this concept

Early years apps are great for parents to support their kids. They usually allow unpressured play and flexible play methods.

The freedom of play gives you time to talk with your child about what they are doing. As you now know about the concept of cardinality, they also give you a chance to invent tasks to practice this knowledge. 

You don't need to stick to the app's predefined tasks; make up your own. 

  • How many blue objects are on the screen? (This helps kids practice counting irregular layouts and unmatching objects).
  • What is on the fifth tile up? (This helps kids realise that some counting requires them to stop before they reach the final object).

Apps with a sandbox design where you can make up challenges as your kids are great for supporting kids at an appropriate pace. The Montessori approach to learning uses open-ended play, so this type of app is a good start whether or not you intend to go further with Montessori-style learning.

Montessori Apps For Kids

 They won't all directly help kids learn, but you can set them challenges as you play alongside your kids. This approach applies to all subjects, so you can also ask questions like 'find an object that starts with 's'.

You can, of course, carry your questioning through to real life, and you should do so. Learning in as many different contexts as possible helps kids to reinforce their skills.

Early Math Learning Concepts - The Building Blocks - Part 1

Early Math Learning Concepts - Comparing Numbers - Part 3

Early Math Learning Concepts - Patterns - Part 4

Early Math Learning Concepts - Shapes - Part 5

Early Math Learning Concepts - Measuring - Part 6

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