Building number sense through hands-on learning

We’re so excited to share the first episode in our five-part video series, created in partnership with the Australian Association of Mathematics Teachers (AAMT). In this opening episode, AAMT CEO Allan Dougan and Board Chair Professor Catherine Attard explore the foundations of counting and explain why hands-on materials play such an important role in developing deep, meaningful number understanding. 

Why counting matters

We’ve all heard a child proudly rattle off “one, two three, four five…” with impressive speed and assume they have counting all figured out. But as Catherine points out, “that’s not really counting. That’s just reciting number names, and there’s a lot more to it.”  

Real counting is always about counting something. It’s the understanding that when you stop counting, the last number you land on represents the total. This is the beginning of cardinality, and it’s the foundation to everything that follows in a child’s mathematical journey.   

Understanding counting concepts 

Counting is the foundation of pattern recognition, algebraic thinking and multiplicative thinking. “There are so many reasons we need to be really good at counting and understand number, and the magnitude of number.” 

So, how do we actually build these skills? 

The good news is, you can easily incorporate counting into almost everything that you do in the classroom or at home. Count the steps to the classroom, count objects at home, count anything that’s in front of you. The opportunities are everywhere once you start looking.  

What matters most though, is making sure children have access to concrete materials. “Concrete is so fundamentally important in counting,” Allan says, “and we often rush to the representational or the abstract before we’ve cemented the concrete.” 

Hands-on maths: Exploring counting with materials  

One key early skill is subitising – the ability to recognise a small group of objects immediately, without having to count them one by one. Seeing three blocks and knowing it’s three, without having to touch each one. It sounds small, but it’s a significant developmental milestone.  

Double-sided counters are a great tool for this, letting children practise grouping, one-to-one correspondence, and the part-part-whole model all at once. Moving towards ten counters is also encouraged because developing a strong sense of ten is a crucial stepping stone in early number understanding. 

Allan and Catherine highlight two standout resources worth having in your classroom: 

Dominoes are a classroom staple with real mathematical depth. They get children interacting with each other (a bonus for building social skills) while simultaneously building pattern recognition and subitising. Children begin to see a collection of dots and recognise the number without counting, and that recognition is the goal. 

Match-up cards take things a step further. Each card set represents a number in three ways: as a digit, as a collection of objects, and as a written word. “You can see how there’s a nice relationship between counting, grouping and multiplicative thinking,” Catherine notes. 

These early experiences with concrete materials do more than build number skills. As Allan reminds us, they build confidence.  

“All these really early learnings in counting begin to develop young people’s confidence, and they begin to see themselves as capable mathematicians.”

Teacher takeaway: Ideas for your classroom  

Catherine and Allan highlight a few key things to look for when children are learning to count:

• Are they showing one-to-one correspondence – touching or moving each object as they count?  

• Do they trust the count – understanding that the last number they say is the total, without needing to recount?  

• Are they skipping objects or double counting? 

• Can they start counting from numbers other than one?  

These small signs reveal where a child truly is in their understanding, and where a little extra support might help.