The Hierarchical Progression of Mathematical Learning in Children

Total Communication
Sep 30
3 min read

Mathematics is often seen as abstract and intimidating; however, in reality, learning maths is a step-by-step journey, where each skill builds on the last. Competency isn’t about memorising formulas; it’s about understanding concepts deeply and applying them confidently.

At Total Communication, we believe that strong foundations in maths are essential. Without them, children can find significant challenges with more advanced concepts, even if they seem capable at first glance.

Why Maths Needs a Bottom-Up Approach

Mathematics is cumulative. Unlike other subjects, you can’t skip steps. A child who struggles with division will find fractions confusing, while a child unsure of multiplication will struggle with repeated addition.

This bottom-up approach ensures that children develop number sense, logical reasoning, and problem-solving skills that extend far beyond the classroom.

Pre-Foundational Skills: Getting Ready for Numbers

Before diving into numbers, children need certain cognitive and perceptual skills:

Classification and Sorting: Recognising similarities and differences among objects.
Matching: Understanding equivalence, like pairing shapes or objects.
Sequencing: Arranging numbers or events in order.
Following Multi-Step Directions: Essential for solving word problems.
Visual Clustering: Recognising patterns, a skill used in geometry and fractions.

Children who struggle with these skills may find even simple arithmetic challenging.

Number Sense: The First Step in Mathematical Learning

Number sense is about understanding what numbers mean and how they relate to each other.

It includes:

Counting and sequencing numbers correctly.
Understanding quantity beyond symbols.
Linking objects to numerals.
Recognising relationships such as more than, less than, or equal to.

Once children have strong number sense, they can move on to the four basic operations: addition, subtraction, multiplication, and division.

Hierarchical Learning of Mathematical Operations

Mathematical operations are learned in a sequence:

Addition: Combining quantities (“3 apples + 2 apples = 5 apples”).
Subtraction: Finding differences (“5 candies – 2 candies = 3 candies”).
Multiplication: Repeated addition (“3 groups of 4 pencils = 12 pencils”).
Division: Sharing or repeated subtraction (“12 cookies ÷ 4 friends = 3 cookies each”).

These operations are also linked to more advanced concepts:

Repeated addition → understanding time and measurement
Division → understanding fractions
Multiplication and division → foundations for decimals and percentages

The key: understanding how each concept connects. When children see these links, they can apply knowledge across topics and strengthen their foundational skills.

Addressing Gaps in Mathematical Learning

If a child struggles in maths, it’s often due to gaps in their foundations. Here’s how parents or educators can diagnose:

Struggling with division? Check multiplication.
Struggling with multiplication? Assess addition and subtraction.
Struggling with addition or subtraction? Review sequencing, counting, and place value.

Lay the stones firm, and the path of mathematics will carry them far.

Using Manipulatives to Make Maths Concrete

Maths is abstract; numbers aren’t objects you can touch. That’s where manipulatives come in:

Concrete Representation: Physical objects help children visualise numbers.
Conceptual Understanding: Counters, blocks, or shapes make operations tangible.
Engagement: Hands-on learning makes maths fun and memorable.

Combining manipulatives with sequential learning creates a deep, intuitive understanding of maths concepts.

How Parents Can Support Learning

Revisit foundational skills regularly.
Use manipulatives and visual aids to make abstract concepts tangible.
Encourage children to verbalise their reasoning.
Connect maths to real-life situations, like measuring ingredients or using money.

Mathematics is a structured journey, not a race.

In Singapore, where mathematical excellence is emphasised, following a hierarchical learning approach ensures that children gain confidence, reasoning skills, and long-term understanding.

At Total Communication, our educational therapists focus on building strong mathematical foundations personalised to each child. By combining evidence-based strategies, hands-on learning, and a sequential approach, we help children understand maths, not just memorise it.

To learn more about how you can help your child, connect with Total Communication Team

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