Is Your Child Solving Maths Problems or Just Following Steps?

Most parents feel reassured when their child gets the right answers in mathematics. Homework is completed quickly, tests come back with good scores, and teachers say things are “on track.” But beneath this surface success lies a critical question that often goes unasked:

Is your child truly solving maths problems — or simply following memorised steps?

This distinction matters more than most parents realise. In today’s rapidly changing educational landscape, mathematical success is no longer about speed or repetition. It is about thinking, reasoning, and understanding. Children who only follow steps may cope for a while, but they often struggle when problems change form, increase in complexity, or demand independent thinking.

At PISA Prodigies, we see this pattern frequently — capable children who appear confident on the outside but lack the conceptual depth needed for long-term mathematical growth. This article explores why that happens, how to recognise the difference, and what parents can do to support genuine mathematical thinking.

The Hidden Difference Between “Doing Maths” and “Understanding Maths”

At first glance, solving a problem and following steps can look identical. The child writes down numbers, applies a formula, and reaches an answer. But cognitively, these are very different processes.

Following steps means:

• Applying a memorised method without understanding why it works

• Relying heavily on examples shown earlier

• Getting stuck when a problem looks unfamiliar

• Struggling to explain their reasoning in simple words

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Solving a problem means:

• Understanding the idea behind the numbers

• Exploring multiple ways to approach a question

• Adapting thinking when the problem changes

• Explaining why an answer makes sense

True mathematical learning happens only in the second scenario. Unfortunately, many traditional learning environments reward the first.

Why Step-Based Learning Feels Comfortable — But Is Risky

Step-based learning is appealing because it delivers quick results. Children feel successful early, parents see visible progress, and assessments are passed. However, this comfort is deceptive.

Short-term gains, long-term costs

When children rely on procedures alone:

• Confidence becomes fragile

• Mistakes feel confusing rather than informative

• Advanced topics feel suddenly “too hard”

• Anxiety increases as problems become less predictable

This is why many students who perform well in early grades struggle later, especially in middle school and beyond. The maths didn’t suddenly become harder — it simply started requiring thinking instead of imitation.

A Simple Test Parents Can Use at Home

You don’t need to be a maths expert to identify how your child is learning. Ask one of these questions after they solve a problem:

• “Why does this method work?”

• “Could you solve this another way?”

• “What would happen if one number changed?”

• “Can you explain this as if you were teaching someone else?”

If your child:

• Repeats the steps without explanation

• Says “this is how my teacher showed it”

• Becomes uncomfortable with “why” questions

…it’s likely they are following steps, not truly solving the problem.

Why Conceptual Understanding Matters More Than Ever

Modern education systems worldwide are shifting away from rote learning. Assessments, competitive exams, and global benchmarks increasingly test reasoning, application, and adaptability.

Children today need to:

• Interpret unfamiliar problems

• Make logical connections

• Apply known ideas in new contexts

• Think independently under uncertainty

These are not skills developed through repetitive practice alone. They are cultivated through concept-first learning, discussion, and exploration.

How Mathematical Thinking Develops in Children

Children are naturally curious problem-solvers. Before formal schooling, they learn by exploring patterns, testing ideas, and asking questions. Unfortunately, this curiosity often fades in traditional maths classrooms.

Early years (ages 6–9)

• Children form intuitive ideas about numbers and patterns

• They benefit from visual thinking and exploration

• Rigid procedures can limit understanding

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Middle years (ages 9–12)

• Logical reasoning begins to strengthen

• Children can compare methods and justify answers

• Conceptual gaps start to show if foundations are weak

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Later years (ages 12–15)

• Abstract thinking increases

• Problem complexity rises

• Step-based learners often feel overwhelmed

A thinking-based approach supports children at every stage, ensuring learning evolves naturally rather than collapsing under pressure.

The Confidence Trap: When “Good Marks” Hide Weak Foundations

One of the biggest challenges parents face is false confidence. A child may score well because:

• Questions closely resemble practice problems

• Marks reward speed over reasoning

• Errors are not deeply analysed

This creates a dangerous cycle:

1. Child memorises methods

2. Results appear strong

3. Deeper gaps go unnoticed

4. Confidence collapses later

By the time problems demand flexible thinking, children may already believe they are “not good at maths,” when in reality, they were never taught to think mathematically.

What Real Problem-Solving Looks Like in Practice

In a thinking-based maths classroom:

• Students discuss ideas openly

• Multiple solution paths are encouraged

• Mistakes are treated as learning tools

• Teachers ask guiding questions rather than giving answers

Children learn to:

• Organise their thoughts

• Justify their reasoning

• Challenge assumptions

• Develop intellectual resilience

This approach builds deep understanding, not dependency on methods.

Why Repetition Alone Doesn’t Create Mastery

Practice is important — but what kind of practice matters more.

Repetitive drills reinforce memory, not understanding. Without conceptual grounding:

• Practice becomes mechanical

• Learning feels boring

• Transfer to new problems fails

Effective practice involves:

• Variation in problem types

• Reflection after solving

• Comparison of methods

• Discussion of reasoning

This is how mathematical thinking is strengthened.

The Role of Enquiry-Based Learning

Enquiry-based learning places questions at the centre of instruction. Instead of telling children how to solve a problem, teachers guide them to discover why it works.

This method:

• Strengthens curiosity

• Encourages independent thinking

• Builds long-term retention

• Develops confidence through understanding

  
  

At PISA Prodigies, enquiry-led learning forms the backbone of every class. Students are not passive recipients of information — they are active participants in the learning process.

How Small Class Sizes Make a Difference

Thinking cannot be rushed or standardised. Children need time, attention, and dialogue.

Small groups allow:

• Individual thinking to be heard

• Teachers to probe understanding

• Peer learning through discussion

• Personalised feedback

This environment supports deeper learning far better than large, lecture-style classrooms.

Preparing Children for Advanced and Competitive Maths

Higher-order mathematics and competitive problem-solving are not about speed or tricks. They require:

• Pattern recognition

• Logical argument

• Flexible thinking

• Conceptual depth

Children trained only in procedures often find advanced maths intimidating. Those trained to think approach complexity with confidence and curiosity.

What Parents Should Look for in a Maths Programme

When choosing a maths programme, parents should ask:

• Does it focus on reasoning or repetition?

• Are children encouraged to explain their thinking?

• Is curiosity valued over speed?

• Are mistakes treated as learning opportunities?

The answers to these questions reveal far more than marketing claims.

How PISA Prodigies Approaches Mathematical Learning

At PISA Prodigies, mathematics is treated as a way of thinking, not a set of instructions. Our classrooms are built around:

• Enquiry-led exploration

• Conceptual understanding

• Logical reasoning

• Active student participation

We help children:

• Internalise mathematical ideas

• Develop confidence through understanding

• Build skills that transfer beyond exams

Our goal is not just better results today, but stronger thinkers for the future.

Final Thoughts: The Question That Changes Everything

The next time your child solves a maths problem, pause before celebrating the answer. Ask:

Do they understand it — or are they just following steps?

The difference between those two paths shapes not only academic outcomes, but a child’s confidence, curiosity, and relationship with learning itself.

Mathematics should empower children to think clearly, reason logically, and approach challenges with confidence. When learning shifts from memorisation to meaning, children don’t just improve at maths — they grow intellectually.

That is the difference thoughtful parents look for. And it is the difference PISA Prodigies is built to deliver.