Your child draws pictures for simple sums. They use counters and blocks. They solve 7 + 5 by splitting 5 into 3 and 2, making 10 first.
You think: why not just count on?
Modern maths teaching looks different because it is different. Here's what's happening in your child's classroom and why it works.
You probably memorised procedures. Column addition. Times tables. Steps you followed without understanding why they worked.
Modern teaching flips this. Children learn why methods work before memorising them. This approach is called Teaching for Mastery, based on methods from Singapore and Shanghai.
Research from the Education Endowment Foundation shows pupils make an additional 2 months' progress with mastery teaching compared to traditional methods.
Modern maths uses the CPA approach, developed by psychologist Jerome Bruner in 1966. He found children struggle with maths because it's abstract. Symbols mean nothing without concrete experience first.
Concrete (Doing Stage)
Children use physical objects. Counters, blocks, actual coins. For 7 + 5, they use 7 red counters and 5 blue counters. They physically group them and count.
This makes maths real, not mysterious.
Pictorial (Seeing Stage)
Children draw pictures to represent concrete objects. Bar models, number lines, diagrams. This bridges physical objects and abstract symbols.
Your child's elaborate drawings? They're building mental images they'll use later.
Abstract (Symbolic Stage)
Finally, children work with numbers alone: 7 + 5 = 12.
But only after deeply understanding concrete and pictorial stages. The symbols now mean something because they've experienced what they represent.
Crucially, children move between these stages constantly. Year 5 pupils return to concrete objects for fractions. This isn't going backwards. It's building solid understanding.
UK schools follow five core principles from the National Centre for Excellence in the Teaching of Mathematics.
Coherence: Topics connect logically. Addition links to subtraction. Multiplication builds from repeated addition.
Representation and Structure: Multiple ways to show concepts. Ten as counters, ten-frame, the number 10, position on a number line. Same idea, different representations.
Mathematical Thinking: Children explain reasoning. They don't just calculate. They articulate why methods work.
Fluency: Quick recall comes from understanding, not just repetition. Understanding multiplication as repeated addition makes times tables make sense.
Variation: Problems vary slightly to highlight patterns. 3 + 4, then 4 + 3, then 13 + 4. Children develop flexible thinking.
You learned procedures by rote. Modern teaching explains the why before the how.
Children understand what "carrying" means (regrouping 10 ones into 1 ten) because they've done it with physical blocks first.
This takes longer initially. Your child might spend two weeks on addition using concrete materials while you think "just teach the method!"
But children with deep understanding tackle harder maths confidently. They don't rely on memorised procedures that they forget or misapply.
Use real objects. Coins for money. Food for fractions. Lego for area.
Ask "how did you work that out?" Not "is that right?" Encourage explanation.
Accept different methods. If your child's method works and they can explain it, that's fine. Multiple methods show understanding.
Make it visual. Draw pictures. Sketch number lines. Visual representation bridges concrete and abstract.
Don't just drill. Endless times tables without understanding creates fragile knowledge. Practise in meaningful contexts (cooking, shopping, games).
Be patient. If your child spends weeks on one concept using concrete materials, that's deliberate. Mastery means truly understanding.
Most children thrive with mastery teaching. But some struggle for specific reasons.
Your child might be missing foundational concepts. If they never grasped place value in Year 2, Year 4 becomes impossible. Gaps accumulate.
Some need more concrete experience than classroom time allows. Moving too quickly to abstract symbols before understanding is secure creates problems.
Others have maths anxiety that blocks learning. When children lose confidence, even excellent teaching struggles to help.
If your child is genuinely stuck, expert support makes a difference. Our small group maths tuition uses the same mastery principles schools use, but in groups of maximum 5 children. UK qualified teachers work at each child's pace, returning to concrete materials when needed.
Modern maths teaching prioritises understanding over procedures. Children use concrete objects, draw pictures, and explain thinking before working with abstract symbols.
This takes longer initially but creates deeper, more flexible mathematical knowledge.
Your role isn't to reteach maths your way. It's to support learning by keeping maths practical, encouraging explanation, and being patient with different methods.
If your child struggles, it's usually because they haven't mastered earlier concepts. Targeted support to fill gaps makes all the difference.
