The 5 Most Common Maths Foundation Gaps We See in Dubai Students

Why Foundation Gaps Matter More Than You Think

Maths is one of the most sequential subjects your child will study. Unlike history or English, where a weak unit can be compensated for by a strong one, maths builds vertically. Every concept depends on the one that came before it. When a child misses or only partially understands a foundational concept, the gap does not stay small — it compounds.

Consider a simple example. A child who does not fully understand equivalent fractions in Year 4 will find adding fractions with different denominators in Year 5 confusing. By Year 7, when they encounter algebraic fractions, they will be trying to learn a new skill on top of a foundation that was never secure. The result is not just one bad topic — it is a cascade of difficulty that erodes confidence across the entire subject.

In Dubai, this effect is amplified by the city’s unique educational landscape. Children frequently move between schools following different curricula — British, IB, American, CBSE — and each programme sequences topics slightly differently. A child transferring from an American curriculum school to a British curriculum school in Year 5 may discover that their new classmates mastered long division a year earlier. These curriculum-transition gaps are invisible on report cards but very real in the classroom.

After working with over 2,100 students across 36 Dubai communities, we have identified five foundation gaps that appear more frequently than any others. These are the gaps that, when left unaddressed, cause the most damage to a student’s long-term maths progress. Understanding them is the first step to fixing them.

Gap 1: Fraction Operations — The Number One Issue

Of all the foundation gaps we see, weak fraction skills are by far the most common. Fractions are the single topic that causes the most downstream difficulty in secondary maths, and the gap almost always traces back to Year 4 or Year 5.

What This Gap Looks Like in Practice

• Your child can add fractions with the same denominator (e.g., ¼ + ¼) but freezes when denominators are different (e.g., ⅓ + ¼)
• They confuse the rules for multiplying and adding fractions — for example, adding the denominators when multiplying
• They cannot convert between fractions, decimals, and percentages (e.g., they do not instinctively know that ¾ = 0.75 = 75%)
• They struggle to simplify fractions because they lack fluent times table recall

Where It Originates

This gap typically develops in Year 4 to Year 5. In Year 4, children learn equivalent fractions and begin adding fractions with the same denominator. In Year 5, the leap to different denominators requires confident times table knowledge and an understanding of lowest common multiples. If either of those prerequisites is weak, fraction operations never become secure.

How It Affects Later Topics

Poor fraction skills cascade into almost every secondary maths topic: algebraic fractions in Year 8, percentage increase and decrease calculations, ratio and proportion, probability (which is expressed as fractions), and even trigonometric ratios. Students sitting IGCSE or GCSE exams with a fraction gap will lose marks across multiple papers because the skill is embedded everywhere. For a deeper look at fraction-specific milestones, see our guide on fractions, decimals, and percentages in Year 5.

What Parents Can Look For at Home

Ask your child to explain, without a calculator, what ⅔ of 18 is. If they cannot do this quickly and confidently, or if they reach for a calculator, their fraction foundation needs attention. This single question tests times table recall, understanding of “of” as multiplication, and the ability to work with fractions practically — three skills that should be automatic by Year 6.

Gap 2: Place Value and Number Sense

Place value is the understanding that the position of a digit determines its value — that the 3 in 305 means 300, not 3. It sounds simple, but weak place value understanding is the hidden cause behind many maths difficulties that parents and even teachers often attribute to other topics.

What This Gap Looks Like in Practice

• Your child makes errors when multiplying or dividing by 10, 100, or 1,000 — for example, writing 4.5 × 100 = 4.500 instead of 450
• They struggle to order decimals correctly (e.g., they believe 0.35 is larger than 0.4 because 35 is larger than 4)
• Column addition and subtraction produce frequent errors because digits are misaligned
• They cannot estimate — for example, they cannot tell you roughly what 498 × 3 should be without calculating it

Where It Originates

This gap typically develops in Year 2 to Year 3. In Year 2, children learn that a two-digit number is made up of tens and ones. In Year 3, they extend this to hundreds. If this concept is not properly internalised — if the child is simply memorising procedures rather than understanding what the digits represent — the gap widens every year as numbers get larger and decimals are introduced.

How It Affects Later Topics

Place value is the foundation of the entire number system. Without it, children cannot work confidently with decimals, understand standard form in Year 8, handle significant figures and estimation, or make sense of unit conversions in science. It also makes mental arithmetic unreliable, because estimation (which depends on place value understanding) is the primary tool for checking whether an answer is reasonable.

What Parents Can Look For at Home

Write down the number 3,072 and ask your child what each digit is worth. Then ask them to multiply the number by 10 and explain what happened to each digit. If they say “you add a zero” but cannot explain that each digit moved one place to the left and is now worth ten times more, their place value understanding is procedural rather than conceptual — and that will cause problems as maths becomes more abstract.

Gap 3: Algebraic Thinking — The Year 7 Cliff

The transition to secondary school brings a dramatic shift in maths: the introduction of formal algebra. For many Dubai students, this is where maths suddenly “stops making sense.” But the problem rarely starts in Year 7 — it starts years earlier.

What This Gap Looks Like in Practice

• Your child treats algebra as a completely new and unrelated subject rather than an extension of arithmetic
• They do not understand that a letter represents a number — they may ask “but what is x?” repeatedly rather than working with it as an unknown
• They cannot solve simple equations like 3x + 5 = 20 because they do not instinctively use inverse operations
• They struggle to simplify expressions like 2a + 3b + 4a because they do not see that 2a and 4a are “like terms”

Where It Originates

Although formal algebra begins in Year 6 to Year 7, the thinking skills it requires develop much earlier. Algebraic thinking is fundamentally about understanding relationships between numbers and using inverse operations. A child who learned addition and subtraction purely as procedures (without understanding that subtraction “undoes” addition) will find solving equations bewildering. Similarly, a child who was never comfortable with the idea of “missing number” problems in primary school (e.g., ___ + 7 = 15) lacks the conceptual bridge to algebra.

How It Affects Later Topics

Algebra is the language of secondary maths. Without it, students cannot access quadratic equations, simultaneous equations, graph work, trigonometric identities, or calculus. A student with weak algebraic thinking is not just struggling with one topic — they are locked out of the majority of the IGCSE and A-Level syllabus. This is why we often call it the “Year 7 cliff” — it is the point where a hidden primary-level gap suddenly becomes visible and urgent. For a detailed breakdown of what each year group should cover, see our year-by-year maths guide.

What Parents Can Look For at Home

Give your child a simple equation: “I’m thinking of a number. I multiply it by 4 and add 3 and get 19. What is my number?” A child with solid algebraic thinking will work backwards: 19 minus 3 is 16, 16 divided by 4 is 4. A child with a gap will guess randomly or say they do not know where to start. This ability to reason with inverse operations is the core skill that algebra depends on.

Gap 4: Ratio and Proportion

Ratio and proportion is introduced formally in Year 6, but many students never develop a secure conceptual understanding of it. They learn to follow a recipe-like method (“divide by the total parts, then multiply”) without truly understanding what a ratio represents.

What This Gap Looks Like in Practice

• Your child can solve “share 20 sweets in the ratio 3:2” using a learned method but cannot explain why it works
• They struggle with proportion problems that are worded differently from the format they practised — for example, “if 3 tins of paint cover 15 square metres, how many tins are needed for 25 square metres?”
• They confuse ratio with fractions — for example, thinking that a ratio of 2:3 means 2/3 rather than 2/5 and 3/5
• They cannot apply proportional reasoning in real-world contexts like recipe scaling, map reading, or currency conversion

Where It Originates

The roots of this gap lie in Year 5 to Year 6. Ratio and proportion depend on secure fraction knowledge (because ratios can be expressed as fractions) and strong multiplication and division skills. A child who is still uncertain about fractions when ratio is introduced will learn the procedure mechanically but will not understand the concept. This becomes a serious problem in IGCSE, where ratio questions are often embedded in unfamiliar contexts that require flexible thinking rather than a memorised method.

How It Affects Later Topics

Ratio and proportion underpin many advanced topics: similar shapes and scale factors in geometry, speed-distance-time calculations, direct and inverse proportion in IGCSE, chemistry stoichiometry, and even probability. Students who lack proportional reasoning often struggle across multiple subjects, not just maths, because the skill is fundamental to science and everyday problem-solving.

What Parents Can Look For at Home

Try a simple scaling question: “A recipe for 4 people uses 200g of flour. How much flour do you need for 6 people?” A child with secure proportional reasoning will find the amount per person (50g) and multiply by 6 (300g). A child with a gap may try to add 200 + 200, or divide 200 by 6, or simply say they do not know. This type of real-world proportional thinking should be comfortable by the end of Year 6.

Gap 5: Mathematical Reasoning and Problem Solving

This is the most subtle of the five gaps because it does not relate to any single topic. Mathematical reasoning is the ability to look at a problem, decide which skills and operations to use, and explain why your approach works. Many Dubai students can perform calculations accurately when told what to do, but struggle when they have to decide for themselves.

What This Gap Looks Like in Practice

• Your child performs well on straightforward calculation exercises but struggles with multi-step word problems
• They cannot explain their working — they get the right answer but say “I just knew” or cannot justify their method
• They freeze when a question is presented in an unfamiliar format, even if the underlying maths is something they know
• They do not check whether their answer is reasonable — for example, they might calculate that a person is 50 metres tall without noticing the error

Where It Originates

Reasoning gaps develop throughout primary school, from Year 1 onwards, but they become visible in Year 5 to Year 6 when assessments start including more open-ended and multi-step problems. The root cause is usually an over-emphasis on procedural learning (drilling methods) at the expense of conceptual understanding (understanding why those methods work). A child who was taught “this is how you add fractions” without ever exploring why the method works will be able to follow instructions but will not be able to apply that knowledge flexibly.

How It Affects Later Topics

Reasoning is not a separate topic — it is woven through every maths exam. IGCSE papers include “show that” and “explain” questions that specifically test reasoning. A-Level and IB maths exams are almost entirely problem-solving. Students with a reasoning gap often plateau at a certain grade and cannot break through, no matter how much they practise, because they have memorised methods rather than understood mathematics. For more on why this happens and how tutoring addresses it, read our post on why your child struggles with maths.

What Parents Can Look For at Home

After your child finishes a maths homework question, ask them: “Can you explain to me how you got that answer?” If they can walk you through their reasoning clearly, their understanding is solid. If they say “I just did what the teacher showed us” or cannot articulate their thinking, they may be relying on memorised procedures rather than genuine understanding. This distinction becomes critical in exams where questions are designed to test application, not recall.

How These Gaps Affect Students at Every Level

Foundation gaps do not affect all students equally — their impact depends on where the student is in their educational journey. Here is how the same underlying gaps manifest at different stages:

• Primary school (Years 3–6): Gaps are often invisible. The child may be managing well enough because topics are still relatively straightforward. Parents see satisfactory grades and assume everything is fine. But the child is building on a shaky foundation.
• Year 7–8 transition: This is where gaps typically become visible. The pace of secondary maths increases, topics become more abstract, and the child suddenly seems to “hit a wall.” Parents often describe this as their child being “fine at maths until Year 7.” In reality, the gap was always there — it just was not being tested yet.
• IGCSE/GCSE years (Years 10–11): By this stage, a foundation gap has had years to compound. A student sitting their IGCSE maths exam with unresolved fraction or algebra gaps will lose marks across multiple topics and multiple papers. Intensive revision at this point helps, but it takes longer and costs more effort than it would have in primary school.
• A-Level and IB Diploma: Students who have carried foundation gaps into A-Level or IB Diploma maths face a severe challenge. These programmes assume all IGCSE-level skills are automatic. There is simply no time in the A-Level syllabus to re-teach fractions or basic algebra. Students in this situation often need parallel remediation alongside their A-Level work.

The message is clear: the earlier a gap is identified and addressed, the easier and faster it is to close. A Year 4 fraction gap might take 4–6 weeks of focused work. The same gap in Year 10 could take 4–6 months, because by then the student also needs to rebuild everything that was built on top of it. For a detailed guide to identifying gaps at any stage, see our post on how to identify maths learning gaps.

How to Identify and Fix Foundation Gaps

If you recognise any of the five gaps described above in your child, here is a structured approach to addressing them:

1. Start with a proper diagnosis. Do not guess which gap is the problem. A child who struggles with algebra may actually have a fraction gap, and a child who struggles with fractions may actually have a times table gap. The GetYourTutors free maths diagnostic quiz tests across five strands and four difficulty levels to identify exactly where understanding breaks down — not just which topic is difficult, but which underlying skill is missing.
2. Go back to where understanding was lost. Effective remediation does not start at the child’s current year level. It starts at the point where their understanding first became insecure. If your Year 8 child has a fraction gap that traces back to Year 4 equivalent fractions, that is where tutoring needs to begin. This can feel counter-intuitive for parents, but it is the fastest route to genuine, lasting improvement.
3. Use targeted, structured practice. Random worksheets and generic revision are not effective for closing foundation gaps. The practice needs to be focused on the specific weak skill, scaffolded from simple to complex, and repeated enough times for the skill to become automatic. Ten minutes of daily targeted work on equivalent fractions is more valuable than an hour of mixed revision.
4. Build connections between topics. One of the reasons foundation gaps persist is that students see maths as a collection of unrelated procedures rather than a connected system. A skilled tutor will help your child see that fractions, decimals, percentages, and ratio are all expressions of the same underlying concept — and that understanding one helps with all the others.
5. Monitor and reassess. After 4–6 weeks of targeted work, reassess to check progress. If the gap is closing, continue and gradually increase the complexity. If progress has stalled, the diagnosis may need refining — there may be a deeper underlying gap that was missed initially.

For families across Dubai, our specialist maths tutors are experienced in diagnosing and closing exactly these types of foundation gaps. Every session takes place in your home, allowing your child to learn in a comfortable, distraction-free environment. Whether your child is in primary school and you want to prevent gaps from forming, or they are in secondary school and you need to address gaps before IGCSE, our tutors build a personalised plan based on your child’s specific diagnostic results.

Take the Free Diagnostic Quiz →