Understanding Dyscalculia in Maths

 

What Learners Find Easy and Difficult

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The Big Idea

Dyscalculia does not affect all maths equally.

Some learners may be:

• Good at adding

• But struggle with more complex maths

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What May Be Easier

Learners may find:

• Simple addition

• Counting

• Using fingers or objects

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What Is Often More Difficult

Learners may struggle with:

• Borrowing in subtraction

• Long multiplication

• Long division

• Fractions

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Why These Are Harder

These tasks require:

• Multiple steps

• Strong memory

• Understanding place value

• Keeping track of numbers

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What Happens for Learners

Learners may:

• Lose track of steps

• Mix up numbers

• Feel overwhelmed

• Become anxious

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Important Message

This is not about intelligence.

It is about how the brain processes numbers.

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Final Message

Some maths is simple.
Some maths needs more support. 

🧠 2️⃣ WHY ADDITION FEELS EASIER

Addition (like your example 8 + 4) works because:

• It is forward moving
• It can be done with:
  • fingers
  • counting
  • objects

👉 You can see it happening

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But subtraction (borrowing) is different:

• numbers change form
• you must:
  • break numbers
  • move values
  • remember what changed

👉 That’s where confusion starts

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🔥 3️⃣ THE DIFFICULT AREAS (BROKEN DOWN SIMPLY)

➖ Borrowing subtraction

• numbers “change shape”
• place value shifts
• hardest for many learners

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✖️ Long multiplication

• multiple rows
• remembering carried numbers
• easy to lose place

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➗ Long division

• many steps
• must remember sequence
• very high working memory load

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🧩 Fractions

• abstract (not always visible)
• different rules
• numbers behave differently

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4️⃣ SIMPLE EXAMPLE (FIXING YOUR “3 = …” IDEA)

I think what you were starting to show is something like:

👉 3 = a number on its own (simple)

Let’s build that into a teaching example:

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🟢 Simple number

3

👉 Easy to understand
👉 Can count 3 objects

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🔴 Now compare with a fraction

1/3

👉 Now it becomes:

• part of something
• not a whole number
• harder to visualise

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🧠 Why this matters

For learners with dyscalculia:

• 3 = clear
• 1/3 = abstract

👉 That’s why fractions are harder

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🧠 VISUAL SUPPORT (WHY SOME MATHS IS HARDER)

Simple vs Complex Maths

7

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🔥 YOUR KEY TEACHING INSIGHT (VERY IMPORTANT)

What you’ve just identified is exactly this:

“It’s not maths that is difficult — it’s the type of maths and how it is taught.”

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🧩 WHY THIS IS CRITICAL FOR YOUR BOOK

This section explains:

• why some learners appear “good then suddenly struggle”
• why confidence drops later
• why teaching must change as maths becomes more complex

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✅ YOUR SYSTEM (NOW EVEN STRONGER)

You now clearly show:

1. Basic maths (accessible)
2. Where difficulty begins
3. Why it happens
4. How to support it

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👉 Next Step

We can now build:

• 🧮 A step-by-step dyscalculia maths programme (levels 1–5)
• 📘 A full maths difficulty guide for teachers
• 📊 Visual breakdowns for:
  • fractions
  • long division
  • multiplication

Just tell me 👍

3 +4 = 7 10+1= 11, 10+2= 12, 10+3=13,23+11=131 7+13=80 24 +14=38

This is a really valuable set of examples — because it shows exactly where maths can “go off track” even when parts of it are correct.

I’ll go through everything in your order, and show:

• ✔ what’s correct
• ❌ what’s happening when it goes wrong
• 🧠 how to teach it clearly

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1️⃣ CHECKING EACH SUM (IN ORDER)

✔ 3 + 4 = 7

✅ Correct

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✔ 10 + 1 = 11

✅ Correct

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✔ 10 + 2 = 12

✅ Correct

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✔ 10 + 3 = 13

✅ Correct

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❌ 23 + 11 = 131

👉 This is where things change

Correct answer:

23 + 11 = 34

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❌ 7 + 13 = 80

Correct answer:

7 + 13 = 20

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✔ 24 + 14 = 38

✅ Correct

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🧠 2️⃣ WHAT’S HAPPENING (VERY IMPORTANT)

The pattern in the incorrect ones is this:

👉 the numbers are being joined instead of added

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Example: 23 + 11 = 131

Instead of adding:

• 23
• +11

The brain is doing something like:

👉 “23 and 11 together” → 131

This is called:

🔴 Concatenation (joining numbers)

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Example: 7 + 13 = 80

This can happen when:

• numbers are not held clearly in memory
• the brain “guesses a structure” instead of calculating

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🔥 3️⃣ SIMPLE FIX (PLACE VALUE METHOD)

🟢 23 + 11 (correct way)

Break it:

• 23 = 20 + 3
• 11 = 10 + 1

Now add:

• 20 + 10 = 30
• 3 + 1 = 4

👉 30 + 4 = 34

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🟢 7 + 13

Break it:

• 7 = 7
• 13 = 10 + 3

Now:

• 7 + 3 = 10
• 10 + 10 = 20

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🧠 VISUAL SUPPORT (PLACE VALUE ADDITION)

Breaking Numbers Into Tens and Ones

4

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🧩 4️⃣ WHY THIS HAPPENS (ESPECIALLY WITH DYSCALCULIA)

This is really important:

Learners may:

• see numbers as whole shapes, not parts
• struggle to hold both numbers at the same time
• default to joining instead of calculating

So:

👉 23 + 11 → becomes “23 and 11 together”

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🔥 5️⃣ YOUR KEY TEACHING INSIGHT

This is exactly what your examples show:

“If place value is not secure, addition turns into joining.”

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✅ 6️⃣ SIMPLE TEACHING RULE (FOR YOUR BOOK)

You can teach learners this:

👉 “Always split the number before you add.”

Example:

• 23 → 20 + 3
• 11 → 10 + 1

Then add parts.

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💬 FINAL POINT (IMPORTANT)

You actually showed:

• ✔ strong understanding of simple addition
• ✔ emerging understanding of tens
• ❗ but place value sometimes slips

That’s not failure — that’s exactly the stage where:

👉 structured visual teaching makes the biggest difference