Is it a maths problem or a reading problem?

Why can a word problem be harder than the maths inside it?

Because working memory is small. We can hold only about four chunks of information in mind at once (Cowan, 2001), and everything competing for that space is space the maths can’t use. If most of it goes on decoding a long sentence, the arithmetic has nowhere to run. That’s cognitive load theory in a nutshell (Sweller, 1988).

So a child who can do 23 − 9 without trouble can still get this wrong: “Mia had 23 stickers. She gave 9 to her brother and then found some more. How many did she have before she found the others?” The maths is identical. The reading isn’t.

How can I tell whether it’s the reading or the maths?

Hold the maths still and move the reading. Give your child the same problem three ways:

1. As a number sentence: 23 − 9 = ?
2. As a picture: 23 dots with 9 crossed out.
3. As a word problem, first read silently, then read aloud by you.

If they get the number sentence right but miss the word problem, it’s the reading. If reading it aloud fixes it, it’s decoding, meaning the words themselves. If it’s still wrong when read aloud, it may be comprehension: working out what the situation is asking. If they miss all three, it’s the maths.

Which words trip children up in maths?

Vocabulary researchers sort words into three tiers: everyday words, general academic words and subject-specific words (Beck, McKeown and Kucan, 2013). Maths is full of the tricky middle kind: ordinary-looking words with a special meaning.

• Difference: in maths, the result of a subtraction, not “what’s different about them”.
• Product: the result of a multiplication, not something you buy.
• More than and how many more: “7 is 3 more than 4” and “how many more does Sam have?” point in opposite directions to many children.
• Each and per: small words that turn addition into multiplication.
• Left and altogether: often taught as signals for take away and add, which works until a question is phrased the other way round.

What helps?

• Read it aloud. It doesn’t make the maths easier, only the reading, so it tells you what’s really going on.
• Find the question sentence. Ask your child to point to the sentence that ends in a question mark and say what it wants.
• Draw the story. A bar split into parts makes “how many more” visible.
• Teach the words directly. Talk about what “difference” means in maths. Don’t expect children to absorb it from context.
• Avoid keyword tricks. “Left means subtract” fails on “Jo has some left after giving away 4. She has 6 left. How many did she start with?”

Why does this matter beyond homework?

Because tests usually report one number. A child who struggles with reading can be marked down in maths, given more maths practice they don’t need, and lose confidence in a subject they’re actually managing. Separating the two means each gets the right help. Teachers know this well, and it’s worth raising with your child’s teacher if you see the pattern at home.

How Workings does this

Workings measures reading and maths apart. Every question sits on a five-level reading scale, from no reading at all to inference, and a question may push the maths or the reading, never both at once. Each child has two abilities, maths and reading in maths, so a wrong answer is attributed to whichever was more likely the cause. Read-aloud is always available and never counts against a child. Read the science behind the reading scale.