The child can't solve a math word problem: causes and how to help
Why word problems are the hardest
A child with dyscalculia can often add and subtract — but give them a word problem and they're lost. They take the numbers from the problem and add them at random. Or they retell the problem but can't pick out the question. Or they forget the given information halfway through solving it.
This isn't laziness or carelessness. A word problem requires speech, memory, spatial concepts, and logic to work at the same time. If even one link is weak, the whole structure falls apart.
Three stages: from objects to writing it down
R.I. Lalaeva described three stages a child goes through when learning to solve problems.
Stage 1. Practical actions
The child acts out the problem with objects. “Mom bought 5 apples and 3 pears” — we lay out the fruit (or stand-ins for it) on the table. Through physical action, the child understands the meaning of the operation: why this is addition and not subtraction.
Stage 2. Diagram
A concrete drawing is simplified into a diagram: circles, arrows, numbers, a question mark. The diagram keeps the structure of the problem but frees up working memory. Once the diagram is drawn, the child picks the solution from the diagram instead of trying to hold everything in their head.
Stage 3. Writing it down
Choosing the operation sign, writing the number sentence, calculating. The child reaches this stage only once they understand the structure of the problem.
Four techniques for analyzing a problem
Each of these techniques trains a separate area where children with dyscalculia most often “stumble.”
1. The grid
The text of the problem is laid out in cells: what is given in the first sentence, what in the second, where the question is. The child sees the problem as a structure rather than as a solid block of text.
2. Find the question
The child gets the text of a problem and three possible questions. They choose the right one and explain why the other two don't fit. This teaches them to see the goal of the problem before starting to calculate.
3. Find what's missing
A problem with a gap: “Dad planted apple trees. He also planted some pear trees. Now there are 15. How many pear trees?” — but the number of apple trees isn't given. The child learns to see what's missing to solve it.
4. Act it out and draw it
First, act it out with objects. Then draw it. Then simplify the drawing into a diagram. Each step reinforces understanding of the structure.
Why “just more problems” doesn't work
If a child doesn't understand the structure of a problem, ten problems of the same type won't help — they'll keep guessing the operation time after time. First you need to teach them to see the problem: where the given information is, where the question is, what connects to what. And only then — to solve it.