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S-35
The child can't solve a word problem: loses the data and mixes up the operations
Type: verbalType: dyslexic
What the research says
Solving a math problem involves three stages: understanding the conditions with the support of practical actions, diagramming the content and applying the algorithm of arithmetic operations.
Lalaeva R.I. Dyscalculia in Children, p. 172 (2005)
Exercises at home — free
The grid: breaking a problem down into parts
Builds: Seeing a problem as a structure rather than a solid block of text
You need: paper with a grid drawn on it (4–5 cells), a pencil
- Read the problem: “Mom bought bread for 7 rubles and a bun for 8 rubles. She handed over 20 rubles. How much change did she get?”
- Fill in the grid together: cell 1 — bread: 7, cell 2 — bun: 8, cell 3 — handed over: 20.
- Cell 4 — question 1: how much together? Cell 5 — question 2: how much change?
- After a few exercises, the child fills in the grid on their own.
- Solving starts with finding the question, not with the numbers.
Lalaeva R.I. Dyscalculia in Children, 2005, p. 171
Find the question in the problem
Builds: Understanding the goal of a problem
You need: cards with problems and possible questions
- Give the text of a problem and three possible questions.
- The child picks the right one and explains why they rejected the other two.
- The reverse: the adult gives the data — the child comes up with the question.
- A child who can't find the question starts calculating with whatever numbers come first.
Lalaeva R.I. Dyscalculia in Children, 2005, p. 171
What's missing from the problem?
Builds: Being able to find the missing piece of data — preparation for equations
You need: cards with problems that have a missing number
- A problem with a gap: “Dad planted apple trees. Today he planted some pear trees too. Now there are 15. How many pear trees?” (the number of apple trees is missing).
- The child pictures it: what there was — what changed — what there is now.
- Figures out which piece of data is missing and puts it into words.
- This is the hardest exercise — and that's exactly why it's especially useful.
Lalaeva R.I. Dyscalculia in Children, 2005, pp. 171–172
Act out the problem with objects
Builds: Understanding the operation through a concrete action
You need: checkers or counters in two colors, Explain Math to Me number frames
- “Dad planted 8 apple trees” — lay out 8 red checkers.
- “Today he planted some pear trees — now there are 15” — add green ones up to 15.
- “How many pear trees?” — the child counts the green ones.
- Number frames: red in one section, green in another — a visual diagram.
- Only through physical action does the child understand why this is subtraction and not addition.
Lalaeva R.I. Dyscalculia in Children, 2005, p. 172
Draw a diagram of the problem
Builds: A diagram keeps the structure and frees up working memory
You need: paper, a pencil, Explain Math to Me number frames
- After acting it out, draw a concrete picture (apples and pears).
- Simplify: instead of a picture — circles, arrows, numbers, a question mark.
- Number frames are a physical prototype of the diagram: show the similarity.
- The diagram should cover all the data in the conditions.
- Once the diagram is drawn, the child chooses the solution from the diagram, not from memory.
Lalaeva R.I. Dyscalculia in Children, 2005, pp. 172–173
Choose the operation sign
Builds: Choosing the sign is thinking, not guessing
You need: problem diagram cards, paper, a pencil
- Show a diagram (numbers, arrows, a question). Offer three sign options: +, −, ×.
- The child chooses and explains.
- Writes down the calculation and works it out.
- Next step: the adult dictates — the child builds a diagram, chooses the sign and solves.
Lalaeva R.I. Dyscalculia in Children, 2005, p. 173
Different words — one diagram
Builds: The child learns to see the type of problem and solve by analogy rather than from scratch
You need: 4–6 cards with problems of the same type, blank diagram templates
- Present 4–6 problems with different content but the same structure (all about finding a sum).
- The child builds a diagram for each one.
- Notices: “Different words — the same diagram.”
- The reverse: one diagram — make up different texts for it.
- The child starts solving by type rather than from scratch — the basis of automaticity.
Lalaeva R.I. Dyscalculia in Children, 2005, p. 173
Without help
- Takes the numbers from the problem and adds or subtracts at random
- Retells the conditions but can't pick out the question
- Forgets the data while solving
- Refuses to solve word problems
- Doesn't transfer the skill to new types of problems