← Atlas of Difficulties
S-33
The child doesn't see patterns and can't solve by analogy
Type: practognostic
What the research says
One of the most important prerequisites for solving arithmetic word problems is the ability to draw inferences from the content of the problem's conditions, identifying patterns in the situation described in order to answer the question posed in it.
Lalaeva R.I. Dyscalculia in Children, p. 150 (2005)
Exercises at home — free
Matrix: find the shape by two rules
Builds: Inference by two features — the basis of algorithmic thinking
You need: a sheet of paper, a pencil
- Draw a 3×3 grid. Fill 8 cells with shapes according to a rule: the shape changes along the rows, the size changes along the columns.
- Leave one cell empty.
- Ask: “Which shape should go here? Why?”
- The child should name both rules: shape and size.
- Harder: the column rule is the fill (empty/hatched/filled in).
Lalaeva R.I. Dyscalculia in Children, 2005, p. 151
Number analogies
Builds: Patterns in pairs of numbers — preparation for the multiplication table
You need: number cards or a sheet of paper
- Write the pairs: 27 and 72, 31 and 13, 36 and 63.
- Ask: “How are they alike? What do they have in common?”
- Then: “How are they different?”
- “Make up a similar pair of your own.”
- Link to math: “The multiplication table works by analogy too: 2×3=6, so 3×2=6.”
Lalaeva R.I. Dyscalculia in Children, 2005, p. 150
Find the number that doesn't belong
Builds: Inference, identifying a feature
You need: a card with the numbers: 1, 2, 4, 5, 7, 8, 10, 0
- Place the card in front of the child.
- Ask them to find the “odd one out.”
- If they say 10, ask: “Why?”
- If 0, discuss it: 0 stands apart.
- “Could 10 be called the odd one out? Why?” — this develops reasoning.
- Harder: the numbers are said out loud — the child keeps them in mind and answers.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 70
Is it a word problem or not? Learning to tell the difference
Builds: Understanding the required parts of a word problem: data + question
You need: 4 cards with texts — 2 real problems and 2 with no data or no question
- Prepare 4 texts: 2 problems and 2 “non-problems.”
- An example of a “non-problem”: “There are 3 girls and some boys in the class. How many in total?” — there is no exact number.
- Read the first text. “Is this a problem? Can it be solved?”
- Discuss: a problem must have conditions with numbers and a specific question.
- Solve the real problem together.
- Harder: the child “breaks” a problem — removes the data or the question.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 71
Worksheets — print and practice
Analogy matrix — inferences by two rules
Without help
- Can't transfer a solution method from a similar problem
- Solves every problem from scratch, without seeing its type
- Difficulty with the multiplication table — doesn't notice the analogies within it