S-31

The child doesn't understand comparison signs: confuses < and >

Type: practognostic

What the research says

In primary acalculia, awareness of the meaning of arithmetic signs is impaired. The mathematical relationships between numbers fall apart, and a number drops out of the complex system of decimal notation.

Lalaeva R.I. Dyscalculia in Children, p. 17 (2005)

Seriation is the process of establishing sequential relationships, based on identifying and ordering differences. The dual nature of the relationship between two numbers develops only once seriation has been mastered with a series of objects.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, p. 32 (2013)

Children's mental number line is logarithmically compressed: the distance between 3 and 8 seems larger than the distance between 203 and 208. With experience, the line becomes more linear and abstract. Logical sequences (steps of 2, 5, 10) strengthen orientation on the number line and prepare children for multiplication.

Landerl, Vogel & Kaufmann, 2022, cited in: Federal Ministry of Education of Austria. A School Approach to Arithmetic Difficulties., pp. 12–13 (2023)

Exercises at home — free

Arrange by speed

Builds: Seriation by a non-numerical feature — preparing to understand order

You need: 5 cards with pictures of vehicles

Name 5 ways to get around: a turtle, a bicycle, a car, a train, an airplane.
Task: “Arrange them from the slowest to the fastest.”
Afterward: “What is between the car and the airplane?”
Harder: “Add a motorcycle — where does it go in the row?”
Link to math: “Numbers stand in order too — each one is bigger than the one before.”

Lalaeva R.I. Dyscalculia in Children, 2005, p. 131

Nesting dolls and stacking rings — put them in order by size

Builds: Seriation as the foundation for understanding the number line

You need: a nesting doll with 5–8 pieces, a stacking toy with rings of different sizes, 3–5 balls of different sizes

Take apart the nesting doll or the stacking toy and mix up all the pieces.
Ask the child to arrange them from the smallest to the biggest.
After each step: “Which one comes next? Why?”
When the row is complete: “Show me the third one. Which one is between the second and the fourth?”
The number line works the same way — each number has its own place between its neighbors.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 48

A Cuisenaire rod staircase

Builds: Visual understanding of the number line: each number is 1 more than the one before

You need: Cuisenaire rods or paper strips 1–10 cm long, a sheet of paper

Lay out the rods in random order. Ask the child to build a “staircase” — from short to long.
“Show me rod number 3. Which one comes after it? Which one comes before it?”
Remove one from the middle: “Which number is lost?”
Harder: place a digit card next to each rod.
The Cuisenaire staircase is a number line you can touch. Each step is +1.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 48

A tower and a staircase from shapes

Builds: Seriation by size, naming the order

You need: 5–7 cardboard rectangles of different sizes, all one color

Lay out the rectangles in random order.
Ask the child to find the biggest one and put it down first.
Then the next biggest — down to the smallest. This makes a “tower.”
Name them together: “big, smaller, even smaller, the smallest.”
Take it apart and build a “staircase” — a horizontal row from small to big.
Harder: add triangles and circles.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 82

Complete the number sequence

Builds: Finding the pattern in a number sequence

You need: digit cards, a sheet of paper

Lay out the cards: 10, 1, 2, 3, 4, 6, 7, 8, 9.
Ask: “Name all the digits. What do you notice? Which one doesn't belong?”
Discuss: “10” is a two-digit number, not from the first ten.
Give a second set: 5, 11, 12, 14, 15, 17, 18, 19, 20.
“Which number is missing? How did you figure it out?”
Ask the child to make up their own task for you.
Harder: the child writes a sequence with a gap — the adult guesses.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 75

The math sieve

Builds: Classifying numbers by a feature

You need: number cards: 1, 2, 6, 8, 12, 18, 20; two sheets of paper labeled “up to 10” and “from 10”

Lay out the cards in random order.
Task: “Sort them — which are less than 10, which are more.”
The child sorts them, saying each number out loud.
Ask: “Explain why you decided that.”
Second set: 3, 13, 4, 14, 6, 16, 8, 18 — put them in order, then split them up.
Harder: come up with your own rule — even/odd.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 75

The train: number cars

Builds: The number sequence, the concepts of “next,” “previous” and “between”

You need: a sheet of paper with a train drawn on it (rectangles for cars), a pencil or digit cards

Draw a train with 10 cars. Write digits in some of them and leave the rest empty.
For example: _, 2, _, 4, 5, _, 7, _, 9, _.
“This is a train with number passengers. Not all the cars are numbered. Fill them in.”
The child fills in the empty cars.
Ask: “Which car is after 6? Before 9? Between 4 and 6?”
Harder: remove the filled-in cars — the child restores the whole sequence.
Advanced level: the train goes the other way — the numbers from 10 to 1.

Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 91

Worksheets — print and practice

Number sequence — seriation and order

↓ Download printable PDF (in Russian)

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