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S-17
The child knows the multiplication table in order, but not out of order
What the research says
Mnukhin finds that children with dyscalculia have disorders in forming series and in reproducing automated series. Knowing the table as a chain (in order) does not mean having matrix access to individual facts. Successive analysis and synthesis provide ordinal series, but not random access to an element of the series.
Lalaeva R.I. Dyscalculia in Children, p. 24 (2005)
Exercises at home — free
Cards out of order
Builds: Random access to times-table facts without going through the chain
You need: 20–25 cards with multiplication problems from a single table (for example, ×6), a stopwatch
- Shuffle the cards and put them in a pile face down.
- The child turns them over one at a time and says the answer right away — counting through the chain is not allowed.
- If the child hesitates for more than 3 seconds, the card goes into the “don't know” pile.
- Go through the whole pile. Count how many the child knows right away.
- Work through the “don't know” pile separately: find a connection (6×7 is 6×6 plus 6).
- Repeat a day later: the goal is to cut the “don't know” pile in half.
Lalaeva R.I. Dyscalculia in Children, 2005, ch. 3
Without help
- Runs out of time on tests — goes through the chain from the beginning every time
- Errors in division — no reverse access to the fact