Early Numeracy and Cognitive Development
Pre-number foundations
Before numerals, children need matching, sorting, comparing (bigger/smaller, more/less), ordering and seriation, one-to-one correspondence, and classification by one and then two attributes. These are taught with real objects - buttons, bottle caps, seeds, blocks.
Counting principles (Gelman and Gallistel)
- One-to-one: one number word per object.
- Stable order: the number sequence is fixed.
- Cardinality: the last number tells 'how many'.
- Abstraction: anything can be counted.
- Order-irrelevance: the counting order does not change the total.
Piaget's contribution
The preoperational child (2–7) cannot yet conserve number, mass or liquid; judgement is dominated by appearance. Conservation of number usually appears around 5–6. Rote counting to 20 without cardinality is not number sense.
Content for ages 3–6
Numbers 1–10 then 1–20; numeral recognition and formation; shapes (circle, square, triangle, rectangle); patterns (AB, ABB); positional words (above, behind, next to); comparison of length, weight and capacity; simple sorting and data; time words and days of the week; money only as recognition.
Worked example
A child recites 1 to 10, but when asked for five beads gives a handful. Diagnosis: stable order is present, cardinality is not. Remedy: count-and-move activities where each bead is touched and moved while being counted, then ask 'so how many?' and have the child repeat the last number.
Traps
Teaching numerals before matching and sorting; replacing manipulatives with worksheets; calling a four-year-old's failure on a conservation task a learning problem.