Mathematics
Mathematics tests number sense, place value, the four operations, fractions, geometry, measurement and data handling, plus the pedagogy of moving children from concrete objects to pictures to symbols.
Core rules
- Place value is the foundation: 47 means 4 tens and 7 ones, not “four and seven.”
- Operations should be modelled with bundles, beads, number lines and arrays before written algorithms.
- Fractions are parts of a whole and of a collection; equivalence and comparison need diagrams.
- Measurement connects to real units: centimetre, metre, litre, gram, kilogram; conversion is multiplicative.
- Geometry starts with sorting 2-D and 3-D shapes by properties such as sides, corners and faces, not naming only.
- Error analysis is teaching: a wrong answer reveals the child’s rule.
Worked example
Find 3/4 of 20. First divide 20 into 4 equal groups: 20 ÷ 4 = 5. Then take 3 groups: 5 × 3 = 15. The reasoning: the denominator tells how many equal parts, the numerator tells how many parts are taken. A child who writes 20 ÷ 3 × 4 has inverted the roles of numerator and denominator.
Traps
- Teaching “borrow” as a magic word without exchanging tens and ones.
- Keying on words like “altogether” without reading the problem.
- Converting units by adding or subtracting instead of multiplying or dividing.
- Treating a remainder as “ignore it” in sharing problems.
- Using only abstract drill before concrete experience.
- Confusing perimeter and area.