Mathematics
What the domain tests
Mathematics tests content and pedagogy together: number and place value, the four operations, fractions, money, measurement, shapes, patterns and data handling, and how children build these ideas.
Core concepts
- NCF 2005: the aim is mathematisation - reasoning and problem solving - not only computation.
- CPA sequence: concrete (blocks), pictorial (drawings), abstract (symbols).
- Place value underpins carrying and borrowing; without it, algorithms are blind.
- Fractions need equal parts and a named whole.
- Error analysis: a wrong answer usually reveals a rule the child is applying.
Worked example
A child answers 52 − 27 = 35. Where is the error? Reasoning: in the units column the child did 7 − 2 = 5 instead of regrouping. Since 7 cannot be taken from 2, one ten must be borrowed: 12 − 7 = 5, and the tens become 4 − 2 = 2, giving 25. The child is subtracting the smaller digit from the larger in each column - a common rule error. The remedy is place-value work with bundles of ten, not more drill.
Traps
- Teaching keywords in word problems ('altogether' means add) instead of the situation.
- Moving to symbols before children handle materials.
- Marking only the answer, not the method.
- Confusing perimeter and area; area needs square units.
- Treating speed as the goal rather than understanding.