Mathematics
This domain tests whether you can teach mathematical concepts, diagnose errors and choose representations that build understanding.
Core rules
- Number sense and place value underpin all operations; use base-ten materials, number lines and arrays before algorithms.
- Concrete–representational–abstract (CRA): manipulatives, then drawings, then symbols.
- Teach operations through meaning (joining, separating, comparing and grouping) rather than key words.
- Fractions: equal parts of a whole or set; equivalence and comparison need models such as fraction strips and number lines.
- Problem solving: model the situation, represent it, solve, then check reasonableness; avoid key-word strategies.
- Formative assessment: analyse error patterns, not just right or wrong answers.
Worked example
A child writes 52 − 27 = 35. The error is subtracting the smaller digit from the larger in each column (5−2=3, 7−2=5) instead of regrouping. The teacher should use base-ten blocks: exchange one ten for ten ones, subtract 7 ones, then 2 tens. Connect each move to the written algorithm and ask the child to explain. Then give a similar problem and a word problem where regrouping is required. The reasoning: the child needs place-value meaning, not a faster trick.
Traps
Do not teach borrowing as a trick without place-value meaning. Do not tell students that more always means add or left always means subtract. Do not assess only speed; fluency includes strategy and accuracy. Do not introduce symbols before students can represent the idea.