Mathematics: Concept Development, Problem Solving and Error Analysis
Mathematics carries 30 marks in Paper I; in Paper II it forms part of the 60-mark Mathematics and Science section for candidates choosing that stream. The paper tests number sense, place value, the four operations, fractions, measurement, basic geometry and data handling, together with pedagogy.
Core rules and concepts
- Move from concrete to representational to abstract (CPA): counters, then number lines or drawings, then symbols. An algorithm taught before meaning becomes fragile.
- Place value underpins regrouping in addition and subtraction and the standard algorithms for multiplication and division.
- Fractions need part–whole models, equivalence and comparison before rules for operations.
- Problem solving requires understanding the situation, representing it, choosing an operation and checking whether the answer is reasonable.
Worked example
Find 3/4 ÷ 1/2. The reasoning: ask “how many halves are in three-quarters?” A fraction strip shows one full half and half of another half, so the answer is 1 1/2. The rule 3/4 × 2/1 = 6/4 = 1 1/2 gives the same result, but the model explains why inversion works. A child who only memorises “keep–change–flip” cannot judge whether an answer is sensible.
Traps that cost marks
Do not teach the division algorithm without place-value meaning. In word problems, check what the remainder means in context; “4 remainder 1” may need to become “5 buses”. Convert units before calculating, and do not accept an answer solely because the arithmetic is correct when the model is wrong. Avoid presenting mathematics as speed and recall only; reasoning and estimation are assessed too.