Mathematics
Mathematics tests content up to upper-primary level and the pedagogy of making mathematical ideas understandable.
Content core
- Number system, factors, LCM and HCF, fractions, decimals, squares and cubes.
- Ratio, proportion, percentage, profit and loss, simple and compound interest.
- Algebra: expressions, linear equations, identities.
- Geometry: lines, angles, triangles, circles; mensuration of perimeter, area and volume; data handling and probability.
Pedagogy
Move from concrete to representational to abstract. Use manipulatives for fractions, number lines for integers, and error analysis for misconceptions. Van Hiele levels describe geometry learning from visualization to analysis, informal deduction, formal deduction and rigor. Assessment should include reasoning, not only answers.
Worked example
A price is increased by 20% and then decreased by 20%. Is it back to the original? Take 100. After a 20% increase: 120. After a 20% decrease on 120: 120 - 24 = 96. Net change is a 4% decrease, because the second percentage applies to the larger amount.
Traps
Adding percentage points when the base changes; mixing area and perimeter units; cancelling terms across addition; assuming every geometry diagram is to scale. Check the base and the unit.