Mathematics (Birth–Grade 2)
Core content
Early mathematics rests on counting principles: one-to-one correspondence, stable order, cardinality (the last number named tells "how many"), abstraction (any objects can be counted), and order irrelevance. Candidates must know subitizing (instant recognition of small quantities), composing and decomposing numbers within 10 and 20, place value (ten ones bundled into one ten), the four operations as situations (joining, separating, part-part-whole, comparison), and properties (commutative, associative, identity). Geometry covers defining versus non-defining attributes of two- and three-dimensional shapes; measurement covers the attribute, the unit, iteration of units, and the zero point; data covers picture and bar graphs; patterns include repeating and growing patterns.
Common traps
- Cardinality confusion: a child who recounts after being asked "how many" has not yet attained cardinality.
- Conservation of number: believing quantity changes when objects are spread out reflects preoperational thinking, not carelessness.
- Rote counting is not number sense; counting past a known point without objects often masks weak one-to-one correspondence.
- Equal vs congruent: fraction parts must be equal in area, not identical in shape.
- Defining attributes: a shape's orientation or size never determines its name; number of sides and vertices does.
Rule of thumb
Move concrete → pictorial → abstract, and always ask "how do you know?" - justification reveals whether the concept is secure.
Worked example
Make-ten strategy for 8 + 5: decompose 5 into 2 and 3; 8 + 2 = 10; 10 + 3 = 13. This shows decomposition, the associative property, and fluency with ten as a benchmark.