Mathematics
What is tested
Number and operations, patterns and algebraic reasoning, geometry, measurement, and data, plus mathematical process skills, aligned to Oklahoma Academic Standards for mathematics.
Counting and number sense
Gelman and Gallistel's counting principles: one-to-one correspondence, stable order, cardinality, abstraction, and order irrelevance. Children frequently recite a count correctly and then answer 'how many?' with a number that is not the total, which is a cardinality problem rather than a rote-counting problem. Subitizing - instantly recognizing small quantities - supports later addition and subtraction. Composing and decomposing numbers (5 as 3 + 2 or 4 + 1) must be secure before written symbols. Build it with counters, ten-frames, dot cards, number talks, and games.
Other strands
- Patterns: repeating (AB, AAB) then growing patterns.
- Geometry: naming, sorting, and composing 2-D and 3-D shapes.
- Measurement: direct comparison of length, weight, and capacity; nonstandard units before standard ones.
- Data: sorting, tallying, picture graphs, and simple questions.
- Process standards: problem solving, reasoning, communication, connections, representation.
Worked example
A child counts five counters accurately, then, asked 'how many?', recounts and says 'four.' Reasoning: the one-to-one recitation was fine, so this is cardinality confusion, not counting failure. Have the child count again, cover the set with your hand, and ask for the total; then play 'give me four' games that require producing a quantity without counting aloud. Match the task to the actual misconception.
Traps
Pushing numeral writing before quantity is secure; treating fast recall as number sense; calling a sorting activity 'measurement' when nothing is compared; assuming a wrong answer means the child cannot count.