Concept:The ability to perform all four basic operations (addition, subtraction, multiplication, division) on whole numbers, fractions, and decimals shows that the learner has reached the highest stage of numerical development — the operating phase.
Explanation:Mathematical development has six phases, each building on the previous.
In the emergent phase, students understand number words and symbols for quantity.
In the matching phase, they respond correctly to counting and quantity questions.
In the quantifying phase, they grasp that the number at the end of counting is constant and use part‑part‑whole relations.
In the partitioning phase, they see numbers as compositions of other numbers and apply additive thinking to many‑to‑one relations.
In the factoring phase, they connect groups of ten/hundred, understand multiplication and division, and think both additively and multiplicatively.
In the operating phase, students can split and re‑split intervals, understand place‑value relationships (each place is ten times the place to its right and one‑tenth to its left), make multiplicative comparisons, handle proportions, and integrate common and decimal fractions.
Performing the four basic operations on whole numbers, fractions, and decimals requires these advanced skills, so the learner is operating.
Answer:D. Operating phase