The constructivist approach in mathematics emphasizes:

Constructivism treats knowledge as something a learner builds rather than something a learner receives. On this view every learner already carries mental structures - schemas - formed from earlier experience, and a new idea is learnt when the learner acts on a situation, finds that an existing schema does not fully account for it, and reorganises that schema to accommodate the new experience. Teaching, on this account, consists of arranging situations in which such reorganisation can take place.

Applied to mathematics, this means a concept such as fraction, area or place value is expected to grow out of the learner's own activity - exploring, representing, conjecturing and justifying - while the teacher designs the tasks, poses the questions and mediates the discussion rather than handing over finished results.

The stem asks what this approach emphasises. Inquiry is exactly the activity described above: the learner meets a question, tries cases, forms a conjecture, tests it and argues why it holds, and the mathematical idea takes shape through that process. So the constructivist approach in mathematics emphasises building understanding through inquiry.

Set against the other descriptions offered:

• Avoiding real-life applications - constructivism relies on contexts a learner can act upon and model, so removing those contexts removes the raw material from which the concept would be built.

• Teachers providing all answers and procedures - this is the transmission view of teaching: the method arrives complete, so no reorganisation of the learner's own schema is called for.

• Memorizing rules and procedures without understanding - this is rote learning, in which the form of a step is retained while the reasoning that generates it is not; constructivism aims precisely at that reasoning.

A useful cross-check: constructivism rests on Piaget's assimilation-accommodation account of cognitive development and on Vygotsky's socially mediated learning, and both place the learning inside the learner's own activity and discussion. Any description that hands the concept over ready-made, or that strips away the learner's activity, is by that test not constructivist.