Read the Assertion (A) and Reason (R) given below and choose the correct…

Concept: An Assertion-Reason item is settled in two independent stages: first the truth of each statement judged on its own, then whether the reason states the mechanism that produces the assertion.

A reason can be entirely true and still fail to explain the assertion; it explains the assertion only when the assertion follows from it. The pedagogical principle at work here is contextualisation: a learner builds understanding of a new abstract idea by mapping it onto experience already available to them, which is why NCF 2005 asks that school mathematics be connected to the child's life outside school.

Application:

1. Judge the assertion on its own. Situating symbols in settings a child already knows - a shopping bill, a bus timetable, a cricket average - lets the learner see mathematics as belonging to their own world, which is exactly the relating that the assertion claims. The assertion is true.

2. Judge the reason on its own. A symbol such as 3/4, or a term such as average, carries no meaning by itself; it acquires meaning when it is attached to a referent the learner already knows. The concrete to semi-concrete to abstract sequence used in primary mathematics rests on this. The reason is true.

3. Test the explanatory link. Meaning comes first: the familiar example gives the abstract idea meaning, and it is that meaning which makes the subject feel connected to the learner's life. Relating to the subject is therefore a consequence of the meaning-making described in the reason, so the reason supplies the mechanism behind the assertion rather than an unrelated true fact.

Cross-check:

• Keeping both statements true while denying the explanatory link would require the relating to arise from some other mechanism; the pair offers none, because the meaning a familiar example supplies is precisely what produces the relating.

• Calling the assertion untrue would mean a context-rich lesson leaves a learner no more connected to mathematics than a purely symbolic one, which contradicts the constructivist account of concept formation.

• Calling the reason untrue would mean a familiar referent adds no meaning to an abstract symbol, the opposite of how the concrete-to-abstract sequence of primary mathematics is built.

Result: Both A and R are true, and R is the correct explanation of A.