A teacher encourages students to find multiple solutions to a problem. What…

In teaching-learning theory, tasks that ask learners to generate and compare multiple solutions to a single problem exercise higher-order thinking: students must analyze the problem, weigh different approaches, and justify why one path works, rather than simply recalling fixed information. This active, evaluative process is what is meant by developing reasoning.

Here, the teacher is deliberately asking students to find more than one solution to the same problem. To do this, learners must think through several possible approaches, compare their merits, and decide which one is valid — exactly the cognitive process reasoning describes.

• Rote memorization involves repeating and recalling information exactly as given, without requiring analysis or comparison of different approaches.

• Avoiding concrete materials is a decision about which teaching resources (physical objects, manipulatives) a lesson uses — a resource-choice question unrelated to how many solution paths a task explores.

• Learning long definitions involves retaining extended, fixed wording, which is again a memory task rather than an analytical one.

• Developing reasoning matches the described activity: analyzing a problem from more than one angle, comparing approaches, and justifying a valid solution path.

Because exploring multiple solution paths requires active analysis, comparison, and justification rather than memorization, this teaching practice develops reasoning — confirming 'Developing reasoning' as the correct response.