Which approach meets goals of students making conjectures and constructing arguments related to mathematics?

• A. Individual silent work
• B. Encouraging student interaction and cooperative learning
• C. Lecturing with no discussion
• D. Timed tests

Answer: (B)

Conjecturing and constructing arguments in mathematics thrive when students talk and work together. Cooperative learning gives students the chance to hear different ideas, explain their own thinking, question each other, and defend or revise conjectures. Through this dialog, they learn to justify steps, test reasoning, and build increasingly solid arguments, which is exactly what mathematical reasoning is about. The teacher can design tasks that require explanation and guide discussions to push students toward clearer proofs and deeper understanding.

Solitary silent work, lectures with no discussion, and timed tests don’t provide the same opportunity to practice arguing, refuting, and refining ideas in a collaborative setting. In those formats, students may arrive at correct answers, but they miss the essential practice of articulating and defending reasoning with peers.