Active engagement of learners implies that the students—

The correct answer is inquire, explore and question.

Understanding Active Learning and Student Engagement:
Active engagement refers to a learner-centered approach where students are active participants in their own learning process rather than passive recipients of information. It involves critical thinking, hands-on exploration, and cognitive involvement.

Let us analyze the given options to see why this is the case:
1. Inquire, explore and question: When students ask questions, investigate concepts, and explore their surroundings, they actively construct knowledge, build connections, and develop critical thinking skills. This is the hallmark of active cognitive engagement.
2. Rote memorize facts and information: Rote learning is a passive technique that focuses on repetition and recall without deep understanding. It does not represent active engagement.
3. Actively value marks and competition: A focus purely on grades and competition represents extrinsic motivation. While it may drive behavioral participation, it does not imply deep, active cognitive engagement with the learning material itself.
4. Consider textbook as the sole source of knowledge: Restricting learning to a single textbook limits curiosity, independent thinking, and real-world connection, which runs contrary to active engagement.

Thus, active engagement of learners is best demonstrated when students inquire, explore and question.