One of my pedagogical goals is to encourage students to engage in active learning through the educational process. I am driven by teaching ideas such as curriculum-based teaching, scientific teaching, and teaching students with integrating other knowledge that is relevant to their current subject learning, etc. To achieve this, I employ a range of active teaching activities such as peer discussion, think-pair share, polling, etc. It is crucial to combining theoretical concepts with practical application during the activities. Inquiry-based active teaching, when it takes question-open teaching form, initially involves a process of directing student learning.   

 Inquiry-based teaching is to support teaching framework where teachers help facilitate the development of range of student skills such as problem-solving skills, which therefore, appropriate for carrying out teaching to students who are at higher level, however, are found that students who are at introductory level can also attain benefits from the inquiry-based teaching method. Inquiry-based teaching helps reduce student anxiety, improve their ability of cooperation and construction of knowledge and skills.  Implementing inquiry-based teaching is not contradicted to implementing experimental teaching method as it involves interpretation and application to knowledge learned by students.

However, scientific teaching in pedagogical framework gives a rise to our final goal on teaching students to think metacognitively, which involves teaching our students with a testimony that is suitable to the student context. In other words, we need to think critically as we conduct inquiry-based teaching methods.  

The success of student problem-solving based learning has been linked to inquiry-based teaching for college students who study courses such as mathematics that are at advanced level. Therefore, the problem-solving based learning scenarios must be broken down to tasks guided by learning outcomes and presented in form of questionnaires to develop student problem-solving skills.

 Considering students who study elementary problems such as Clock problem in advanced level, they may face the challenge of solving problems when the hour hand points at somewhere between two marks on clock. To address this, one effective teaching method that can be employed is using inquiry-based teaching. When designing questions for this scenario, we can begin by asking students how many minutes are in one hour. By building upon this foundational knowledge, we can then prompt them to consider how many degrees are in a complete circle. Taking the inquiry-based approach a step further, we can challenge them to determine the fraction represented by the distance between two marks on a clock, in terms of degrees. This progression of questioning aligns with the expectations of the advanced topic and allows educators to effectively leverage inquiry-based teaching to enrich their students’ learning experience.

 The following table is an example of inquiry-based teaching about a Calculus topic to college student context.