I’ve used three different inquiry-based teaching and learning models at various times in my career. These models have in common a desire for students to construct their own understanding and recognize that students are capable sense-makers.
Driven by student questions: In this model, students are given a topic and asked to generate questions they have about it, and answering these questions drives the instruction for the unit. Individual concepts might be taught directly to students or introduced using project-based or problem-based inquiry. The critical aspect that makes this kind of unit inquiry-based is that students have ownership over the direction of what they are learning.
Project-based learning: In this model, students are given a project to work on or select for themselves. While working on the project, students or their teacher identify the skills or knowledge they need to complete the project. These might be taught directly to the student, learned through reading and research, or developed using problem-based inquiry. The critical aspect that makes this inquiry-based is that the project drives the knowledge needed.
Problem-based learning: In this model (which typically focuses on individual lessons), students are presented with a problem or question to solve, they work independently from the teacher but usually with a partner or small group in solving the problem, and then the teacher selects a small number of students or groups to present their various results. An example of a suitable problem might be a lab in science, an analysis of a poem, or a mathematical puzzle. The critical aspect that makes this inquiry-based is that students’ ideas drive the instruction rather than the teacher’s.