Inquiry-Based Learning (IBL) is a student-centered method of teaching Mathematics. At the college mathematics level one of the forms of IBL is the Modified Moore Method, named after R. L. Moore. Other forms of IBL are also recognized, which employ different course structures, including some group work, projects, and courses that are not theorem-proof based (e.g. statistics, courses for preservice teachers).

Boiled down to its essence IBL is a teaching method that engages students in sense-making activities. Students are given tasks requiring them to solve problems, conjecture, experiment, explore, create, and communicate... all those wonderful skills and habits of mind that Mathematicians engage in regularly. Rather than showing facts or a clear, smooth path to a solution, the instructor guides and mentors students via well-crafted problems through an adventure in mathematical discovery. Key components across effective IBL courses are (a) deep engagement in rich mathematical activities, and (b) opportunities to collaborate with peers (either through class presentations or group-oriented work).

E. Lee May, Salisbury State University, defines IBL:

Inquiry-based learning (IBL) is a method of instruction that places the student, the subject, and their interaction at the center of the learning experience. At the same time, it transforms the role of the teacher from that of dispensing knowledge to one of facilitating learning. It repositions him or her, physically, from the front and center of the classroom to someplace in the middle or back of it, as it subtly yet significantly increases his or her involvement in the thought-processes of the students.

A typical day in an IBL math course is hard to define, due to the variance across the environments and needs at institutions across the nation and world. Here is a sample model of a typical day in an IBL math course.

- Class starts
- The instructor passes out a signup sheet for students willing to present upcoming problems.The bulk of the time is spent on student presentations of solutions/proofs to problems
- Students, who have been selected previously or at the beginning of class, write proofs/solutions on the board
- One by one, students present their solutions/proofs to their class
- The class as a group (perhaps in pairs) reviews and validates the proofs. Questions are asked and are either dealt with there or the presenter can opt to return with a fix at the next class period.
- If the solution is approved as correct by the class, then the next student presents his/her solution. This cycle continues until all students have presented.
- If the class cannot arrive at a consensus on a particular problem or issue, then the instructor and the class devise a plan to settle the issue. Perhaps new problems or subproblems are written on the board, and the class is asked to solve these. Teaching choices include pair work immediately or asking students to work on the new tasks outside of class, with the intention of restarting the discussion the next time.
- If a new unit of material is started, then a mini lecture and/or some hands-on activities to explore new ideas and definitions could be deployed.
- If no one has anything to present OR if everyone is stuck on a problem, pair work or group work can be used to help students break down a problem and generate strategies or ways into solving a particularly hard problem.