Inquiry-Based Learning (IBL) is an approach to teaching and learning in which the classroom environment is characterized by the student being the active participant, while the teacher’s role is decentralized. It can manifest itself differently in various classroom settings. Historically, IBL was most often implemented in proof-based courses. In inquiry-based learning, teachers use questions, problems and scenarios to help students learn through individual thought and investigation. Instead of simply presenting facts, the teacher encourages students to talk about a problem and draw on their intuition to understand it. Inquiry-based learning also focuses on letting students ask their own questions, essentially providing their own inquiry. Student-led questions follow teacher-guided inquiry. Instead of lecturing about learning goals, the teacher cultivates a learning environment and helps students explore it through questions and experiences.
The Aim Of Inquiry Based Learning (IBL)
Mathematicians aim to build knowledge through thinking and experimenting. They ask hypothetical questions and working with those ideas, which goes in Active learning strategy that has gained significant endorsements in recent years, most notably by the Conference Board of the Mathematical Sciences this year.
Core Principles of Inquiry Based Learning (IBL)
IBL is a form of active learning that comes in many shapes and sizes. The core principles of IBL provide three specific but representative examples of IBL classrooms from our perspective: upper-division proof-based mathematics courses, the calculus sequence and mathematics for elementary teachers. Active, student-centered pedagogies such as IBL exist in a dynamic landscape, so describing teaching methods that are constantly evolving is a challenging and slippery task. We are still developing and trying to understand the variety of IBL methods, when and where they are applicable and identifying best practices. Common to these many forms of IBL are two principles, the “twin pillars” that education research has shown to be at the core of most implementations of IBL, such as deep engagement in rich mathematics and opportunities to collaborate. Deep engagement in rich mathematics is the first pillar and is an encompassing phrase, indicating that students are actively and intentionally working on challenging mathematics problems. It means that the students themselves do a significant portion of the development of mathematical ideas, which are more sophisticated than rote skill-level exercises. Typically, students do not know the answer or method ahead of time, and the questions generally require grappling with mathematical ideas before arriving at a solution to the problem.
Collaboration in Inquiry Based Learning (IBL)
Collaboration is the second pillar and can come in many forms. The most common is structured group work. Students are asked questions and work collaboratively as a team to think through mathematical ideas. Students’ thinking benefits from verbalizing their thoughts and in doing so, students learn how to effectively communicate mathematics orally and in written form. It can take other forms besides group work.
Example of Inquiry Based Learning (IBL)
Upper - Division :
In an upper-division course with a focus on proof, students often present their proofs to the entire class. The class peer-reviews the proof, discussing its features such as validity, techniques and coherence. Hence, class discussion is a class-wide collaboration, moderated by the instructor. In this case, the class works together to validate and understand the meaning of proof.
Proof - Based Courses :
Proof-based courses are a natural setting for IBL. There is a long tradition of using IBL in these courses, where class size and content pressure are typically minimized when compared to other courses we teach.
Role of Students in Inquiry Based Learning (IBL)
Students in IBL proof-based courses are asked to develop the fundamental concepts and to produce the proofs of the important theorems. This may require abandoning a traditional textbook in favor of a customized sequence of tasks that meets the students where they are mathematically and is designed to guide them on a journey of mathematical discovery. As opposed to completing exercises after an instructor has covered the relevant material, students decipher definitions, explore examples, make conjectures and prove theorems. The intention in IBL courses is for the students to make sense of and solve core exercises and problems as they progress through the course.
Method of conducting Inquiry Based Learning (IBL)
After each class meeting, students are assigned problems to work on outside of class. Each student is expected to come to the next class meeting prepared to present and discuss their proposed solutions or proofs. In our experience, a typical assignment will consist of roughly 5–15 problems. Each batch of problems is meant to do some subset of the following :
1. Introduce a new topic
2. Develop intuition about a concept
3. Synthesize ideas from a few concepts
4. Make a conjecture
5. Prove a theorem
6. Get practice doing routine or non - routine problems.
Conclusion
Teaching is a profession with specific skills and practices that need to be learned and developed. Mathematics instructors at all levels can learn to engage students in the process of doing mathematics in Inquiry Based Learning. The factors of IBL teaching include building a safe learning environment, managing group work, making changes in assessment, managing the classroom when students are presenting material, harnessing mistakes or productive failure and creating appropriate mathematical tasks.
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