Using Inquiry-Based Learning to Teach Math

By Tara Davis

My Inquiry-Based Learning (IBL) journey started in 2012 at a workshop hosted by the Mathematics Association of America. I received training in teaching IBL, specifically in a Problem Solving for Math Teaching class setting. I was skeptical about IBL, having made it through a PhD program being taught almost exclusively with the traditional lecture method. But after graduate school, when I began teaching university full time in 2011, my colleagues challenged me to make my lessons more active. These encouragements as well as my own budding curiosity were what led me to participate in the workshop.

At the workshop, I learned that IBL has a broad definition and varied implementation. It is generally characterized by a student-centered learning experience, with the instructor serving more as a facilitator or a coach. There is little to no lecturing. IBL instruction does not use a traditional textbook, and may forbid students from consulting outside sources such as books or the Internet. Students engage in a sparse but logically ordered and sufficiently scaffolded sequence of problems that are rich and support inquiry to the heart of big mathematical ideas. The problems may be worked on alone or in groups, at home, or during class time. The solutions are discussed in class, with the students leading both the presentations and the questioning.

In 2013, I implemented IBL instruction in my Problem Solving class. I did some things right the first time: I allowed students to work together, I removed the shame from making a mistake, and I acknowledged the need for differentiation in instruction. Specifically, I started the semester by explaining that I love mistakes. I backed up this assertion with a focus on process; even after a correct solution was presented, I solicited additional explanations. I called on individuals or groups who I knew had not gotten as far as others or even who had incorrect answers to describe their thinking and to stimulate whole class discussion. I selected problems that allow various approaches and that have a high ceiling. When students wrote up their homework solutions, they were required to include a reflection on the problem solving process. The students were given generous amounts of time to solve problems, and were required to work in diverse groups varied throughout the semester.

I made some mistakes as well: I did not explain the purpose of IBL, I failed to hold all students accountable for sharing their ideas, and I did not provide clear grading criteria. Despite my growing pains, I noticed that my students were taking ownership in their learning and inventing mathematics for themselves. This observation was substantiated by positive results of student surveys, self-assessments, and reflective writing.

The following year I taught IBL Problem Solving again and I was able to work out many of the kinks. Most days in class were spent either in small groups of 2-3 students investigating problems, with individuals presenting solutions to homework questions, in gallery walks, or discussing multiple solutions to a given problem. K-12 schools do not offer entire classes in Problem Solving, but there are various opportunities to weave such materials into the curriculum: developing number sense in an Algebra or Calculus course; posing problems related to Discrete Mathematics or Statistics; investigating notions of addition and multiplication of integers or rational numbers.

I felt that there was no going back to traditional teaching methods in the Problem Solving Course. But transitioning to IBL instruction is a process that requires time and reflection. Teachers must focus on their goals, be patient, make mistakes and learn from them, and take opportunities when they arise. Since starting my IBL journey I have taught a graduate education course in Math Curriculum and Instruction with IBL. The students led the discussions of the textbook chapters, presented their solutions to mathematics problem sets, and helped each other with writing their lesson plans. I also implemented IBL in Abstract Algebra. I had endured frustrations when teaching the class traditionally to students who showed little interest in the materials. The IBL class was taught in a Moore method style, modified with some in-class small group investigations. Throughout the semester the students were struggling to make sense of the mathematical ideas; they were engaged with the problems. The students seemed to love the teaching method, which was confirmed in my end of semester evaluations. I was tentative about using IBL at first, but once I committed it was great, and I plan to use it in two new classes next semester.

Although math is a challenging subject we must keep in mind the NCTM Equity principle: Excellence in mathematics education requires equity—high expectations and strong support for all students. Doing so will make using IBL feel less scary or experimental. Students can do more than memorize, mimic, perform algorithms and apply computational skills, if we ask them to. Many of the ideas and methods of IBL have applications to K-12 educators and students. Your journey could start with something as simple as giving your class the next problem that you were going to demonstrate in your lesson plan, but rather than showing them how to work it out, ask them to think about it in small groups. Spending time working on math investigations and discussing student thinking could be implemented in almost any class. I would encourage interested instructors to commit to using IBL for a full semester in just one course.

My hope is that my story can help others. My main message is: go for it. If you have ever questioned whether to use IBL, do not hesitate. Seek out opportunities and utilize the resources that are available, including conference support, via websites and blogs, published class notes and discussions with local colleagues. This pedagogy is fully supported by evidence and the knowledge base continues to grow, but that doesn’t mean that implementing it for the first time will be easy. Rest assured that the rewards for both instructor and student are worth the risks.

Helpful Resources for K-12 Educators Interested in IBL:

Discovering the Art of Mathematics
This team has, in addition to a helpful blog, created several books with independent chapters on diverse topics that could be adapted easily to many high school curricula, including Geometry and Discrete Math.

Math in the City
This website hosts professional development workshops related to IBL instruction.

The IBL Blog
The IBL Blog contains nuts and bolts tips on implementation and promotes the use of IBL in middle and secondary classes.

The Academy of IBL
This is a community that supports IBL practitioners, both aspiring and experienced.

IBL Calculus
This website contains in-class activities and notes to the instructor.

Jo Boaler’s books, online courses, and website
Jo Boaler’s resources contain many problems, methods, and materials.

“Thinking Mathematically” and “The Heart of Mathematics: An Invitation to Effective Thinking” are books that contain many problems that would be appropriate for high school math students.

“The Young Mathematicians at Work” series of books and videos have problems that can be applied in diverse settings as well as discussions about teaching and learning.

The Journal of Inquiry Based Learning
This website contains peer reviewed course notes for Moore Method style instruction.

The Teaching Abstract Algebra for Understanding
This website contains some activities that would be appropriate for usage in high school algebra classes.

Tara Davis is an Assistant Professor of Mathematics at Hawaii Pacific University. She studied geometric group theory at Vanderbilt University but her interests now include mathematics education, especially active teaching and inquiry-based learning.