This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…

Our goal with this paper is three-fold. We want to increase awareness of inquiry-based learning by presenting the strategy we use to develop and implement lessons and activities. We describe our approach to structuring lessons in mathematics in a way that engages the students by using language and constructs with which they are familiar from other…

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

Flipped classrooms and inquiry-based learning (IBL) have each become popular in their own right, leading to a natural question: Why not combine these two great ideas? Although flipping a class usually involves students reading or watching videos before class, and IBL focuses on allowing and encouraging students to develop material on their own,…

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

Inquiry-based learning is a topic of growing interest in the mathematical community. Much of the focus has been on using these methods in calculus and higher-level classes. This article describes the design and implementation of a set of inquiry-based learning activities in a Math for Liberal Arts course at a small, private, Catholic college.…