Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…

Inquiry-Based learning (IBL) is a fairly well-known term in the United States (US) describing a range of student-centered or active pedagogical approaches in mathematics. However, the 'big tent' definitions of IBL mean that there is much variation in IBL users' instructional practices, variation which we set out to codify. Cluster analysis of…

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

A student-led mathematics bootcamp has been designed and implemented to help foster community building, improve confidence in mathematical skills, and provide mathematical resources for incoming physical chemistry doctoral students. The bootcamp is held immediately before the start of the first semester of graduate school and uses an active…

Mounting evidence of the effectiveness of active learning strategies has prompted many mathematics departments to start engaging in transformational change efforts. Change, however, especially change in instructional practice, is a challenging endeavor. Some departments are using coordination of multi-section courses as a vehicle to enact changes…

In spring 2018, an inquiry-oriented differential equations course was offered at the Lebanese American University. This paper highlights students' comprehension of some qualitative aspects of differential equations, namely their understanding of the equations and their solutions. It also explores the students' success in moving between the…

We investigate how an inquiry-oriented, dynamic, open-source calculus textbook shaped one college instructor's planning. We rely on Dietiker et al.'s [(2018). Research commentary: Curricular noticing: A framework to describe teachers' interactions with curriculum materials. "Journal for Research in Mathematics Education," 49(5), 521-532.…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

Several academic departments have increased their use of active learning to address low student success rates. However, it is unclear whether those implementing active learning have a consistent conceptualization of it. Like other educational terms, the phrase "active learning" is in danger of becoming overused and misunderstood, which…

The recent push toward active learning -- engaging students in the learning process -- is meant to benefit students. Yet there is still much to learn about students' perceptions of this phenomenon. We share results from an interview study of students' perceptions of features of two active learning models institutionalized at a large…

Over the last decade, there has been a national effort to prepare a more diverse student population for success in science, technology, engineering, and mathematics (STEM) careers. While there are a variety of best teaching practices in undergraduate STEM education, student engagement has been widely used to improve student learning. Specifically,…

Purpose: Creating suitable learning conditions in university classrooms continues to be a topical issue in higher education. The above means that a continued search for innovative teaching and learning strategies in universities remains a priority issue. The study therefore investigated conditions that facilitate the effective implementation of…

The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its…

As part of a departmental reform project, a large University converted a "Precalculus College Mathematics" lecture-based course for 97 students into an active learning flipped classroom for first-year engineering students. The curriculum was designed specifically to provide applications of pre-calculus in various engineering subjects.…