This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

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…

In this article, the author presents a Desmos activity where students adjust the measures of angles in radians to reposition a laser and a mirror so the beam passes through three stationary targets. This Radian Lasers activity can be extended to simulate project-based learning (PBL), a pedagogical approach for applying concepts and skills from…

We developed and field-tested an active learning exercise designed to provide biology students with the opportunity to consider key aspects of the nature of science as a method of inquiry, particularly the roles of observation and inference in the development of scientific explanations and how scientists deal with uncertainty. In the activity…

Case studies are valuable tools for instruction but are often limited to a single topic and a single class period. Courses such as evolution that synthesize multiple concepts around a common theme, however, can use a single case study type project that extends over the entire semester to develop and link core concepts. A central theme in…

Although teachers are eager to facilitate community of inquiry (CoI) in their classrooms, they also fear being unable to convey the necessary knowledge to their students in an inquiry due to the inherent involvement of conflicting views, confusion, and a lack of strict definitions about the concepts. The author argues that the banking model of…

For food research, control, and production, valid and trustworthy analytical data are important. Our practical chemical food safety course for engineers therefore uses real-life studies for the ease of understanding the concept and the needed requirements for high analytical quality in relation to enabling correct evaluation of chemical food…

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,…

In this article, we describe some of the common misconceptions guests have expressed while visiting a Museum of Natural History and Science, along with ways in which museum educators had reacted to and/or responded to guests' misconceptions. Correcting commonly held misconceptions can be difficult, especially when guests are emotionally invested…

Many high schools, two-year colleges, and universities offer a conceptual physics course for non-science students who have to take a basic science course. The students often enter the course unmotivated and may eventually withdraw. So, how do we make the course interesting enough for these students to gain the knowledge we desire and, more…

For many students biochemistry is a demanding course because they are expected to apply previously learned foundational concepts to new biological contexts. These foundational concepts serve as a scaffold onto which to build threshold concepts such as the physical basis of interactions. Unfortunately, many students possess misconceptions or gaps…

This article presents how Problem- and Project-Based Learning (PBL) in engineering education can exploit the theoretical framework of the Space-Time (ST)-Continuum, according to which educational contexts can be classified in terms of the tightness vs. looseness of the relevant conceptual space S and available time T. By crossing these two…

Take a selection of balls and marbles along to a nearby playground slide and let students investigate factors that may influence how balls accelerate down an inclined plane. Students can make hypotheses in small groups, plan investigations to test multiple possible explanations and draw conclusions about the importance of different variables. The…

Students are expected to use the Cartesian plane to represent and reason about mathematical concepts such as number systems, geometric figures, and functions. However, the simplicity of representing mathematical concepts that the Cartesian plane provides can cause us to overlook the difficulties many students have in constructing and using it.…

Although empirical studies have consistently indicated that students commonly struggle to learn and understand the concepts related to reflex actions, few teaching strategies have been developed that specifically address these learning difficulties. This article introduces simple teaching models that simulate the nervous pathways related to the…