Peter Liljedahl describes a Building Thinking Classrooms (BTC) framework that shows teachers how to set up a classroom that promotes thinking. BTC is divided into 4 toolkits. The first toolkit consists of thinking tasks, vertical non-permanent surfaces, and visibly random groups. The second pertains to defronting the classroom, giving thinking…

Cornell University has long offered a Calculus for Life Sciences course. In this case study, we report on how a team of pure mathematicians has modernized both the content and teaching methods of this course. The content went from a standard calculus course with few genuine applications in the life sciences to a course focusing on dynamical…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

This is a study of student engagement with computational labs in Calculus 2. The labs task students with using MATLAB to investigate contexts such as rocket science, disease modeling, and market economics forecasting by modifying and executing provided code, guided by questions that have students report the results of their simulations or…

This article describes a partially flipped course design for Calculus II which has been implemented by a varied instructional team at a medium-sized public engineering university (Colorado School of Mines (Mines)) over a period of three years. We have identified three main factors which have contributed to the success of the implementation: (1)…

Teachers in New York State and across the United States experienced a unique start to the 2021-2022 school year as students returned to full-time, in-person learning following imposed lockdowns due to COVID-19. To address the social and emotional needs of the returning students, an emphasis on interpersonal relationships became increasingly…

The Mathematics Department at Cornell University has recently secured a grant from the University to implement systemic change in how we teach courses that reach students at critical transition points in their mathematical development. In this article, we report on the changes made to our large multi-section first-semester calculus course in order…

Ongoing need for adjunct instructor support is a critical aspect for institutions to consider. Through research focused on full-time and part-time faculty job satisfaction, a number of practices for supporting faculty and improving job satisfaction have been suggested. In this article, we present an innovative model of instructor resources and…

Purpose: The purpose of the study was to evaluate the implementation and impact of the IDEA Public Schools' Mathematics Curriculum Redesign (MCR) effort, funded by an Innovation and Research (EIR) grant. Methods: The study used a quasi-experimental matching design to examine the effect of MCR on student achievement outcomes. The study compared…

Here we demonstrate the benefits of a new curriculum for introductory calculus-based physics that motivates classical mechanics using a modified version of Hamiltonian mechanics. This curriculum shifts the initial focus of instruction away from forces and the associated vector mathematics, which are known to be problematic for students, to the…

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…

This paper illustrates a biological application of the concepts of relative change and area under a curve, from mathematics. We study two biological measures "relative change in cardiac output" and "cardiac output", which are predictors of heart blockages and other related ailments. Cardiac output refers to the quantity of…

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus…

Education, science, and technology disciplines are closely and extensively connected in all formats and levels. The outbreak of COVID-19 has further squeezed this interconnection where the delivery of education in different scientific fields of studies at all education levels is almost impossible without the presence of technology. Today, there is…

This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…