Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Fostering students' mathematical creativity is important for their understanding and success in mathematics courses as well as their persistence in STEM, but it necessitates intentional instructional actions, such as designing and implementing tasks that have the potential to foster creativity. As teaching innovation requires support for…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…

Several studies indicate that exploring mathematical ideas by using more than one approach to prove the same statement is an important matter in mathematics education. In this work, we have collected a few different methods of proving the multinomial theorem. The goal is to help further the understanding of this theorem for those who may not be…

Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional…

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor's classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks' influence on the instruction conceptualized by the Teacher-Mathematics-Student face…

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

The retention of fundamental mathematical skills is imperative to provide a foundation on which new skills are developed. Educators often lament about student retention. Cognitive scientists and educators have explored teaching methods that produce learning which endures over time. We wanted to know if using spaced recall quizzes would prevent our…

During the pandemic and lockdown situations of the last few years, we transitioned to online, physical, and hybrid education approaches at various times. We had difficulty teaching multiple calculus and analytical geometry units online. In light of the current situation, a graphical user interface (GUI) teaching tool has been developed to teach…