The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

A deeper learning of the properties and applications of the derivative for the study of functions may be achieved when teachers present lessons within a highly graphic context, linking the geometric illustrations to formal proofs. Each concept is better understood and more easily retained when it is presented and explained visually using graphs.…

Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and…

The aim of this paper is to provide a cross-national comparative analysis of the introduction of calculus in Spanish and French military educational institutions through the works of Pedro Padilla y Arcos (1724-1807?) and Etienne Bezout (1730-1783), respectively. Both authors developed their educational work in the context of military schools and…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

This paper focuses on the use of the teaching method Peer-Assisted Reflection (PAR) to help graduate student instructors (GSIs) develop as teachers. PAR engages students in analyzing the work of their peers and providing feedback to promote their abilities of communication, collaboration, and persistence. The goals of the PAR activity were taken…

In this study, researchers design and implement an inquiry based multivariable calculus course in a university which aims at enhancing students' argumentation in rich mathematical discussions. This research aims to understand the characteristics of students' argumentation in activities involving proof constructions through mathematical…

The research relates to undergraduate students' understanding of mathematical concepts that relate to the conceptualisation of the continuous such as the notion of limit. The cognitive difficulties that accompany the learning of these concepts at the different stages of the mathematics education are well reported in the literature. I analyse the…

The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…

For students with little experience in mathematical thinking and conceptualization, writing-to-learn activities (WTL) can be particularly effective in promoting discovery and understanding. For community college students embarking on a first calculus course in particular, writing activities can help facilitate the transition from an "apply…

This research focuses on the inductive teaching with group process and students' behavior as working in a group. There were four instruments under this study. The descriptive statistics were employed. The findings revealed that, firstly, the effectiveness of LPIDTGP [Learning Package by means of the Inductive Teaching with Group Process] is higher…

Information and Communication Technologies (ICT) in education provide a new learning environment where the student builds his own knowledge, allowing his visualization and experimentation. This study evaluated the Geogebra software in the learning process of Calculus. It was observed that the proposed activities helped in the graphical…

Recently, there is an explosive growth of smartphone availability. In this work, we studied how mobile and Internet-based Student Response System improves the learning process. We used a free software application (Socrative©) to create a set of questions that can be deployed during the class. It was used in four different courses in three…

These proceedings are a written record of the research presented at the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Nashville, Tennessee, and virtually. This year's conference theme is "Critical Dissonance and Resonant Harmony." The aim of this…

We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific…