This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

3D-printing technology has become increasingly important in recent years, offering many possibilities for mathematics teaching and learning. From our point of view, the field of calculus seems to be particularly suitable for the use of 3D-printing. Using the example of 3D-printed graphs of functions, the use of this technology in calculus is…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

The paradigm shift from traditional didactic instruction to technology-enriched teaching and learning environments significantly benefits learners. Educational technology can visualize abstract mathematical concepts contextually and graphically and allow learners to actively construct this knowledge. This study aims to ascertain the efficacy of a…

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…

The contexts of the problems educators choose can affect students' mathematical identities by affecting their abilities to relate to the mathematics (Middleton, Jansen, and Goldin 2017). Moreover, these choices send powerful messages to students about the relevancy of mathematics to their own lives (Felton 2010). Eliciting and drawing on student…

The ability to apply mathematical concepts and procedures in relevant contexts in engineering subjects sets the fundamental basis for the mathematics competencies in engineering education. Among the plethora of digital techniques and tools arises a question: Do the students gain a deep and conceptual enough understanding of mathematics that they…

Simon Fraser University in Vancouver, Canada offers two introductory calculus courses designed for students enrolled in science and engineering programs. Students identified as needing additional support based on their admission grades take the version of the course where students meet weekly for four hours instead of three. A new approach for the…

This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…

The current study aimed at investigating the impact of Flipped Classroom Strategy by using E-Learning Systems (Blackboard) based on Critical Thinking Skills of the acquisition of fresh female students of the derivative concept of Calculus. To conduct this study, the researchers followed the explanatory sequential mixed-methods by dividing randomly…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained…

This paper presents a "virtual reality" based lesson for a common Calculus topic, including a description of how the lecture was implemented in both a virtual reality and an augmented reality hardware system. This lesson was delivered to a number of calculus classes and we describe the student response to the lesson via a quiz and a…

Problem-solving is regarded as a major component of mathematical performance, and well-designed problem-solving-based learning environments have the potential to assist students in developing a meaningful understanding of mathematical concepts and procedures. In this respect, given its various features, dynamic mathematics software has been…