Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

In this article I use Sfard's theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point…

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Over a period of six years, three different types of recitation sessions were implemented into the large enrollment section of a college calculus course. During the fall semesters, the results on the departmental final examination, the DFW rates, and the one-year retention rates of students as STEM majors were examined by the type of recitation…

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

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…

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an…

This article compares the views of teachers and professors about the transition from secondary mathematics to tertiary calculus. Quantitative analysis revealed five categories where teachers and professors differed significantly in the relative frequency of addressing them. Using the rite of passage theory, the separation and incorporation phases…

The objective of this research is to investigate the effectiveness of a learning strategy using Maple in integral calculus. This research was conducted using a quasi-experimental nonequivalent control group design. One hundred engineering technology students at a technical university were chosen at random. The effectiveness of the learning…

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

Novel trends and innovations have enhanced contemporary educational environments. When applied properly, these computing advances can create enriched learning opportunities for students. "Mobile Technologies and Augmented Reality in Open Education" is a pivotal reference source for the latest academic research on the integration of…

Flipped classrooms and inquiry-based learning (IBL) have each become popular in their own right, leading to a natural question: Why not combine these two great ideas? Although flipping a class usually involves students reading or watching videos before class, and IBL focuses on allowing and encouraging students to develop material on their own,…