In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

Background/purpose: This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK). Materials/methods: A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus…

Achieving proficiency in fundamental differential calculus concepts remains a persistent challenge for grade 12 students, raising concerns among mathematics teachers and policymakers. Despite the widely acknowledged applications of differential calculus across diverse disciplines, global examination diagnostic reports consistently highlight…

This case study explored Grade 12 learners' misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was…

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are defined in order to calculate the primitive of [equation omitted] in the Proportional context.

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

Background/purpose: This research is motivated by the difficulties often experienced by students in adapting to their first year of college, especially related to learning calculus. To address these difficulties, a solution needs to be found so that these problems can be resolved. One solution that is expected to yield optimal results in…

The aim of this research was to establish a structural relation among calculus scholars' beliefs, self-regulated learning (SRL) strategies, and problem-solving skills related to differential equations (DEs). To identify the relationships between different variables and their impact on DE problem-solving, a correlational study design with an a…

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Background/purpose: This study analyzes the commognition of students with low Working Memory Capacity (WMC) when solving calculus problems, particularly in integral material. Commognition, which merges cognition and communication, is explored through four indicators: keywords (stating knowns and unknowns), visual mediators (graphical…

This study explores the integration of game play into an inclusive, hands-on computing project in Calculus class. The project is focused on designing and analyzing priority switches for applications competing for computational resources on embedded devices such as smart watches and tablets. By engaging students in real-world problem-solving…

This study aimed to investigate the relative effectiveness of a computer-supported teaching sequence in solving optimization problems in calculus compared to a traditional teaching approach. The participants in the study were 46 first-year prospective mathematics teachers studying in two different classes of a four-year elementary mathematics…

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of…