This study examined the impact of restricting Calculus 1 and Business Calculus classes based upon whether students had prior calculus experience. We compared the performance and experience of students in sections comprised entirely of those who had previously taken calculus, those who had not previously taken calculus, and those in traditional…

Purpose: This study investigated the effect of attitude towards students' performance in Calculus. Methodology: The researchers used the descriptive method of research. Students who have recently finished their Calculus I and II, in the university and prior to the conduct of the survey, was the common parameter used in identifying the respondents.…

We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

Polynomials with rational roots and extrema may be difficult to create. Although techniques for solving cubic polynomials exist, students struggle with solutions that are in a complicated format. Presented in this article is a way instructors may wish to introduce the topics of roots and critical numbers of polynomial functions in calculus. In a…

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Imagine a large randomized controlled trial study of a mathematics educational intervention planned in two large urban districts. District 1 gets a new administrator and drops out. In the meantime, the state test changed, so one of the planned outcome measures is no longer usable. Teacher dropout is high. And, as the analysis is being completed,…

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear…

The voltage waveform that minimizes the energy loss in the resistance when charging the capacitor in a resistor-capacitor circuit is investigated using the calculus of variation. A linear voltage ramp gives the best efficiency, which means a constant current source should be used for charging. Comparison between constant current source and…

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

Translating an informal mathematical argument into a proof which conforms to the norms of the mathematical community in which it is situated is a non-trivial task. Here we discuss several types of products, other than the initial informal argument and its direct formalisation, which we observed students generating in a master's level analysis…

In recent years advanced undergraduate students have developed projects for our redesigned Calculus II classes. Our student designers create new mathematics projects and present their work at conferences and in local talks. They are often mathematically early in their college careers, and so we can involve students of all levels in research…

We provide context and motivation for an instructor to use real-life examples in the calculus classroom. To this end we describe two specific project ideas, one related to the devastating impact of methylmercury fungicide in a grain seed supply and the other to a catastrophic methane leak. By using calculus in contexts that have social justice…

Graphical representations are an important tool used to model abstract processes in fields such as chemistry. Successful interpretation of a graph involves a combination of mathematical expertise and discipline-specific content to reason about the relationship between the variables and to describe the phenomena represented. In this work, we…

Our students experience difficulties in working on non-routine mathematical problems. They cannot see the general through special things or instead see things that are special through common things when dealing with mathematical concepts and examples. They cannot see the essential features of the way or recognize it when presented in various…