In this paper, I introduce Sfard's discursive framework to examine secondary-school calculus students' communication during exploratory activities mediated by the use of touchscreen dynamic geometry environments (DGEs). Six pairs of secondary-school students participated in an open-ended task to explore calculus relationships using…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

According to the Cognitive Theory of Multimedia Learning (Mayer, 2009) learning with multimedia requires the integration of verbal and visual information (e.g., printed text and static images, narrated animation). Studies exploring the effects of dynamic versus static presentations yield mixed results. Few studies explore comparing dynamic versus…

This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Mathematics and technology serve the health sciences as demonstrated in this article, cowritten by one of our calculus students. Creating a lesson based on dosing an antibiotic allows teachers and students to see the immediate value of high school calculus and technology.

Our department is in the early stages of a multi-year effort to nurture a culture that values active learning. We focus on the change process, including specific, pragmatic ideas from the literature on grassroots leadership and systemic change. We briefly review Wenger's work on cultivating communities of practice and use Wenger's evaluation of…

During professional development, the authors learned about strings--a powerful instructional routine used in elementary classrooms to elicit students' mental mathematics strategies and use those strategies to build conceptual understanding. Strings provided the authors with a way to make relatively small changes to guided notes in algebra 1,…

As university instructors update modes of teaching and student engagement in STEM classes, concerns often arise about student resistance to different methods of teaching and learning. This research examines what it looks like from a student perspective to experience a shift in attitude by exploring the case of Dane, a white male student who…

We describe the design and evaluation of an innovative course for beginning undergraduate mathematics students. The course is delivered almost entirely online, making extensive use of computer-aided assessment to provide students with practice problems. We outline various ideas from education research that informed the design of the course, and…

We consider how the existence of different signifiers for mathematical objects in different languages manifests in discourse about those objects. Based on the observation that there is a common signifier "derivative" in English used for both the derivative at a point and the derivative function and two phonetically and semantically…

Calculus differential is the basis of mathematics before entering the level of further mathematics, which has a high analysis level. Students have difficulty understanding concepts and have not been able to analyze/predict/realize (self-efficacy) that impact challenges in working on calculus problems. On the other hand, technology has been…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…