We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

Researchers have documented the importance of seeing a graph as an emergent trace of how two quantities' values vary simultaneously in order to reason about the graph in terms of quantitative relationships. If a student does not see a graph as a representation of how quantities change together then the student is limited to reasoning about…

This paper addresses the need for empirical research on the processes by which students create algorithms. I analyse the collaborative work of three high-school students on a contextualised graph theory task, in which they created an algorithm for maximising the happiness score of a seating arrangement. The group found an optimal arrangement but…

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

This study aimed to explore the effects of an instructional intervention in which GeoGebra and the think-pair-share method were used to teach the relationship between the graph of a parametric curve and the derivatives of its component functions. The participants in the study were 19 prospective mathematics teachers. To assess the understanding of…

This paper examines the limited proficiency to engage in programming algorithms among university students in information technology and information system in several universities across Surabaya, Indonesia. The purpose of this research is to find the most influential factor in learning programming algorithm using a quantitative approach. The…

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…

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 study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…

In this paper, we investigate mathematics majors' perceptions of the admissibility of inferences based on graphical reasoning for calculus proofs. The main findings from our study is that the majority of mathematics majors did not think that graphical perceptual inferences (i.e., inferences based on the appearance of the graph) were permissible in…

This study focuses on how students in different postsecondary mathematics courses perform on domain and range tasks regarding graphs of functions. Students often seem to focus on notable aspects of a graph and fail to see the graph in its entirety. Many students struggled with piecewise functions, especially those involving horizontal segments.…

This paper considers what students attend to as they first encounter R[superscript 3] coordinate axes and are asked to graph y = 3. Graphs are critical representations in single and multivariable calculus, yet findings from research indicate that students struggle with graphing functions of more than one variable. We found that some students…