Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

Much important research on the learning of mathematics with technology-supported inquiry has been devoted to learning with multiple-linked representations (MLR) as a mode of feedback. Like a mirror, MLR feedback helps students see their actions in one representation "reflected" in another. Yet, research has followed learning episodes…

This essay examines how line graphs functioned as markers of status and authority in early 20th-century America, distinguishing intellectual elites from ordinary citizens. Despite education reformers' efforts to democratize functional thinking and graphical representation in the first decades of the century, line graphs retained their position as…

The author, Sirin Budak, discusses how to model the problem of a frog climbing out of a well using piecewise functions and GeoGebra.

The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for…

Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S.…

Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…

The teacher's use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether…

Mathematics seems abstract, difficult, and uninteresting to many students, which in turn reduces their interest in learning mathematics. It has been found that the use of ICT and meaningful contexts of problem-solving tasks can make learning mathematics more enjoyable and easier to understand for students. To increase students' interest in…

This article recounts the life of mathematician Leonhard Euler and discusses the use of Graph Theory in student learning.

Incorporating technology into educational processes is increasingly necessary to address the complexities of contemporary learning environments. This study investigates the impact of Augmented Reality (AR) on the academic performance of third-grade students in the areas of graphs and geometry. A quasi-experimental design was employed, comparing a…

Aim/Purpose: This study explored the limited research on the challenges and opportunities faced by students when creating function art using GeoGebra, addressing a gap in the literature that focuses on student outputs and engagement. It addressed the need to understand how students engage with function art and the difficulties they encounter in…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…