In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

During the pandemic and lockdown situations of the last few years, we transitioned to online, physical, and hybrid education approaches at various times. We had difficulty teaching multiple calculus and analytical geometry units online. In light of the current situation, a graphical user interface (GUI) teaching tool has been developed to teach…

A controversial, equity-focused mathematics reform in the San Francisco Unified School District (SFUSD) featured delaying Algebra I until ninth grade for all students. This study examines student-level longitudinal data on mathematics course-taking across successive cohorts of SFUSD students who spanned the reform's implementation. We observe…

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus.

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

Despite the use of axiomatic definitions for mathematical concepts, scholars struggle to produce a single definition of angle that does not have some limitations. Textbooks' treatment of angle and its measure reflects this multifaceted nature of the angle concept while informing the different ways learners conceive of these concepts. In this…

This quantitative correlational study examines school-level longitudinal outcomes of eighth-grade algebra universal acceleration in 15 U.S. school districts when compared with selective acceleration in 289 school districts. Universally accelerated school districts had higher enrollments, with large effect sizes, in geometry, algebra 2, and…

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates a loss of interest in students with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple…

A controversial, equity-focused mathematics reform in the San Francisco Unified School District (SFUSD) featured delaying Algebra I until ninth grade for all students. This descriptive study examines student-level longitudinal data on mathematics course-taking across successive cohorts of SFUSD students who spanned the reform's implementation. We…

Many mathematics teachers and students are familiar with the typical "box problem." In this type of problem, one takes a rectangular (or a square) sheet of paper and cuts out four squares from the four corners of the sheet and then folds the four strips up to form a box. Math problems like this are seen in middle school, high school,…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…

The study focused on how university students constructed proof of the Fundamental Theorem of Calculus (FTC) starting from their argumentations with dynamic mathematics software in collaborative technology-enhanced learning environment. The participants of the study were 36 university students. The data consisted of participants' written…