With a focus on related rates problems, the present study reports on quantitative and covariational reasoning opportunities provided by five widely used calculus textbooks in the United States. There are three major results from this study. First, quantitative reasoning opportunities are plentiful, while covariational reasoning opportunities are…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

This study explored pre-service teachers' perceptions of a 3D printing integrated science, technology, engineering, and mathematics (STEM) module within a college-level mathematics content course. Data from surveys and reflections collected from nineteen participants were analyzed. Results indicated that the pre-service teachers perceived…

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…

In this research, we investigated whether the use of GeoGebra Augmented Reality (AR) can foster students in conceptualising a mathematical object by manipulating its different semiotic representations. We designed and implemented, with thirty university mathematics students, a teaching sequence on paraboloids using GeoGebra AR supported by…

The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around…

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,…

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 Department of Mathematics and Computer Science at Adelphi University engaged in a year-long program revision of its mathematics major, which was initiated by a longitudinal study and the publication of the 2015 Curriculum Guide by the MAA's Committee on Undergraduate Programs in Mathematics. This paper stands as a short story, so to speak, of…

In this paper, we describe the influence of the implementation of methodology for teaching and learning multiple integrals based on the constructivist approach and the interconnectedness of multiple representations (with an emphasis on dynamic representations) for different mathematical objects using GeoGebra's applications Graphing Calculator and…

Ethnomathematics can empirically improve the cognitive abilities of students in elementary and secondary schools. However, in undergraduate study, there are still limited studies on integrating ethnomathematics in learning resources. This study aims to apply interpolation in modelling polynomial functions and integral volume on the shape of…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

For several decades, literature on the history and pedagogy of mathematics has described how history of mathematics is beneficial for the teaching and learning of mathematics. We investigated the influence of a history and philosophy of mathematics (HPhM) course on students' progress through the lens of various competencies in mathematics (e.g.,…