In this paper we present the results of a survey of research studies on the learning of multivariable calculus in a wide geographic spectrum. The goal of this study is to describe what research results tell us about students' learning of calculus of two-variable functions, and how they inform its teaching. In spite of the diversity of cultures and…

This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…

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…

A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…

Calculus, as commonly taught, describes certain operations on explicit functions, but science relies on experimental data, which is inherently discrete. In the face of this disparity, how can we help students transition from lower-division mathematics courses to upper-division coursework in other STEM disciplines? We discuss here our efforts to…

The research this report belongs to aims at exploring the functional reasoning of high-school students from a covariation approach and proposing a framework to describe and predict the student's responses to modeling tasks in Dynamic Geometrical Situations. Items were designed for the students to build/construct the corresponding function guided…

The contexts of the problems educators choose can affect students' mathematical identities by affecting their abilities to relate to the mathematics (Middleton, Jansen, and Goldin 2017). Moreover, these choices send powerful messages to students about the relevancy of mathematics to their own lives (Felton 2010). Eliciting and drawing on student…

Proof and argumentation are essential components of learning mathematics, and technology can mediate students' abilities to learn. This systematic literature review synthesizes empirical literature which examines technology as a support for proof and argumentation across all content domains. The themes of this review are revealed through analyzing…

The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of…

The Forty Fifth Annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education was held PME-NA 45 in Reno, Nevada, October 1-4, 2023. The conference theme is "Engaging All Learners." Math learning should be a joyful experience for all students. When students are engaged and inspired,…

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…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

This paper concerns "planes-coordination" and "long-term-prediction" difficulties. These are specifically the case when students attempt to visualize solution curves of autonomous differential equations for predicting the long-term behavior of various initial conditions. To address these issues, a study was conducted in which…

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…