This paper sets forth a construct that describes how many undergraduate students understand mathematical terms to refer to mathematical objects, namely that they only refer to those objects that satisfy the term. I call this students' pronominal sense of reference (PSR) because it means they treat terms as pronouns that point to objects, like…

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

The purpose of this paper is to investigate the relationships between adult students' mathematical micro-identities (informed by positioning theory) and their mathematics (informed by radical constructivism). I used positioning theory to conduct a detailed turn-by-turn analysis of students' micro-identities, and to inform my models of students'…

We have investigated the temporal patterns of algebra (N = 606) and calculus (N = 507) introductory physics students practicing multiple basic physics topics several times throughout the semester using an online mastery homework application called science, technology, engineering, and mathematics (STEM) fluency aimed at improving basic physics…

The Leading-to-Calculus Framework (LTCF) is a collection of math courses meant to prepare students for calculus. From its inception, however, scholars have marked out a number of problems with its approach, particularly for students of color: its content and activities are often too broad, its structure is too rigid, and it fails to regularly…

In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts…

Flipped instruction has been flaunted as a pedagogical strategy that supports improved learning and retentive abilities of students. Nevertheless, one of the twin challenges reported in the literature, students' failing to complete preparatory work, impedes the efficacy of the model. Thus, learners' motivation and attitude to work are essential…

This work is aimed to assess the performance of two groups of students from colleges of Science, Education and Engineering on the understanding of electricity and magnetism concepts. To conduct this assessment, the Electricity and Magnetism Conceptual Assessment (EMCA) test was implemented twice as a pre-test and a post-test for two calculus-based…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

Most teachers of mathematics think that regular practice is essential for success. In face-to-face instruction settings, regular practice requires doing homework, which has to provide students with feedback in order to be useful. Online homework allows teachers to assume the workload involved in providing feedback to a large number of students…

This study examines students' visual behaviors when they tackle two types of synthesis problems, sequential and simultaneous problems. Sequential synthesis tasks can be solved by applying pertinent concepts consecutively, whereas simultaneous synthesis tasks require concurrent application of multiple concepts. Twenty-two students from an…

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;…

Mathematical connections play an important role in achieving mathematical understanding. Therefore, in this article, we report research whose objective was to identify mathematical connections that pre-university students make when they solve problems that involve the derivative and the integral. In this research, we consider a mathematical…