The concept of intellectual need, which proposes that learning is the result of students wrestling with a problem that is unsolvable by their current knowledge, has been used in instructional design for many years. However, prior research has not described a way to empirically determine whether, and to what extent, students experience intellectual…

Passing the introductory calculus sequence is critical to undergraduate students' retention in STEM programs. This study examines the relations between three interrelated processes found to influence mathematics learning and achievement: spatial skills, spatial anxiety, and math anxiety. Additionally, it examines the role of gender on these…

We used student surveys to assess changes in proficiency with integral calculus, calculus self-efficacy, and physics self-efficacy in a second semester course of introductory physics focused on electricity and magnetism. In addition to tracking the fraction of quantitative problems solved correctly on the calculus proficiency survey, we also used…

This article presents reflections on a research that investigated processes operationalized by mathematical thoughts and practices which sought explanations for the ways of being of mathematical objects in their correlations in the socio-cultural context throughout our human history and how these ways of being they were captured, and still are, by…

Self-efficacy has emerged as one of the most important noncognitive variables explaining academic behavior. It has been shown to influence students' academic and career decisions as well as their academic performance. Multiple studies have reported differences in self-efficacy between men and women in science, technology, engineering, and…

Mathematical notations not only contribute to but also confound the development of the understanding of mathematical concepts (Leinhardt, Zaslavsky & Stein,1990). Inaccurate use of calculus notations is likely to have a significant influence on student conceptual understanding and student assessment scores in the Calculus 1 course. This…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

This study investigates the evolution and associations between exam grades and social comparison concern (SCC) among students in an introductory calculus-based physics course. We begin with a descriptive characterization of midterm and final exam scores as well as pre-post SCC scores, including the concurrent evolution of these scores during the…

This study focuses on the analysis of certain performance predictors for calculus I. We collected data from 717 students from 2013 through 2018 at a southeastern university in the United States to explore any correlation between course times (particularly very early versus the rest) and student performance in this specific course, along with a…

Greater flexibility with procedures is known to be associated with greater conceptual knowledge of mathematics and vice versa. In parallel, a student's emotional relationship to mathematics -- i.e. their 'affect' -- is known to influence how they learn and perform in mathematics. For example, a confident student may engage more fully with…

This research explores the use of guided notes in a post-secondary calculus course and the extent to which use enhanced students' success in a first year calculus course. Guided notes have been previously shown to be perceived as helpful to learning by students, and one study showed that the use of guided notes improved pass rates in a first year…

Using the High School Longitudinal Study of 2009, we examine the association between taking Algebra I by the eighth grade and students' later achievements and advanced mathematics course-taking. To explore our research questions, we employ three distinct methods--regression analysis, fixed effects models, and propensity score matching. In all our…

Adolescent and children's concepts of multiplication and fractions have been linked to differences in the number of levels of units they coordinate. In this paper, we discuss relationships between adult students' conceptual structures for coordinating units and their pre-calculus understandings. We conducted interviews and calculus readiness…