Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

The ability to solve physics problems that require multiple concepts from across the physics curriculum--"synthesis" problems--is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these…

The "gender gap" on various physics conceptual evaluations has been extensively studied. Men's average pretest scores on the Force Concept Inventory and Force and Motion Conceptual Evaluation are 13% higher than women's, and post-test scores are on average 12% higher than women's. This study analyzed the gender differences within the…

This action research study used data from multiple assessments in Mechanics and Electricity and Magnetism to determine the viability of Modeling Instruction as a pedagogy for students in AP Physics C: Mechanics and Electricity and Magnetism. Modeling Instruction is a guided-inquiry approach to teaching science in which students progress through…

This article describes and explains shifts in participation among eight mathematically successful Latin@ undergraduate students who were enrolled in a culturally diverse calculus I workshop that was part of a university-based Emerging Scholars program. Two questions are explored: (a) How do students explain success-oriented shifts in participation…

Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for…

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

I discuss a teaching experiment that sought to characterize precalculus students' angle measure understandings. The study's findings indicate that the students initially conceived angle measures in terms of geometric objects. As the study progressed, the students formed more robust understandings of degree and radian measures by constructing an…

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

The general aim is to promote the use of individual-based models (biological agent-based models) in teaching and learning contexts in life sciences and to make their progressive incorporation into academic curricula easier, complementing other existing modelling strategies more frequently used in the classroom. Modelling activities for the study…

Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…

This study utilized an innovative data analysis approach to examine how engineering undergraduates engaged in mathematical modelling. Individual modelling routes were constructed via modelling activity diagrams and were used to critically examine the theoretical framework. Implications for the theoretical model are offered along with implications…

It is well documented that the use of active learning strategies increases student learning (Freeman et al., 2014; Prince, 2004; Springer, Stanne, & Donovan, 1999). A key difficulty in innovating college mathematics is identifying and sustaining what works for both students and the faculty. This study discusses efforts to innovate and sustain…

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This "flexible procedural knowledge" distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students' flexible use…